Thesis analysis
Anna Gorobtsova
20 04 2021
Data + dealing with NAs
Performing kNN imputation
library(VIM)
set.seed(123)
df_imp <- df %>%
kNN(variable=c("foreign_language_scores","social_studies_scores","russian_language_scores","math_scores","certificate_social_studiesgrade", "profile", "adaptation2", "intrgoal14", "statanxiety24_1","statanxiety22","testanxiety4", "statanxiety23_1", "statanxiety21_1", "statanxiety15_1", "statanxiety3_1", "testanxiety1", "intrgoal12", "testanxiety3", "statanxiety9_1", "statanxiety13_1", "statanxiety14_1", "statanxiety27", "extrgoal13", "adaptation1", "inter1_5", "statanxiety1_1", "statanxiety18_1", "efficacy17", "statanxiety7_1", "statanxiety12_1", "inter1_6", "efficacy15", "mathanxiety2", "mathanxiety3", "mathanxiety4", "mathanxiety5", "mathanxiety6", "mathanxiety7", "mathanxiety8", "mathanxiety9", "extrgoal11", "statanxiety5_1", "inter1_3", "statanxiety8_1", "efficacy12", "testanxiety5", "statanxiety6_1", "statanxiety16_1", "efficacy13", "intrgoal11", "inter1_1", "inter1_4", "living", "job", "certificate_mathgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "father_ISCO", "mother_ISCO"))EFA
Stat anxiety
stat_save1<-c("statanxiety16_1", "statanxiety6_1", "statanxiety8_1", "statanxiety5_1", "statanxiety12_1", "statanxiety7_1", "statanxiety18_1", "statanxiety1_1", "statanxiety14_1", "statanxiety9_1", "statanxiety3_1", "statanxiety15_1", "statanxiety21_1", "statanxiety23_1", "statanxiety22", "statanxiety24_1", "statanxiety10_1", "statanxiety17", "statanxiety28_1", "statanxiety25_1", "statanxiety11", "statanxiety19_1", "statanxiety26_1", "statanxiety4_1", "statanxiety2_1", "statanxiety20_1", "statanxiety13_1", "statanxiety27")stat_save2<-c("statanxiety16_1", "statanxiety6_1", "statanxiety8_1", "statanxiety5_1", "statanxiety12_1", "statanxiety7_1", "statanxiety18_1", "statanxiety1_1", "statanxiety14_1", "statanxiety9_1", "statanxiety3_1", "statanxiety15_1", "statanxiety21_1", "statanxiety23_1", "statanxiety22", "statanxiety24_1", "statanxiety10_1", "statanxiety17", "statanxiety28_1", "statanxiety25_1", "statanxiety11", "statanxiety19_1", "statanxiety26_1", "statanxiety4_1", "statanxiety2_1", "statanxiety20_1", "statanxiety13_1", "statanxiety27", "math_scores", "social_studies_scores", "russian_language_scores", "foreign_language_scores", "certificate_mathgrade", "certificate_social_studiesgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "gpa", "subject_mark")Building a factor model with 4 factors
## Factor Analysis using method = minres
## Call: fa(r = stat_fa, nfactors = 4, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 h2 u2 com
## statanxiety16_1 0.00 0.67 0.14 -0.12 0.63 0.37 1.2
## statanxiety6_1 0.32 0.28 0.61 0.08 0.81 0.19 2.0
## statanxiety8_1 0.00 0.06 0.63 -0.23 0.58 0.42 1.3
## statanxiety5_1 -0.09 -0.22 -0.03 0.70 0.77 0.23 1.2
## statanxiety12_1 0.14 0.02 0.79 0.06 0.74 0.26 1.1
## statanxiety7_1 -0.02 0.04 0.76 0.00 0.57 0.43 1.0
## statanxiety18_1 -0.10 -0.46 0.00 0.29 0.47 0.53 1.8
## statanxiety1_1 -0.17 -0.24 0.08 0.73 0.81 0.19 1.4
## statanxiety14_1 0.27 -0.43 -0.03 0.48 0.62 0.38 2.6
## statanxiety9_1 0.50 -0.10 0.20 -0.09 0.40 0.60 1.5
## statanxiety3_1 0.58 0.06 0.24 0.03 0.55 0.45 1.4
## statanxiety15_1 0.34 -0.46 -0.05 0.33 0.49 0.51 2.8
## statanxiety21_1 -0.06 0.79 0.14 0.05 0.63 0.37 1.1
## statanxiety23_1 0.72 0.06 0.06 -0.02 0.59 0.41 1.0
## statanxiety22 -0.31 -0.02 -0.29 0.24 0.41 0.59 2.9
## statanxiety24_1 -0.48 0.09 0.07 0.30 0.30 0.70 1.8
## statanxiety10_1 -0.09 0.11 -0.32 0.62 0.58 0.42 1.6
## statanxiety17 0.06 0.54 0.14 -0.02 0.38 0.62 1.2
## statanxiety28_1 0.52 -0.17 0.05 -0.12 0.32 0.68 1.3
## statanxiety25_1 0.71 -0.06 0.11 -0.05 0.60 0.40 1.1
## statanxiety11 -0.02 0.09 -0.44 0.43 0.45 0.55 2.1
## statanxiety19_1 0.15 0.70 -0.01 0.06 0.50 0.50 1.1
## statanxiety26_1 0.59 0.24 -0.24 0.10 0.32 0.68 1.7
## statanxiety4_1 0.65 0.06 0.14 -0.24 0.73 0.27 1.4
## statanxiety2_1 0.43 0.11 0.18 -0.27 0.52 0.48 2.2
## statanxiety20_1 0.10 0.44 -0.11 -0.28 0.39 0.61 2.0
## statanxiety13_1 0.06 0.67 -0.09 -0.19 0.59 0.41 1.2
## statanxiety27 0.57 0.02 0.13 0.19 0.39 0.61 1.3
##
## MR1 MR2 MR3 MR4
## SS loadings 4.46 4.04 3.34 3.32
## Proportion Var 0.16 0.14 0.12 0.12
## Cumulative Var 0.16 0.30 0.42 0.54
## Proportion Explained 0.29 0.27 0.22 0.22
## Cumulative Proportion 0.29 0.56 0.78 1.00
##
## With factor correlations of
## MR1 MR2 MR3 MR4
## MR1 1.00 0.19 0.52 -0.21
## MR2 0.19 1.00 0.25 -0.53
## MR3 0.52 0.25 1.00 -0.31
## MR4 -0.21 -0.53 -0.31 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 378 and the objective function was 18.91 with Chi Square of 6085
## The degrees of freedom for the model are 272 and the objective function was 3.57
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 333 with the empirical chi square 448.15 with prob < 9e-11
## The total number of observations was 333 with Likelihood Chi Square = 1139.39 with prob < 1.9e-106
##
## Tucker Lewis Index of factoring reliability = 0.787
## RMSEA index = 0.098 and the 90 % confidence intervals are 0.092 0.104
## BIC = -440.42
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4
## Correlation of (regression) scores with factors 0.95 0.94 0.95 0.94
## Multiple R square of scores with factors 0.90 0.89 0.89 0.89
## Minimum correlation of possible factor scores 0.79 0.78 0.79 0.78
Description of the model fit:
First of all, looking at the factor loadings it can be seen that almost all variables belong to only one factor, this is also proved by the low complexity values.
Proportion explained: the explained variance should be evenly distributed among factors which is exactly what we can observe in this case
Proportion variance: A factor should explain at least 10% of the variance. In this model it can be seen that all the factors meet this criterion.
Cumulative Variance: looking at this parameter we can see that all in all our model explains 54% of variance
Also Chi Square of 6104.67 tells us that observed and expected data aren’t significantly different, which is good
Tucker Lewis Index of factoring reliability = 0.784, which is not very good measure of model fit (it should be >0.9)
RMSR index = 0.04 , which is somewhat good, as it should be <0,05
Scale reliability:
stat_MR1<- as.data.frame(stat_fa [c("statanxiety23_1", "statanxiety25_1", "statanxiety4_1", "statanxiety26_1", "statanxiety27", "statanxiety3_1", "statanxiety28_1", "statanxiety9_1", "statanxiety24_1", "statanxiety2_1", "statanxiety22")])
psych::alpha(stat_MR1,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = stat_MR1, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.85 0.85 0.34 5.7 0.012 2.7 0.52 0.32
##
## lower alpha upper 95% confidence boundaries
## 0.83 0.85 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## statanxiety23_1 0.83 0.83 0.83 0.33 4.9 0.013 0.011 0.31
## statanxiety25_1 0.83 0.83 0.83 0.33 4.9 0.013 0.010 0.31
## statanxiety4_1 0.83 0.82 0.82 0.32 4.7 0.014 0.009 0.30
## statanxiety26_1 0.85 0.85 0.85 0.36 5.7 0.012 0.011 0.34
## statanxiety27 0.85 0.84 0.85 0.35 5.4 0.012 0.012 0.32
## statanxiety3_1 0.84 0.83 0.84 0.33 5.0 0.013 0.011 0.32
## statanxiety28_1 0.85 0.84 0.85 0.35 5.4 0.012 0.013 0.34
## statanxiety9_1 0.84 0.84 0.84 0.34 5.3 0.012 0.013 0.31
## statanxiety24_1- 0.85 0.85 0.85 0.36 5.5 0.012 0.012 0.34
## statanxiety2_1 0.84 0.84 0.84 0.34 5.2 0.013 0.011 0.31
## statanxiety22- 0.84 0.84 0.84 0.35 5.3 0.012 0.012 0.32
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## statanxiety23_1 333 0.73 0.73 0.71 0.66 2.8 0.77
## statanxiety25_1 333 0.74 0.74 0.71 0.66 2.7 0.86
## statanxiety4_1 333 0.79 0.78 0.78 0.72 2.1 0.93
## statanxiety26_1 333 0.48 0.49 0.40 0.37 3.0 0.74
## statanxiety27 333 0.55 0.57 0.50 0.46 2.9 0.74
## statanxiety3_1 333 0.71 0.68 0.65 0.60 2.9 0.97
## statanxiety28_1 333 0.57 0.57 0.50 0.46 2.7 0.82
## statanxiety9_1 333 0.62 0.62 0.56 0.52 2.3 0.78
## statanxiety24_1- 333 0.52 0.54 0.47 0.43 3.1 0.72
## statanxiety2_1 333 0.66 0.64 0.60 0.56 2.3 0.86
## statanxiety22- 333 0.59 0.60 0.55 0.50 2.8 0.78
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## statanxiety23_1 0.03 0.32 0.46 0.19 0
## statanxiety25_1 0.06 0.35 0.38 0.21 0
## statanxiety4_1 0.29 0.41 0.21 0.09 0
## statanxiety26_1 0.04 0.18 0.56 0.22 0
## statanxiety27 0.04 0.21 0.55 0.20 0
## statanxiety3_1 0.08 0.28 0.29 0.34 0
## statanxiety28_1 0.06 0.35 0.42 0.17 0
## statanxiety9_1 0.14 0.54 0.25 0.07 0
## statanxiety24_1 0.29 0.53 0.16 0.02 0
## statanxiety2_1 0.15 0.45 0.29 0.10 0
## statanxiety22 0.20 0.47 0.29 0.04 0Cronbach’s alpha is 0.8517994, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
NAME OF THE SCALE: Difficulty
stat_MR2<- as.data.frame(stat_fa [c("statanxiety21_1", "statanxiety19_1", "statanxiety16_1", "statanxiety13_1", "statanxiety17", "statanxiety18_1", "statanxiety15_1", "statanxiety20_1")])
psych::alpha(stat_MR2,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = stat_MR2, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.83 0.83 0.82 0.38 4.8 0.014 1.9 0.55 0.37
##
## lower alpha upper 95% confidence boundaries
## 0.8 0.83 0.85
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## statanxiety21_1 0.80 0.80 0.78 0.36 4.0 0.017 0.0037
## statanxiety19_1 0.80 0.81 0.79 0.37 4.2 0.016 0.0049
## statanxiety16_1 0.80 0.80 0.78 0.36 4.0 0.017 0.0045
## statanxiety13_1 0.80 0.80 0.78 0.37 4.1 0.016 0.0050
## statanxiety17 0.81 0.82 0.80 0.39 4.4 0.016 0.0049
## statanxiety18_1- 0.81 0.81 0.79 0.38 4.2 0.016 0.0053
## statanxiety15_1- 0.82 0.82 0.80 0.40 4.6 0.015 0.0038
## statanxiety20_1 0.82 0.82 0.80 0.39 4.5 0.015 0.0051
## med.r
## statanxiety21_1 0.37
## statanxiety19_1 0.37
## statanxiety16_1 0.36
## statanxiety13_1 0.37
## statanxiety17 0.39
## statanxiety18_1- 0.37
## statanxiety15_1- 0.39
## statanxiety20_1 0.39
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## statanxiety21_1 333 0.73 0.73 0.69 0.62 2.0 0.82
## statanxiety19_1 333 0.70 0.69 0.63 0.57 1.8 0.86
## statanxiety16_1 333 0.73 0.74 0.69 0.63 1.7 0.80
## statanxiety13_1 333 0.69 0.71 0.67 0.60 1.5 0.69
## statanxiety17 333 0.62 0.63 0.55 0.50 1.7 0.75
## statanxiety18_1- 333 0.69 0.67 0.61 0.55 2.8 0.94
## statanxiety15_1- 333 0.60 0.60 0.51 0.46 1.9 0.82
## statanxiety20_1 333 0.63 0.62 0.53 0.49 1.9 0.86
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## statanxiety21_1 0.30 0.51 0.13 0.06 0
## statanxiety19_1 0.41 0.41 0.12 0.06 0
## statanxiety16_1 0.47 0.40 0.09 0.04 0
## statanxiety13_1 0.55 0.37 0.06 0.02 0
## statanxiety17 0.44 0.44 0.10 0.03 0
## statanxiety18_1 0.24 0.39 0.26 0.11 0
## statanxiety15_1 0.05 0.16 0.47 0.33 0
## statanxiety20_1 0.41 0.36 0.20 0.04 0Cronbach’s alpha is 0.8296787, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
NAME OF THE SCALE: Value
stat_MR3<- as.data.frame(stat_fa [c("statanxiety12_1", "statanxiety7_1", "statanxiety8_1", "statanxiety6_1")])
psych::alpha(stat_MR3,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = stat_MR3, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.83 0.83 0.8 0.55 5 0.015 2 0.72 0.56
##
## lower alpha upper 95% confidence boundaries
## 0.8 0.83 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## statanxiety12_1 0.77 0.77 0.70 0.53 3.4 0.022 0.0034 0.53
## statanxiety7_1 0.80 0.80 0.73 0.57 4.0 0.019 0.0064 0.59
## statanxiety8_1 0.81 0.81 0.75 0.59 4.3 0.018 0.0033 0.61
## statanxiety6_1 0.77 0.77 0.69 0.52 3.3 0.022 0.0058 0.48
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## statanxiety12_1 333 0.83 0.84 0.77 0.70 2.2 0.85
## statanxiety7_1 333 0.80 0.80 0.70 0.64 2.0 0.90
## statanxiety8_1 333 0.78 0.78 0.67 0.61 1.9 0.85
## statanxiety6_1 333 0.85 0.84 0.78 0.71 2.1 0.93
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## statanxiety12_1 0.21 0.49 0.22 0.08 0
## statanxiety7_1 0.35 0.40 0.18 0.07 0
## statanxiety8_1 0.37 0.44 0.13 0.06 0
## statanxiety6_1 0.26 0.43 0.20 0.11 0Cronbach’s alpha is 0.8315706, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
NAME OF THE SCALE: Cognitive competences
stat_MR4<- as.data.frame(stat_fa [c("statanxiety1_1", "statanxiety5_1", "statanxiety10_1", "statanxiety14_1", "statanxiety11")])
psych::alpha(stat_MR4,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = stat_MR4, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.81 0.81 0.8 0.46 4.2 0.017 2.7 0.64 0.47
##
## lower alpha upper 95% confidence boundaries
## 0.78 0.81 0.84
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## statanxiety1_1 0.72 0.73 0.69 0.40 2.6 0.025 0.014 0.42
## statanxiety5_1 0.72 0.73 0.69 0.40 2.7 0.025 0.015 0.43
## statanxiety10_1 0.78 0.77 0.76 0.46 3.4 0.020 0.039 0.45
## statanxiety14_1 0.80 0.80 0.79 0.50 3.9 0.018 0.022 0.47
## statanxiety11 0.81 0.81 0.79 0.52 4.3 0.016 0.021 0.50
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## statanxiety1_1 333 0.85 0.84 0.84 0.74 2.6 0.88
## statanxiety5_1 333 0.85 0.84 0.83 0.73 2.4 0.89
## statanxiety10_1 333 0.72 0.74 0.64 0.57 2.8 0.75
## statanxiety14_1 333 0.70 0.69 0.56 0.51 2.9 0.91
## statanxiety11 333 0.63 0.65 0.51 0.44 2.6 0.80
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## statanxiety1_1 0.13 0.30 0.44 0.13 0
## statanxiety5_1 0.16 0.37 0.36 0.11 0
## statanxiety10_1 0.06 0.25 0.56 0.13 0
## statanxiety14_1 0.08 0.19 0.42 0.30 0
## statanxiety11 0.08 0.33 0.47 0.12 0Cronbach’s alpha is 0.806576, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
NAME OF THE SCALE: Affect
Adding factors to the data set:
fascores<-as.data.frame(fa1$scores)
data_reg1<-cbind(stat_reg,fascores)
names(data_reg1)[names(data_reg1) == "MR1"] <- "stat_difficulty"
names(data_reg1)[names(data_reg1) == "MR2"] <- "stat_value"
names(data_reg1)[names(data_reg1) == "MR3"] <- "stat_cognitivecomp"
names(data_reg1)[names(data_reg1) == "MR4"] <- "stat_affect"
names(data_reg1)## [1] "statanxiety16_1" "statanxiety6_1"
## [3] "statanxiety8_1" "statanxiety5_1"
## [5] "statanxiety12_1" "statanxiety7_1"
## [7] "statanxiety18_1" "statanxiety1_1"
## [9] "statanxiety14_1" "statanxiety9_1"
## [11] "statanxiety3_1" "statanxiety15_1"
## [13] "statanxiety21_1" "statanxiety23_1"
## [15] "statanxiety22" "statanxiety24_1"
## [17] "statanxiety10_1" "statanxiety17"
## [19] "statanxiety28_1" "statanxiety25_1"
## [21] "statanxiety11" "statanxiety19_1"
## [23] "statanxiety26_1" "statanxiety4_1"
## [25] "statanxiety2_1" "statanxiety20_1"
## [27] "statanxiety13_1" "statanxiety27"
## [29] "math_scores" "social_studies_scores"
## [31] "russian_language_scores" "foreign_language_scores"
## [33] "certificate_mathgrade" "certificate_social_studiesgrade"
## [35] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [37] "gpa" "subject_mark"
## [39] "stat_difficulty" "stat_value"
## [41] "stat_cognitivecomp" "stat_affect"MSLQ scales
mslq_save1<-c("extrgoal14", "extrgoal12", "extrgoal13", "extrgoal11", "intrgoal14", "intrgoal12", "intrgoal13", "intrgoal11", "efficacy18", "efficacy17", "efficacy15", "efficacy12", "efficacy13", "testanxiety2", "testanxiety4", "testanxiety1", "testanxiety3", "testanxiety5")
mslq_fa <- df_imp[mslq_save1] mslq_save2<-c("extrgoal14", "extrgoal12", "extrgoal13", "extrgoal11", "intrgoal14", "intrgoal12", "intrgoal13", "intrgoal11", "efficacy18", "efficacy17", "efficacy15", "efficacy12", "efficacy13", "testanxiety2", "testanxiety4", "testanxiety1", "testanxiety3", "testanxiety5", "math_scores", "social_studies_scores", "russian_language_scores", "foreign_language_scores", "certificate_mathgrade", "certificate_social_studiesgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "gpa", "subject_mark")
mslq_reg <- df_imp[mslq_save2] Building a factor model with 4 factors
## Factor Analysis using method = minres
## Call: fa(r = mslq_fa, nfactors = 4, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 MR4 h2 u2 com
## extrgoal14 -0.03 0.31 0.09 0.49 0.42 0.58 1.8
## extrgoal12 -0.14 -0.03 -0.08 0.84 0.68 0.32 1.1
## extrgoal13 0.29 -0.08 0.10 0.53 0.37 0.63 1.7
## extrgoal11 0.12 0.01 0.09 0.79 0.70 0.30 1.1
## intrgoal14 0.05 0.76 -0.08 0.02 0.63 0.37 1.0
## intrgoal12 0.04 0.87 -0.03 0.02 0.81 0.19 1.0
## intrgoal13 0.09 0.63 -0.01 -0.01 0.46 0.54 1.0
## intrgoal11 0.28 0.61 0.00 -0.04 0.63 0.37 1.4
## efficacy18 0.60 0.22 -0.08 -0.05 0.57 0.43 1.3
## efficacy17 0.75 0.20 0.03 0.01 0.75 0.25 1.1
## efficacy15 0.87 -0.03 -0.08 0.00 0.78 0.22 1.0
## efficacy12 0.71 0.17 0.06 0.02 0.63 0.37 1.1
## efficacy13 0.65 0.10 0.07 0.03 0.49 0.51 1.1
## testanxiety2 -0.22 0.22 0.30 0.03 0.19 0.81 2.8
## testanxiety4 0.07 -0.09 0.87 0.06 0.77 0.23 1.0
## testanxiety1 -0.43 0.18 0.54 0.01 0.57 0.43 2.2
## testanxiety3 -0.29 0.17 0.58 0.13 0.58 0.42 1.8
## testanxiety5 0.06 -0.10 0.79 -0.03 0.59 0.41 1.0
##
## MR1 MR3 MR2 MR4
## SS loadings 3.50 2.75 2.34 2.00
## Proportion Var 0.19 0.15 0.13 0.11
## Cumulative Var 0.19 0.35 0.48 0.59
## Proportion Explained 0.33 0.26 0.22 0.19
## Cumulative Proportion 0.33 0.59 0.81 1.00
##
## With factor correlations of
## MR1 MR3 MR2 MR4
## MR1 1.00 0.51 -0.28 -0.02
## MR3 0.51 1.00 0.01 0.16
## MR2 -0.28 0.01 1.00 0.44
## MR4 -0.02 0.16 0.44 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 153 and the objective function was 10.02 with Chi Square of 3258.38
## The degrees of freedom for the model are 87 and the objective function was 0.7
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 333 with the empirical chi square 72.42 with prob < 0.87
## The total number of observations was 333 with Likelihood Chi Square = 227.27 with prob < 1.8e-14
##
## Tucker Lewis Index of factoring reliability = 0.92
## RMSEA index = 0.07 and the 90 % confidence intervals are 0.059 0.081
## BIC = -278.03
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR3 MR2 MR4
## Correlation of (regression) scores with factors 0.95 0.95 0.93 0.92
## Multiple R square of scores with factors 0.91 0.89 0.87 0.85
## Minimum correlation of possible factor scores 0.82 0.79 0.75 0.69
Description of the model fit:
First of all, looking at the factor loadings it can be seen that almost all variables belong to only one factor, this is also proved by the low complexity values.
Proportion explained: the explained variance should be evenly distributed among factors.In this case the first factor explain the largest proportion of variance which is 33% but still more or less clode to all the other factors.
Proportion variance: A factor should explain at least 10% of the variance. In this model it can be seen that all the factors meet this criterion.
Cumulative Variance: looking at this parameter we can see that all in all our model explains 100% of variance
Also Chi Square of 3249.21 tells us that observed and expected data aren’t significantly different, which is good
Tucker Lewis Index of factoring reliability = 0.919, which is very good measure of model fit (it should be >0.9)
RMSR index = 0.03 , which is somewhat good, as it should be <0,05
Scale relaibility:
mslq_MR1<- as.data.frame(mslq_fa [c("efficacy18", "efficacy17", "efficacy15", "efficacy12", "efficacy13")])
psych::alpha(mslq_MR1,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = mslq_MR1, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.86 0.83 0.54 5.9 0.012 2.7 0.71 0.54
##
## lower alpha upper 95% confidence boundaries
## 0.83 0.85 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## efficacy18 0.83 0.83 0.80 0.56 5.0 0.015 0.0069 0.55
## efficacy17 0.81 0.81 0.77 0.51 4.2 0.017 0.0046 0.48
## efficacy15 0.81 0.81 0.78 0.52 4.4 0.017 0.0054 0.50
## efficacy12 0.82 0.82 0.78 0.54 4.6 0.016 0.0063 0.54
## efficacy13 0.85 0.85 0.82 0.59 5.7 0.014 0.0043 0.60
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## efficacy18 333 0.77 0.78 0.69 0.64 2.7 0.85
## efficacy17 333 0.84 0.85 0.81 0.75 2.9 0.84
## efficacy15 333 0.83 0.83 0.78 0.72 2.3 0.92
## efficacy12 333 0.82 0.80 0.74 0.68 2.4 1.01
## efficacy13 333 0.72 0.73 0.61 0.57 3.1 0.85
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## efficacy18 0.10 0.28 0.46 0.16 0
## efficacy17 0.06 0.21 0.46 0.27 0
## efficacy15 0.23 0.38 0.30 0.10 0
## efficacy12 0.22 0.31 0.30 0.17 0
## efficacy13 0.05 0.18 0.43 0.34 0Cronbach’s alpha is 0.8553633, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
mslq_MR4<- as.data.frame(mslq_fa [c("intrgoal14", "intrgoal12", "intrgoal13", "intrgoal11")])
psych::alpha(mslq_MR4,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = mslq_MR4, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.83 0.83 0.79 0.54 4.8 0.016 2.3 0.76 0.53
##
## lower alpha upper 95% confidence boundaries
## 0.8 0.83 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## intrgoal14 0.77 0.77 0.70 0.53 3.3 0.022 0.0103 0.51
## intrgoal12 0.74 0.74 0.66 0.48 2.8 0.025 0.0032 0.47
## intrgoal13 0.83 0.83 0.77 0.61 4.8 0.016 0.0035 0.64
## intrgoal11 0.78 0.78 0.72 0.55 3.6 0.021 0.0097 0.51
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## intrgoal14 333 0.82 0.83 0.75 0.68 2.1 0.91
## intrgoal12 333 0.87 0.87 0.82 0.74 2.3 0.95
## intrgoal13 333 0.75 0.75 0.60 0.55 2.5 0.95
## intrgoal11 333 0.80 0.81 0.71 0.65 2.2 0.91
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## intrgoal14 0.27 0.44 0.20 0.10 0
## intrgoal12 0.21 0.42 0.24 0.14 0
## intrgoal13 0.17 0.32 0.36 0.15 0
## intrgoal11 0.26 0.43 0.22 0.09 0Cronbach’s alpha is 0.8243069, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
mslq_MR2<- as.data.frame(mslq_fa [c("testanxiety4", "testanxiety1", "testanxiety3", "testanxiety5")])
psych::alpha(mslq_MR2,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = mslq_MR2, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.79 0.79 0.76 0.49 3.8 0.019 2.9 0.77 0.48
##
## lower alpha upper 95% confidence boundaries
## 0.75 0.79 0.83
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## testanxiety4 0.71 0.71 0.63 0.45 2.5 0.027 0.0047 0.42
## testanxiety1 0.75 0.76 0.69 0.51 3.1 0.024 0.0110 0.49
## testanxiety3 0.74 0.75 0.68 0.50 3.0 0.025 0.0124 0.47
## testanxiety5 0.75 0.75 0.66 0.50 3.0 0.024 0.0011 0.49
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## testanxiety4 333 0.81 0.82 0.75 0.66 3.2 0.89
## testanxiety1 333 0.77 0.77 0.64 0.57 2.8 1.00
## testanxiety3 333 0.79 0.78 0.66 0.59 2.8 1.06
## testanxiety5 333 0.77 0.78 0.68 0.58 3.0 0.98
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## testanxiety4 0.05 0.17 0.31 0.47 0
## testanxiety1 0.11 0.28 0.29 0.33 0
## testanxiety3 0.15 0.23 0.30 0.32 0
## testanxiety5 0.10 0.20 0.35 0.36 0Cronbach’s alpha is 0.7941098, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
mslq_MR3<- as.data.frame(mslq_fa [c("extrgoal14", "extrgoal12", "extrgoal13", "extrgoal11")])
psych::alpha(mslq_MR3,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = mslq_MR3, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.72 0.72 0.67 0.39 2.6 0.025 2.8 0.71 0.38
##
## lower alpha upper 95% confidence boundaries
## 0.67 0.72 0.77
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## extrgoal14 0.69 0.70 0.63 0.43 2.3 0.028 0.0157 0.44
## extrgoal12 0.62 0.63 0.54 0.36 1.7 0.036 0.0068 0.37
## extrgoal13 0.70 0.70 0.62 0.44 2.4 0.029 0.0101 0.39
## extrgoal11 0.59 0.59 0.49 0.32 1.4 0.038 0.0037 0.31
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## extrgoal14 333 0.71 0.69 0.51 0.44 2.1 1.05
## extrgoal12 333 0.79 0.76 0.66 0.55 2.6 1.07
## extrgoal13 333 0.65 0.69 0.51 0.42 3.4 0.83
## extrgoal11 333 0.79 0.80 0.73 0.61 3.1 0.92
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## extrgoal14 0.35 0.29 0.22 0.14 0
## extrgoal12 0.18 0.26 0.29 0.27 0
## extrgoal13 0.04 0.09 0.28 0.58 0
## extrgoal11 0.08 0.14 0.36 0.42 0Cronbach’s alpha is 0.7190665, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
Adding factors to the data set:
fascores2<-as.data.frame(fa2$scores)
data_reg2<-cbind(mslq_reg,fascores2)
names(data_reg2)[names(data_reg2) == "MR1"] <- "efficacy"
names(data_reg2)[names(data_reg2) == "MR2"] <- "testanxiety"
names(data_reg2)[names(data_reg2) == "MR3"] <- "extrgoal"
names(data_reg2)[names(data_reg2) == "MR4"] <- "intrgoal"
names(data_reg2)## [1] "extrgoal14" "extrgoal12"
## [3] "extrgoal13" "extrgoal11"
## [5] "intrgoal14" "intrgoal12"
## [7] "intrgoal13" "intrgoal11"
## [9] "efficacy18" "efficacy17"
## [11] "efficacy15" "efficacy12"
## [13] "efficacy13" "testanxiety2"
## [15] "testanxiety4" "testanxiety1"
## [17] "testanxiety3" "testanxiety5"
## [19] "math_scores" "social_studies_scores"
## [21] "russian_language_scores" "foreign_language_scores"
## [23] "certificate_mathgrade" "certificate_social_studiesgrade"
## [25] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [27] "gpa" "subject_mark"
## [29] "efficacy" "extrgoal"
## [31] "testanxiety" "intrgoal"MATH
math_save1<-c("mathanxiety2", "mathanxiety3", "mathanxiety4", "mathanxiety5", "mathanxiety6", "mathanxiety7", "mathanxiety8", "mathanxiety9")
math_fa <- df_imp[math_save1] math_save2<-c("mathanxiety2", "mathanxiety3", "mathanxiety4", "mathanxiety5", "mathanxiety6", "mathanxiety7", "mathanxiety8", "mathanxiety9", "math_scores", "social_studies_scores", "russian_language_scores", "foreign_language_scores", "certificate_mathgrade", "certificate_social_studiesgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "gpa", "subject_mark")
math_reg <- df_imp[math_save2] Building a factor model with 1 factor
## Factor Analysis using method = minres
## Call: fa(r = math_fa, nfactors = 1, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## mathanxiety2 0.71 0.51 0.49 1
## mathanxiety3 0.79 0.62 0.38 1
## mathanxiety4 0.74 0.54 0.46 1
## mathanxiety5 0.70 0.48 0.52 1
## mathanxiety6 0.81 0.66 0.34 1
## mathanxiety7 0.78 0.61 0.39 1
## mathanxiety8 0.75 0.56 0.44 1
## mathanxiety9 0.82 0.68 0.32 1
##
## MR1
## SS loadings 4.66
## Proportion Var 0.58
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 6.02 with Chi Square of 1978.99
## The degrees of freedom for the model are 20 and the objective function was 1.45
##
## The root mean square of the residuals (RMSR) is 0.11
## The df corrected root mean square of the residuals is 0.13
##
## The harmonic number of observations is 333 with the empirical chi square 220.25 with prob < 1.1e-35
## The total number of observations was 333 with Likelihood Chi Square = 475.34 with prob < 4.2e-88
##
## Tucker Lewis Index of factoring reliability = 0.673
## RMSEA index = 0.261 and the 90 % confidence intervals are 0.242 0.283
## BIC = 359.17
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.96
## Multiple R square of scores with factors 0.92
## Minimum correlation of possible factor scores 0.84
Description of the model fit:
Proportion Var 0.58
Also Chi Square of 474.78 tells us that observed and expected data aren’t significantly different, which is good
Tucker Lewis Index of factoring reliability = 0.673, which is not very good measure of model fit (it should be >0.9)
RMSR index = 0.11 , which is also not very good, as it should be <0,05
Scale relaibility:
math_MR1<- as.data.frame(math_fa [c("mathanxiety2", "mathanxiety3", "mathanxiety4", "mathanxiety5", "mathanxiety6", "mathanxiety7", "mathanxiety8", "mathanxiety9")])
psych::alpha(math_MR1,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = math_MR1, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.88 0.88 0.89 0.47 7.2 0.01 2.3 0.67 0.46
##
## lower alpha upper 95% confidence boundaries
## 0.86 0.88 0.9
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## mathanxiety2 0.87 0.87 0.87 0.48 6.5 0.011 0.013 0.47
## mathanxiety3 0.86 0.86 0.88 0.47 6.1 0.012 0.020 0.42
## mathanxiety4 0.86 0.86 0.87 0.48 6.3 0.011 0.016 0.47
## mathanxiety5 0.87 0.87 0.88 0.49 6.7 0.011 0.017 0.51
## mathanxiety6 0.86 0.86 0.87 0.46 6.0 0.012 0.015 0.46
## mathanxiety7 0.86 0.86 0.87 0.47 6.2 0.012 0.013 0.47
## mathanxiety8 0.87 0.87 0.88 0.49 6.6 0.011 0.013 0.46
## mathanxiety9 0.86 0.86 0.87 0.47 6.1 0.012 0.018 0.46
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## mathanxiety2 333 0.71 0.71 0.68 0.61 3.1 0.89
## mathanxiety3 333 0.77 0.77 0.72 0.68 2.6 0.97
## mathanxiety4 333 0.73 0.73 0.69 0.64 2.9 0.92
## mathanxiety5 333 0.68 0.68 0.61 0.57 3.2 0.88
## mathanxiety6 333 0.79 0.78 0.76 0.70 2.0 0.96
## mathanxiety7 333 0.75 0.75 0.72 0.66 1.8 0.92
## mathanxiety8 333 0.69 0.69 0.64 0.59 1.5 0.83
## mathanxiety9 333 0.77 0.77 0.73 0.68 1.7 0.91
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## mathanxiety2 0.06 0.18 0.37 0.39 0
## mathanxiety3 0.16 0.31 0.35 0.18 0
## mathanxiety4 0.08 0.24 0.38 0.30 0
## mathanxiety5 0.06 0.13 0.36 0.45 0
## mathanxiety6 0.38 0.32 0.23 0.08 0
## mathanxiety7 0.50 0.31 0.12 0.07 0
## mathanxiety8 0.63 0.24 0.08 0.05 0
## mathanxiety9 0.52 0.30 0.11 0.07 0Cronbach’s alpha is 0.878703, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
Adding factors to the data set:
fascores3<-as.data.frame(fa3$scores)
data_reg3<-cbind(math_reg,fascores3)
names(data_reg3)[names(data_reg3) == "MR1"] <- "mathanxiety"
names(data_reg3)## [1] "mathanxiety2" "mathanxiety3"
## [3] "mathanxiety4" "mathanxiety5"
## [5] "mathanxiety6" "mathanxiety7"
## [7] "mathanxiety8" "mathanxiety9"
## [9] "math_scores" "social_studies_scores"
## [11] "russian_language_scores" "foreign_language_scores"
## [13] "certificate_mathgrade" "certificate_social_studiesgrade"
## [15] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [17] "gpa" "subject_mark"
## [19] "mathanxiety"Interest
interest_save1<-c("inter1_2", "inter1_5", "inter1_6", "inter1_3", "inter1_1", "inter1_4")
interest_fa <- df_imp[interest_save1] interest_save2<-c("inter1_2", "inter1_5", "inter1_6", "inter1_3", "inter1_1", "inter1_4", "math_scores", "social_studies_scores", "russian_language_scores", "foreign_language_scores", "certificate_mathgrade", "certificate_social_studiesgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "gpa", "subject_mark")
interest_reg <- df_imp[interest_save2] Building a factor model with 1 factor
## Factor Analysis using method = minres
## Call: fa(r = interest_fa, nfactors = 1, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## inter1_2 -0.82 0.67 0.33 1
## inter1_5 0.83 0.69 0.31 1
## inter1_6 0.86 0.74 0.26 1
## inter1_3 0.93 0.87 0.13 1
## inter1_1 0.92 0.84 0.16 1
## inter1_4 0.84 0.70 0.30 1
##
## MR1
## SS loadings 4.51
## Proportion Var 0.75
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 5.73 with Chi Square of 1886.06
## The degrees of freedom for the model are 9 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 333 with the empirical chi square 5.24 with prob < 0.81
## The total number of observations was 333 with Likelihood Chi Square = 46.64 with prob < 4.6e-07
##
## Tucker Lewis Index of factoring reliability = 0.966
## RMSEA index = 0.112 and the 90 % confidence intervals are 0.082 0.145
## BIC = -5.64
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.98
## Multiple R square of scores with factors 0.96
## Minimum correlation of possible factor scores 0.91
Description of the model fit:
Proportion Var 0.75
Also Chi Square of 1887.07 tells us that observed and expected data aren’t significantly different, which is good
Tucker Lewis Index of factoring reliability = 0.967, which is very good measure of model fit (it should be >0.9)
RMSR index = 0.02 , which is also very good, as it should be <0,05
Scale relaibility:
interest_MR1<- as.data.frame(interest_fa [c("inter1_2", "inter1_5", "inter1_6", "inter1_3", "inter1_1", "inter1_4")])
psych::alpha(interest_MR1,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = interest_MR1, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.92 0.92 0.91 0.67 12 0.0066 2.5 0.82 0.67
##
## lower alpha upper 95% confidence boundaries
## 0.91 0.92 0.94
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## inter1_2- 0.91 0.91 0.90 0.68 10.7 0.0074 0.0026 0.70
## inter1_5 0.91 0.91 0.90 0.68 10.7 0.0074 0.0028 0.70
## inter1_6 0.91 0.91 0.90 0.67 10.2 0.0078 0.0039 0.69
## inter1_3 0.90 0.90 0.88 0.64 8.9 0.0088 0.0026 0.63
## inter1_1 0.90 0.90 0.89 0.65 9.2 0.0085 0.0031 0.63
## inter1_4 0.91 0.91 0.90 0.67 10.3 0.0077 0.0032 0.69
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## inter1_2- 333 0.82 0.82 0.77 0.74 2.7 0.99
## inter1_5 333 0.82 0.82 0.77 0.73 2.8 0.96
## inter1_6 333 0.84 0.84 0.80 0.76 2.1 0.95
## inter1_3 333 0.90 0.90 0.89 0.85 2.6 0.96
## inter1_1 333 0.88 0.88 0.86 0.83 2.3 0.97
## inter1_4 333 0.84 0.84 0.79 0.76 2.5 0.96
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## inter1_2 0.24 0.36 0.26 0.15 0
## inter1_5 0.13 0.21 0.41 0.25 0
## inter1_6 0.32 0.38 0.20 0.10 0
## inter1_3 0.15 0.29 0.37 0.19 0
## inter1_1 0.24 0.39 0.24 0.13 0
## inter1_4 0.16 0.32 0.35 0.18 0Cronbach’s alpha is 0.9229752, which indicates good scale reliability. Which means that if we use this scale to measure this construct multiple times we will get the same results showing very good internal consistency.
Adding factors to the data set:
fascores4<-as.data.frame(fa4$scores)
data_reg4<-cbind(interest_reg,fascores4)
names(data_reg4)[names(data_reg4) == "MR1"] <- "interest"
names(data_reg4)## [1] "inter1_2" "inter1_5"
## [3] "inter1_6" "inter1_3"
## [5] "inter1_1" "inter1_4"
## [7] "math_scores" "social_studies_scores"
## [9] "russian_language_scores" "foreign_language_scores"
## [11] "certificate_mathgrade" "certificate_social_studiesgrade"
## [13] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [15] "gpa" "subject_mark"
## [17] "interest"Final dataset with factor scores for further analysis:
reg_save2<-c("math_scores", "social_studies_scores", "russian_language_scores", "foreign_language_scores", "certificate_mathgrade", "certificate_social_studiesgrade", "certificate_russianlanggrade", "certificate_foreign_langgrade", "gpa", "subject_mark", "gender", "father_ISCO", "mother_ISCO")
reg_reg <- df_imp[reg_save2] final_reg<-cbind(reg_reg, data_reg1$stat_affect, data_reg1$stat_cognitivecomp, data_reg1$stat_difficulty, data_reg1$stat_value, data_reg2$efficacy, data_reg2$extrgoal, data_reg2$intrgoal, data_reg2$testanxiety, data_reg3$mathanxiety, data_reg4$interest, df_imp$course)
names(final_reg)[names(final_reg) == "data_reg1$stat_affect"] <- "stat_affect"
names(final_reg)[names(final_reg) == "data_reg1$stat_cognitivecomp"] <- "stat_cognitivecomp"
names(final_reg)[names(final_reg) == "data_reg1$stat_difficulty"] <- "stat_difficulty"
names(final_reg)[names(final_reg) == "data_reg1$stat_value"] <- "stat_value"
names(final_reg)[names(final_reg) == "data_reg2$efficacy"] <- "efficacy"
names(final_reg)[names(final_reg) == "data_reg2$extrgoal"] <- "extrgoal"
names(final_reg)[names(final_reg) == "data_reg2$intrgoal"] <- "intrgoal"
names(final_reg)[names(final_reg) == "data_reg2$testanxiety"] <- "testanxiety"
names(final_reg)[names(final_reg) == "data_reg3$mathanxiety"] <- "mathanxiety"
names(final_reg)[names(final_reg) == "data_reg4$interest"] <- "interest"
names(final_reg)[names(final_reg) == "df_imp$course"] <- "course"
names(final_reg)## [1] "math_scores" "social_studies_scores"
## [3] "russian_language_scores" "foreign_language_scores"
## [5] "certificate_mathgrade" "certificate_social_studiesgrade"
## [7] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [9] "gpa" "subject_mark"
## [11] "gender" "father_ISCO"
## [13] "mother_ISCO" "stat_affect"
## [15] "stat_cognitivecomp" "stat_difficulty"
## [17] "stat_value" "efficacy"
## [19] "extrgoal" "intrgoal"
## [21] "testanxiety" "mathanxiety"
## [23] "interest" "course"Checking hypotheses H1-H3
Correlation analysis
library(polycor)
library(corrplot)
dat.cor <- hetcor(final_reg)
dat.cor<- dat.cor$correlations
dat.cor## math_scores social_studies_scores
## math_scores 1.00000000 0.327192422
## social_studies_scores 0.32719242 1.000000000
## russian_language_scores 0.23984168 0.394356726
## foreign_language_scores 0.35776048 0.512822092
## certificate_mathgrade 0.27227228 0.373012807
## certificate_social_studiesgrade 0.07155964 0.271478846
## certificate_russianlanggrade 0.12216889 0.306673614
## certificate_foreign_langgrade 0.02761848 0.264999465
## gpa 0.42578919 0.469967643
## subject_mark 0.23376424 0.308346718
## gender 0.06851771 -0.281730060
## father_ISCO 0.17269341 0.139912622
## mother_ISCO 0.02501915 0.051257475
## stat_affect 0.14089273 0.037435695
## stat_cognitivecomp -0.32968437 -0.015940253
## stat_difficulty -0.21515514 -0.001475602
## stat_value -0.10605834 -0.110049510
## efficacy 0.30324127 0.120022659
## extrgoal 0.22104347 -0.003693572
## intrgoal -0.09766743 -0.075450373
## testanxiety -0.25057675 -0.030548788
## mathanxiety -0.20185990 0.009554514
## interest 0.27471106 0.058476316
## course -0.17121426 -0.073175646
## russian_language_scores foreign_language_scores
## math_scores 0.2398416849 0.357760475
## social_studies_scores 0.3943567262 0.512822092
## russian_language_scores 1.0000000000 0.380804573
## foreign_language_scores 0.3808045734 1.000000000
## certificate_mathgrade 0.3474007961 0.379777902
## certificate_social_studiesgrade 0.1768063822 0.216928181
## certificate_russianlanggrade 0.3001720599 0.316025547
## certificate_foreign_langgrade 0.2851410394 0.305181109
## gpa 0.3683844021 0.468904187
## subject_mark 0.1834082120 0.184988308
## gender -0.3043190630 -0.165096545
## father_ISCO 0.1852142718 0.184217531
## mother_ISCO 0.0873357203 0.008453903
## stat_affect 0.0839230764 0.053409115
## stat_cognitivecomp -0.0116732417 -0.133089641
## stat_difficulty -0.0270903996 -0.112489113
## stat_value -0.0861946654 -0.112381313
## efficacy 0.0264562878 0.099657882
## extrgoal 0.0188051588 -0.057142789
## intrgoal 0.0001241272 -0.117438120
## testanxiety 0.0552634845 -0.091988386
## mathanxiety 0.0472796919 -0.052767832
## interest 0.0107073489 0.046834696
## course -0.0840393535 -0.014617822
## certificate_mathgrade
## math_scores 0.272272283
## social_studies_scores 0.373012807
## russian_language_scores 0.347400796
## foreign_language_scores 0.379777902
## certificate_mathgrade 1.000000000
## certificate_social_studiesgrade 0.525399537
## certificate_russianlanggrade 0.628299631
## certificate_foreign_langgrade 0.498284640
## gpa 0.442735729
## subject_mark 0.242680206
## gender -0.438517343
## father_ISCO 0.227788070
## mother_ISCO 0.005202136
## stat_affect 0.037917029
## stat_cognitivecomp -0.045608957
## stat_difficulty 0.023980111
## stat_value -0.014001819
## efficacy 0.095729787
## extrgoal 0.010094366
## intrgoal -0.064134628
## testanxiety -0.022944634
## mathanxiety -0.023254805
## interest 0.054564167
## course 0.153095698
## certificate_social_studiesgrade
## math_scores 0.071559641
## social_studies_scores 0.271478846
## russian_language_scores 0.176806382
## foreign_language_scores 0.216928181
## certificate_mathgrade 0.525399537
## certificate_social_studiesgrade 1.000000000
## certificate_russianlanggrade 0.488838172
## certificate_foreign_langgrade 0.467877902
## gpa 0.267007084
## subject_mark 0.074224882
## gender -0.332739691
## father_ISCO 0.178329198
## mother_ISCO 0.045637275
## stat_affect 0.032495187
## stat_cognitivecomp 0.001571909
## stat_difficulty 0.064889609
## stat_value -0.041065281
## efficacy 0.011240682
## extrgoal -0.018137106
## intrgoal 0.039594975
## testanxiety 0.063261876
## mathanxiety 0.032790097
## interest -0.056984503
## course 0.044305478
## certificate_russianlanggrade
## math_scores 0.12216889
## social_studies_scores 0.30667361
## russian_language_scores 0.30017206
## foreign_language_scores 0.31602555
## certificate_mathgrade 0.62829963
## certificate_social_studiesgrade 0.48883817
## certificate_russianlanggrade 1.00000000
## certificate_foreign_langgrade 0.52134613
## gpa 0.40422486
## subject_mark 0.17195549
## gender -0.43607037
## father_ISCO 0.19589556
## mother_ISCO 0.12458614
## stat_affect 0.06258597
## stat_cognitivecomp -0.01666650
## stat_difficulty 0.09180853
## stat_value -0.05732558
## efficacy -0.01138230
## extrgoal -0.04498487
## intrgoal 0.01406144
## testanxiety 0.08158489
## mathanxiety 0.07087570
## interest -0.06623677
## course 0.14806940
## certificate_foreign_langgrade gpa
## math_scores 0.027618482 0.42578919
## social_studies_scores 0.264999465 0.46996764
## russian_language_scores 0.285141039 0.36838440
## foreign_language_scores 0.305181109 0.46890419
## certificate_mathgrade 0.498284640 0.44273573
## certificate_social_studiesgrade 0.467877902 0.26700708
## certificate_russianlanggrade 0.521346126 0.40422486
## certificate_foreign_langgrade 1.000000000 0.28507351
## gpa 0.285073510 1.00000000
## subject_mark 0.108331373 0.61366468
## gender -0.430774161 -0.23738074
## father_ISCO 0.093182330 0.15261746
## mother_ISCO 0.013238875 0.06455866
## stat_affect -0.009050429 0.23639481
## stat_cognitivecomp 0.058506110 -0.17263675
## stat_difficulty 0.036706123 -0.08603657
## stat_value -0.034976368 -0.21375725
## efficacy 0.001648678 0.33855523
## extrgoal -0.100210369 0.11751354
## intrgoal 0.032475900 -0.04408093
## testanxiety 0.068240689 -0.07438839
## mathanxiety 0.116524802 -0.07841520
## interest -0.057168045 0.19211190
## course 0.120485972 0.05161812
## subject_mark gender father_ISCO
## math_scores 0.233764237 0.06851771 0.1726934134
## social_studies_scores 0.308346718 -0.28173006 0.1399126223
## russian_language_scores 0.183408212 -0.30431906 0.1852142718
## foreign_language_scores 0.184988308 -0.16509654 0.1842175305
## certificate_mathgrade 0.242680206 -0.43851734 0.2277880701
## certificate_social_studiesgrade 0.074224882 -0.33273969 0.1783291984
## certificate_russianlanggrade 0.171955486 -0.43607037 0.1958955649
## certificate_foreign_langgrade 0.108331373 -0.43077416 0.0931823296
## gpa 0.613664678 -0.23738074 0.1526174596
## subject_mark 1.000000000 -0.13037432 -0.0187772372
## gender -0.130374323 1.00000000 -0.0869173168
## father_ISCO -0.018777237 -0.08691732 1.0000000000
## mother_ISCO 0.048254456 0.02542340 0.1347947400
## stat_affect 0.160946617 0.07553418 -0.0250099422
## stat_cognitivecomp -0.035464550 -0.18643381 0.0001300256
## stat_difficulty 0.014186818 -0.18327079 -0.0010580062
## stat_value -0.109365270 -0.06879662 0.0675691250
## efficacy 0.389094480 0.14351317 -0.0108078430
## extrgoal 0.184238422 0.26527072 -0.0417487490
## intrgoal -0.129005953 -0.12979057 -0.0991381621
## testanxiety -0.109512208 -0.28348584 -0.0810379319
## mathanxiety -0.001112895 -0.25134357 -0.0452578069
## interest 0.203617424 0.18789659 0.0115353915
## course 0.251836503 -0.19031277 0.0298446856
## mother_ISCO stat_affect stat_cognitivecomp
## math_scores 0.025019155 0.140892730 -0.3296843717
## social_studies_scores 0.051257475 0.037435695 -0.0159402535
## russian_language_scores 0.087335720 0.083923076 -0.0116732417
## foreign_language_scores 0.008453903 0.053409115 -0.1330896414
## certificate_mathgrade 0.005202136 0.037917029 -0.0456089569
## certificate_social_studiesgrade 0.045637275 0.032495187 0.0015719089
## certificate_russianlanggrade 0.124586142 0.062585973 -0.0166664951
## certificate_foreign_langgrade 0.013238875 -0.009050429 0.0585061100
## gpa 0.064558660 0.236394815 -0.1726367488
## subject_mark 0.048254456 0.160946617 -0.0354645503
## gender 0.025423404 0.075534176 -0.1864338060
## father_ISCO 0.134794740 -0.025009942 0.0001300256
## mother_ISCO 1.000000000 0.034265985 -0.1100934085
## stat_affect 0.034265985 1.000000000 -0.3788558347
## stat_cognitivecomp -0.110093409 -0.378855835 1.0000000000
## stat_difficulty -0.029756007 -0.268428753 0.6310888372
## stat_value -0.074694986 -0.651758207 0.3131288770
## efficacy -0.102124331 0.355070912 -0.4117984310
## extrgoal -0.093866430 0.352975290 -0.1906013382
## intrgoal -0.110720249 0.071766081 0.2099710010
## testanxiety -0.036959686 -0.063414836 0.4550563804
## mathanxiety -0.047689285 -0.086447877 0.4754442074
## interest -0.054391629 0.394764461 -0.1997396780
## course 0.023851480 -0.034172936 0.0411119507
## stat_difficulty stat_value efficacy
## math_scores -0.215155145 -0.10605834 0.303241268
## social_studies_scores -0.001475602 -0.11004951 0.120022659
## russian_language_scores -0.027090400 -0.08619467 0.026456288
## foreign_language_scores -0.112489113 -0.11238131 0.099657882
## certificate_mathgrade 0.023980111 -0.01400182 0.095729787
## certificate_social_studiesgrade 0.064889609 -0.04106528 0.011240682
## certificate_russianlanggrade 0.091808532 -0.05732558 -0.011382297
## certificate_foreign_langgrade 0.036706123 -0.03497637 0.001648678
## gpa -0.086036569 -0.21375725 0.338555233
## subject_mark 0.014186818 -0.10936527 0.389094480
## gender -0.183270785 -0.06879662 0.143513168
## father_ISCO -0.001058006 0.06756912 -0.010807843
## mother_ISCO -0.029756007 -0.07469499 -0.102124331
## stat_affect -0.268428753 -0.65175821 0.355070912
## stat_cognitivecomp 0.631088837 0.31312888 -0.411798431
## stat_difficulty 1.000000000 0.20997479 -0.322758773
## stat_value 0.209974787 1.00000000 -0.265824022
## efficacy -0.322758773 -0.26582402 1.000000000
## extrgoal -0.070325832 -0.28243474 0.600829413
## intrgoal 0.281992290 0.02817709 -0.025566348
## testanxiety 0.489843786 0.13048589 -0.342588799
## mathanxiety 0.411240563 0.18497722 -0.379012534
## interest -0.154394875 -0.36688530 0.644978388
## course 0.191141331 0.12853089 0.002406911
## extrgoal intrgoal testanxiety
## math_scores 0.221043474 -0.0976674290 -0.250576749
## social_studies_scores -0.003693572 -0.0754503730 -0.030548788
## russian_language_scores 0.018805159 0.0001241272 0.055263485
## foreign_language_scores -0.057142789 -0.1174381197 -0.091988386
## certificate_mathgrade 0.010094366 -0.0641346281 -0.022944634
## certificate_social_studiesgrade -0.018137106 0.0395949745 0.063261876
## certificate_russianlanggrade -0.044984868 0.0140614440 0.081584886
## certificate_foreign_langgrade -0.100210369 0.0324758997 0.068240689
## gpa 0.117513535 -0.0440809344 -0.074388393
## subject_mark 0.184238422 -0.1290059529 -0.109512208
## gender 0.265270723 -0.1297905714 -0.283485840
## father_ISCO -0.041748749 -0.0991381621 -0.081037932
## mother_ISCO -0.093866430 -0.1107202486 -0.036959686
## stat_affect 0.352975290 0.0717660812 -0.063414836
## stat_cognitivecomp -0.190601338 0.2099710010 0.455056380
## stat_difficulty -0.070325832 0.2819922903 0.489843786
## stat_value -0.282434736 0.0281770917 0.130485888
## efficacy 0.600829413 -0.0255663479 -0.342588799
## extrgoal 1.000000000 0.2066146701 0.001397036
## intrgoal 0.206614670 1.0000000000 0.547747406
## testanxiety 0.001397036 0.5477474060 1.000000000
## mathanxiety -0.136183499 0.3651534709 0.603877188
## interest 0.710018920 0.1339214778 -0.064338242
## course -0.145016300 -0.2543210132 -0.063924831
## mathanxiety interest course
## math_scores -0.201859899 0.27471106 -0.171214255
## social_studies_scores 0.009554514 0.05847632 -0.073175646
## russian_language_scores 0.047279692 0.01070735 -0.084039354
## foreign_language_scores -0.052767832 0.04683470 -0.014617822
## certificate_mathgrade -0.023254805 0.05456417 0.153095698
## certificate_social_studiesgrade 0.032790097 -0.05698450 0.044305478
## certificate_russianlanggrade 0.070875698 -0.06623677 0.148069404
## certificate_foreign_langgrade 0.116524802 -0.05716804 0.120485972
## gpa -0.078415204 0.19211190 0.051618119
## subject_mark -0.001112895 0.20361742 0.251836503
## gender -0.251343566 0.18789659 -0.190312767
## father_ISCO -0.045257807 0.01153539 0.029844686
## mother_ISCO -0.047689285 -0.05439163 0.023851480
## stat_affect -0.086447877 0.39476446 -0.034172936
## stat_cognitivecomp 0.475444207 -0.19973968 0.041111951
## stat_difficulty 0.411240563 -0.15439487 0.191141331
## stat_value 0.184977219 -0.36688530 0.128530892
## efficacy -0.379012534 0.64497839 0.002406911
## extrgoal -0.136183499 0.71001892 -0.145016300
## intrgoal 0.365153471 0.13392148 -0.254321013
## testanxiety 0.603877188 -0.06433824 -0.063924831
## mathanxiety 1.000000000 -0.24948765 0.012440510
## interest -0.249487653 1.00000000 -0.147356099
## course 0.012440510 -0.14735610 1.000000000
Correlations (H1:Both USE scores and school grades for four core subjects are assumed to be positively related to academic achievement):
Math USE scores and subject grade: ~0.23
Math USE scores and gpa: ~ 0.42
Math school grade and subject grade: ~0.24
Math school grade and gpa: ~ 0.44
Social Studies USE scores and subject grade: ~0.31
Social Studies USE scores and gpa: ~0.38
Social Studies school grade and subject grade: ~0.07
Social Studies school grade and gpa: ~0.26
Russian language USE scores and subject grade: ~0.17
Russian language USE scores and gpa: ~0.36
Russian language school grade and subject grade: ~0.17
Russian language school grade and gpa: ~0.40
Foreign language USE scores and subject grade: ~0.19
Foreign language USE scores and gpa: ~0.47
Foreign language school grade and subject grade: ~0.11
Foreign language school grade and gpa: ~0.28
Correlation analysis showed that USE scores and school grades are both positively correlated with college gpa and subject grades. Nevertheless, USE scores and school grades turned out to be higher correlated with student’s gpa than with subject grade. Furthemore, the highest correlation can be observed between foreign language USE scores and gpa (0.47). Math USE score and school grade also have relatively high correlation coefficients with student’s gpa in college (>0.40). Other predictors have rather low correlation coefficients (<0.30).
Correlations (H2:both performance and learning goal orientations will be positively related to academic achievement. Though, learning goal orientation is hypothesized to have higher correlation coefficients.):
Intrinsic goal orientation and subject grade: ~0.19
Intrinsic goal orientation and gpa: ~0.12
Extrinsic goal orientation and subject grade: ~-0.12
Extrinsic goal orientation and gpa: ~ -0.04
According to correlation analysis it can be seen that correlation coefficients are rather small. Though there exists a certain pattern, which indicates that intrinsic goal orientation is positively associated with academic performance (both gpa and subject grades) while extrinsic goal orientation has negative correlation with both outcome variables. This support the hypothesis only parrtly. Nevertheless, intrinsic goal orientation has higher correlation coefficients with subject grades, meaning that students who are eager to gain knowledge and develop competences in certain subjects (have high intrinsic goal orientations) get higher grades in this subjects. While extrinsic goal orientation has higher correlation coefficients with gpa.
Correlations (H3:Both self-efficacy beliefs and individual interest are also assumed to have positive relation to the outcome variable. While anxiety is hypothesized to have direct negative relation to academic achievement.):
Self-efficacy and subject grade: ~0.39
Self-efficacy and gpa: ~0.33
Correlation coefficents arer the highest among all motivational vaianles and also support the hypothesis since they indicate that increrased self-efficacy beliefs (beliefs in the ability to perform a certain task) are associated with higher subject grades and gpa in general. Moreover, compared to the gpa, subject grdaes have higher correlation coefficients with the outcome varibale
Interest and subject grade: ~0.20
Interest and gpa: ~0.19
coefficients are rather small but still support the hypothesis about higher interest in the subject being associated with higher academic performance.
Affective states towards statistics and subject grade: ~0.15
Affective states towards statistics and gpa: ~0.23
Beliefs about cognitive competences to statistics and subject grade: ~ -0.03
Beliefs about cognitive competences to statistics statistics and gpa: ~ -0.17
Beliefs about difficulty of statistics and subject grade: ~ 0.01
Beliefs about difficulty of statistics and gpa: ~ -0.08
Statistics value and subject grade: ~ -0.21
Statistics value and subject grade: ~ -0.11
All 4 domains of SATS (survey of attitudes towards statistics) indicate very small correlation coefficients. Though the highest correlations with gpa and subject grades can be observed in case of affective states, which means that students who likes statistics perform better. The second highest correlation coefficients are with belifs of statistics value. They indicate that the more a student believes that statistics is useless the lower his or her grades are.
Math anxiety and subject grade: ~ 0.00016
Math anxiety and subject grade: ~ -0.07
Test anxiety and subject grade: ~ -0.1
Test anxiety and subject grade: ~ -0.07
Math and test anxieties have very small correlations with the outcome variables.
Regression analysis
##
## Call:
## lm(formula = subject_mark ~ math_scores, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3570 -1.3570 -0.1217 0.9875 4.4245
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.64268 0.97586 1.683 0.0933 .
## math_scores 0.05462 0.01249 4.374 1.64e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.693 on 331 degrees of freedom
## Multiple R-squared: 0.05465, Adjusted R-squared: 0.05179
## F-statistic: 19.13 on 1 and 331 DF, p-value: 1.635e-05Explains only 5% of variance (Adjusted R-squared: 0.05229)
##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8840 -1.2335 -0.2378 0.8723 4.2403
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.607283 1.058250 -0.574 0.56646
## math_scores 0.034771 0.012806 2.715 0.00697 **
## social_studies_scores 0.044924 0.009482 4.738 3.22e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.641 on 330 degrees of freedom
## Multiple R-squared: 0.1149, Adjusted R-squared: 0.1095
## F-statistic: 21.41 on 2 and 330 DF, p-value: 1.81e-09Social sciences USE scores add additional 5% of explained variance (now this model explains 10% of variance)
Model comparison with anova also proves that the second model is better than the first one
model3<-lm(subject_mark ~ math_scores+social_studies_scores+russian_language_scores, data = final_reg)
summary(model3)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## russian_language_scores, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8607 -1.2491 -0.2154 0.8764 4.1915
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.15740 1.20356 -0.962 0.3369
## math_scores 0.03319 0.01291 2.570 0.0106 *
## social_studies_scores 0.04159 0.01010 4.117 4.86e-05 ***
## russian_language_scores 0.01064 0.01108 0.960 0.3378
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.641 on 329 degrees of freedom
## Multiple R-squared: 0.1173, Adjusted R-squared: 0.1093
## F-statistic: 14.58 on 3 and 329 DF, p-value: 6.169e-09With addition of russian language USE scores Adjusted R-squared has become smaller nad the coefficient for this variable is statistically insignificant
Model comparison with anova also indicate that adding USE scores for russian language does not improve the model.
model4<-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores, data = final_reg)
summary(model4)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8841 -1.2334 -0.2388 0.8734 4.2445
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5937489 1.1387059 -0.521 0.60242
## math_scores 0.0348710 0.0131927 2.643 0.00861 **
## social_studies_scores 0.0450792 0.0106254 4.243 2.88e-05 ***
## foreign_language_scores -0.0004029 0.0123949 -0.033 0.97409
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.644 on 329 degrees of freedom
## Multiple R-squared: 0.1149, Adjusted R-squared: 0.1068
## F-statistic: 14.23 on 3 and 329 DF, p-value: 9.669e-09The same can be observed with the USE scores for foreign language
model5<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade, data = final_reg)
summary(model5)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8774 -1.2412 -0.2594 0.8476 4.2773
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.574583 1.137227 -1.385 0.167119
## math_scores 0.029816 0.012920 2.308 0.021638 *
## social_studies_scores 0.037991 0.009921 3.829 0.000154 ***
## certificate_mathgrade 0.415613 0.185717 2.238 0.025897 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.631 on 329 degrees of freedom
## Multiple R-squared: 0.1281, Adjusted R-squared: 0.1202
## F-statistic: 16.12 on 3 and 329 DF, p-value: 8.491e-10Adding math school grade has increased Adjusted R-squared from 11% in the second model to 12%. Regression coefficient is also statistically significant in ths model
Model comparison with anova indicated that model5 is better
model6<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+certificate_social_studiesgrade, data = final_reg)
summary(model6)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + certificate_social_studiesgrade,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8477 -1.2290 -0.3081 0.8865 4.5730
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.426457 1.399189 -0.305 0.76072
## math_scores 0.027704 0.012989 2.133 0.03367 *
## social_studies_scores 0.039703 0.009981 3.978 8.57e-05 ***
## certificate_mathgrade 0.560247 0.212118 2.641 0.00866 **
## certificate_social_studiesgrade -0.372678 0.265348 -1.404 0.16112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.629 on 328 degrees of freedom
## Multiple R-squared: 0.1333, Adjusted R-squared: 0.1228
## F-statistic: 12.62 on 4 and 328 DF, p-value: 1.468e-09Adjusted R-squared has only slightly increased and the coefficient is not statistically significant
Model comparison with anova indicates that model5 is better
model7<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+certificate_russianlanggrade, data = final_reg)
summary(model7)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + certificate_russianlanggrade, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8856 -1.2289 -0.2244 0.8488 4.2611
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.68109 1.21731 -1.381 0.168224
## math_scores 0.03012 0.01300 2.317 0.021094 *
## social_studies_scores 0.03769 0.01001 3.766 0.000197 ***
## certificate_mathgrade 0.38224 0.22964 1.664 0.096969 .
## certificate_russianlanggrade 0.05625 0.22709 0.248 0.804508
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.634 on 328 degrees of freedom
## Multiple R-squared: 0.1283, Adjusted R-squared: 0.1177
## F-statistic: 12.07 on 4 and 328 DF, p-value: 3.669e-09Adjusted R-squared has become smaller comparing to the model5 and regression coefficient is also statistically insigniificant
model5 is still better
model8<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+certificate_foreign_langgrade, data = final_reg)
summary(model8)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + certificate_foreign_langgrade, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8647 -1.2649 -0.2672 0.8549 4.3516
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.25152 1.43697 -0.871 0.384420
## math_scores 0.02904 0.01311 2.216 0.027397 *
## social_studies_scores 0.03850 0.01003 3.839 0.000148 ***
## certificate_mathgrade 0.45166 0.21011 2.150 0.032312 *
## certificate_foreign_langgrade -0.09813 0.26623 -0.369 0.712666
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.633 on 328 degrees of freedom
## Multiple R-squared: 0.1285, Adjusted R-squared: 0.1179
## F-statistic: 12.09 on 4 and 328 DF, p-value: 3.54e-09Same as with model8. Model5 is still the best one
model9<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy, data = final_reg)
summary(model9)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3924 -1.0550 -0.3122 0.9809 4.6198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.410440 1.106028 0.371 0.7108
## math_scores 0.006176 0.012609 0.490 0.6246
## social_studies_scores 0.036754 0.009307 3.949 9.61e-05 ***
## certificate_mathgrade 0.406726 0.174189 2.335 0.0201 *
## efficacy 0.593844 0.087551 6.783 5.50e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.53 on 328 degrees of freedom
## Multiple R-squared: 0.2354, Adjusted R-squared: 0.226
## F-statistic: 25.24 on 4 and 328 DF, p-value: < 2.2e-16Adding self-efficacy beliefs to the model has substantially increased Adjusted R-squared (from 12% in the model5 to 22% in this one). Also regrerssion coefficient for this variable is statistically significant
model9 is better
model10<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal, data = final_reg)
summary(model10)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5509 -1.0582 -0.3043 0.9577 4.6239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.427162 1.106999 0.386 0.69984
## math_scores 0.007032 0.012670 0.555 0.57926
## social_studies_scores 0.036063 0.009359 3.853 0.00014 ***
## certificate_mathgrade 0.401366 0.174454 2.301 0.02204 *
## efficacy 0.640346 0.107444 5.960 6.53e-09 ***
## extrgoal -0.080412 0.107555 -0.748 0.45522
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.531 on 327 degrees of freedom
## Multiple R-squared: 0.2367, Adjusted R-squared: 0.225
## F-statistic: 20.28 on 5 and 327 DF, p-value: < 2.2e-16Explained variance has increased from 22% in the model9 to 23% in this one. the regeression coefficient is also statistically significant
model10 is slightly better
model11<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+intrgoal, data = final_reg)
summary(model11)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + intrgoal, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.292 -1.071 -0.271 0.892 4.528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.640345 1.109294 0.577 0.564166
## math_scores 0.004736 0.012688 0.373 0.709187
## social_studies_scores 0.035919 0.009326 3.851 0.000141 ***
## certificate_mathgrade 0.396550 0.173860 2.281 0.023201 *
## efficacy 0.608308 0.108501 5.606 4.4e-08 ***
## extrgoal -0.023423 0.111652 -0.210 0.833964
## intrgoal -0.165119 0.090675 -1.821 0.069522 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.526 on 326 degrees of freedom
## Multiple R-squared: 0.2444, Adjusted R-squared: 0.2305
## F-statistic: 17.57 on 6 and 326 DF, p-value: < 2.2e-16model10 is still better
model12<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+interest, data = final_reg)
summary(model12)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + interest, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5225 -1.0608 -0.2963 0.9458 4.6812
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.340385 1.110736 0.306 0.759458
## math_scores 0.008142 0.012723 0.640 0.522672
## social_studies_scores 0.036059 0.009360 3.852 0.000141 ***
## certificate_mathgrade 0.401539 0.174471 2.301 0.021996 *
## efficacy 0.680867 0.115330 5.904 8.92e-09 ***
## extrgoal -0.016523 0.126224 -0.131 0.895936
## interest -0.123148 0.127305 -0.967 0.334090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.531 on 326 degrees of freedom
## Multiple R-squared: 0.2389, Adjusted R-squared: 0.2249
## F-statistic: 17.05 on 6 and 326 DF, p-value: < 2.2e-16model10 is still better
model13<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety, data = final_reg)
summary(model13)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4252 -0.9645 -0.2163 0.9144 4.9940
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.295945 1.091991 0.271 0.786552
## math_scores 0.012630 0.012608 1.002 0.317222
## social_studies_scores 0.033013 0.009274 3.560 0.000426 ***
## certificate_mathgrade 0.391355 0.171999 2.275 0.023534 *
## efficacy 0.772614 0.113499 6.807 4.79e-11 ***
## extrgoal -0.130065 0.107125 -1.214 0.225572
## mathanxiety 0.285031 0.087912 3.242 0.001309 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.509 on 326 degrees of freedom
## Multiple R-squared: 0.2605, Adjusted R-squared: 0.2469
## F-statistic: 19.14 on 6 and 326 DF, p-value: < 2.2e-16Explained variance is 4% higher compared to the model10.
model13 is better
model14<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal++mathanxiety+testanxiety, data = final_reg)
summary(model14)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + +mathanxiety +
## testanxiety, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3230 -0.9762 -0.2111 0.8551 5.1005
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.398108 1.096381 0.363 0.716758
## math_scores 0.010416 0.012789 0.814 0.415972
## social_studies_scores 0.033362 0.009279 3.595 0.000374 ***
## certificate_mathgrade 0.400054 0.172189 2.323 0.020778 *
## efficacy 0.741682 0.117392 6.318 8.72e-10 ***
## extrgoal -0.099309 0.111196 -0.893 0.372462
## mathanxiety 0.340546 0.103102 3.303 0.001063 **
## testanxiety -0.115693 0.112284 -1.030 0.303609
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.509 on 325 degrees of freedom
## Multiple R-squared: 0.2629, Adjusted R-squared: 0.2471
## F-statistic: 16.56 on 7 and 325 DF, p-value: < 2.2e-16Adjusted R-squared decreased
model13 is better
model15<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety+stat_affect, data = final_reg)
summary(model15)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety +
## stat_affect, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4189 -1.0103 -0.2441 0.8805 5.0357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.313287 1.093651 0.286 0.77471
## math_scores 0.012434 0.012627 0.985 0.32551
## social_studies_scores 0.033025 0.009284 3.557 0.00043 ***
## certificate_mathgrade 0.390691 0.172190 2.269 0.02393 *
## efficacy 0.761349 0.115521 6.591 1.77e-10 ***
## extrgoal -0.140545 0.108982 -1.290 0.19810
## mathanxiety 0.283307 0.088066 3.217 0.00143 **
## stat_affect 0.049352 0.091372 0.540 0.58948
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.511 on 325 degrees of freedom
## Multiple R-squared: 0.2612, Adjusted R-squared: 0.2453
## F-statistic: 16.41 on 7 and 325 DF, p-value: < 2.2e-16model13 is still better
model16<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety+stat_value, data = final_reg)
summary(model16)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety +
## stat_value, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4336 -0.9734 -0.2284 0.9037 5.0410
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.308968 1.094246 0.282 0.777849
## math_scores 0.012721 0.012629 1.007 0.314530
## social_studies_scores 0.032659 0.009352 3.492 0.000545 ***
## certificate_mathgrade 0.393451 0.172359 2.283 0.023091 *
## efficacy 0.770446 0.113855 6.767 6.14e-11 ***
## extrgoal -0.136530 0.109141 -1.251 0.211851
## mathanxiety 0.288648 0.088750 3.252 0.001265 **
## stat_value -0.027851 0.086620 -0.322 0.748019
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.511 on 325 degrees of freedom
## Multiple R-squared: 0.2608, Adjusted R-squared: 0.2448
## F-statistic: 16.38 on 7 and 325 DF, p-value: < 2.2e-16model13 is better
model17<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety+stat_difficulty, data = final_reg)
summary(model17)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety +
## stat_difficulty, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6499 -1.0011 -0.1826 0.9071 4.6717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.208829 1.086083 0.192 0.847645
## math_scores 0.016691 0.012663 1.318 0.188402
## social_studies_scores 0.032005 0.009229 3.468 0.000595 ***
## certificate_mathgrade 0.360552 0.171513 2.102 0.036307 *
## efficacy 0.831262 0.115831 7.176 4.88e-12 ***
## extrgoal -0.166414 0.107714 -1.545 0.123329
## mathanxiety 0.224289 0.091519 2.451 0.014783 *
## stat_difficulty 0.208484 0.093399 2.232 0.026284 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.5 on 325 degrees of freedom
## Multiple R-squared: 0.2717, Adjusted R-squared: 0.256
## F-statistic: 17.32 on 7 and 325 DF, p-value: < 2.2e-16model17 is better
model18<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety+stat_difficulty+stat_cognitivecomp, data = final_reg)
summary(model18)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety +
## stat_difficulty + stat_cognitivecomp, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7183 -1.0149 -0.2204 0.9536 4.4886
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.04008 1.09686 0.037 0.970876
## math_scores 0.01939 0.01290 1.503 0.133851
## social_studies_scores 0.03128 0.00925 3.382 0.000808 ***
## certificate_mathgrade 0.36480 0.17151 2.127 0.034177 *
## efficacy 0.84795 0.11682 7.259 2.91e-12 ***
## extrgoal -0.16443 0.10770 -1.527 0.127802
## mathanxiety 0.20048 0.09409 2.131 0.033862 *
## stat_difficulty 0.14908 0.10823 1.377 0.169324
## stat_cognitivecomp 0.12785 0.11777 1.086 0.278467
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.5 on 324 degrees of freedom
## Multiple R-squared: 0.2743, Adjusted R-squared: 0.2564
## F-statistic: 15.31 on 8 and 324 DF, p-value: < 2.2e-16model 17 seem to be the best
## math_scores social_studies_scores certificate_mathgrade
## 1.310620 1.269651 1.207055
## efficacy extrgoal mathanxiety
## 2.006437 1.664783 1.332843
## stat_difficulty
## 1.307058Values are less than 5. Therefore, it can be concluded that we do not have multicollinearity.
Residuals VS Fitted (we can see that dots are not quite evenly dispersed around zero, whihch means that we face the problem of heteroscedasticity)
Normal Q-Q plot shows that our data is normally distributed
Also we do not have any leverages or influential cases, as Cook’s distance line is not present on the last plot
Checking for heteroscedasticity again:
##
## studentized Breusch-Pagan test
##
## data: model17
## BP = 14.02, df = 7, p-value = 0.05083## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 6.178397, Df = 1, p = 0.012932One of the tests is statistically significant the other is not. The first one proves the presence of heterscedasticity, the pther does not prove its presence
Fianal regression model
model17<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety+stat_difficulty, data = final_reg)
summary(model17)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety +
## stat_difficulty, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6499 -1.0011 -0.1826 0.9071 4.6717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.208829 1.086083 0.192 0.847645
## math_scores 0.016691 0.012663 1.318 0.188402
## social_studies_scores 0.032005 0.009229 3.468 0.000595 ***
## certificate_mathgrade 0.360552 0.171513 2.102 0.036307 *
## efficacy 0.831262 0.115831 7.176 4.88e-12 ***
## extrgoal -0.166414 0.107714 -1.545 0.123329
## mathanxiety 0.224289 0.091519 2.451 0.014783 *
## stat_difficulty 0.208484 0.093399 2.232 0.026284 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.5 on 325 degrees of freedom
## Multiple R-squared: 0.2717, Adjusted R-squared: 0.256
## F-statistic: 17.32 on 7 and 325 DF, p-value: < 2.2e-16final_reg$father_ISCO <- as.numeric(final_reg$father_ISCO)
model30<-lm(subject_mark ~ math_scores+social_studies_scores+certificate_mathgrade+efficacy+extrgoal+mathanxiety*gender+stat_difficulty+course, data = final_reg)
summary(model30)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## certificate_mathgrade + efficacy + extrgoal + mathanxiety *
## gender + stat_difficulty + course, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7306 -0.8969 -0.0515 0.9452 3.8814
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.190488 1.124316 -1.059 0.290460
## math_scores 0.026316 0.012353 2.130 0.033900 *
## social_studies_scores 0.038392 0.008971 4.280 2.47e-05 ***
## certificate_mathgrade 0.176024 0.178127 0.988 0.323800
## efficacy 0.701807 0.113213 6.199 1.74e-09 ***
## extrgoal -0.055931 0.106987 -0.523 0.601486
## mathanxiety 0.406921 0.113645 3.581 0.000396 ***
## gendermale -0.037852 0.188168 -0.201 0.840699
## stat_difficulty 0.090015 0.091736 0.981 0.327215
## course 0.559498 0.109557 5.107 5.62e-07 ***
## mathanxiety:gendermale -0.359673 0.157033 -2.290 0.022642 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.434 on 322 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.3199
## F-statistic: 16.61 on 10 and 322 DF, p-value: < 2.2e-16## Warning: package 'sjPlot' was built under R version 4.0.2## Registered S3 methods overwritten by 'lme4':
## method from
## cooks.distance.influence.merMod car
## influence.merMod car
## dfbeta.influence.merMod car
## dfbetas.influence.merMod car## Learn more about sjPlot with 'browseVignettes("sjPlot")'.
## math_scores social_studies_scores certificate_mathgrade
## 1.364261 1.312265 1.424159
## efficacy extrgoal mathanxiety
## 2.096695 1.796543 2.248111
## gender stat_difficulty course
## 1.325939 1.379304 1.192467
## mathanxiety:gender
## 1.944120Cheking H4: school grades for four core subjects are assumed to be positively correlated with USE scores since USE is supposed to cover main topics studied at school
library(polycor)
library(corrplot)
dat.cor <- hetcor(final_reg)
dat.cor<- dat.cor$correlations
dat.cor## math_scores social_studies_scores
## math_scores 1.00000000 0.327192422
## social_studies_scores 0.32719242 1.000000000
## russian_language_scores 0.23984168 0.394356726
## foreign_language_scores 0.35776048 0.512822092
## certificate_mathgrade 0.27227228 0.373012807
## certificate_social_studiesgrade 0.07155964 0.271478846
## certificate_russianlanggrade 0.12216889 0.306673614
## certificate_foreign_langgrade 0.02761848 0.264999465
## gpa 0.42578919 0.469967643
## subject_mark 0.23376424 0.308346718
## gender 0.06851771 -0.281730060
## father_ISCO 0.12076766 0.124883489
## mother_ISCO 0.02501915 0.051257475
## stat_affect 0.14089273 0.037435695
## stat_cognitivecomp -0.32968437 -0.015940253
## stat_difficulty -0.21515514 -0.001475602
## stat_value -0.10605834 -0.110049510
## efficacy 0.30324127 0.120022659
## extrgoal 0.22104347 -0.003693572
## intrgoal -0.09766743 -0.075450373
## testanxiety -0.25057675 -0.030548788
## mathanxiety -0.20185990 0.009554514
## interest 0.27471106 0.058476316
## course -0.17121426 -0.073175646
## russian_language_scores foreign_language_scores
## math_scores 0.2398416849 0.357760475
## social_studies_scores 0.3943567262 0.512822092
## russian_language_scores 1.0000000000 0.380804573
## foreign_language_scores 0.3808045734 1.000000000
## certificate_mathgrade 0.3474007961 0.379777902
## certificate_social_studiesgrade 0.1768063822 0.216928181
## certificate_russianlanggrade 0.3001720599 0.316025547
## certificate_foreign_langgrade 0.2851410394 0.305181109
## gpa 0.3683844021 0.468904187
## subject_mark 0.1834082120 0.184988308
## gender -0.3043190630 -0.165096545
## father_ISCO 0.1163169421 0.149751939
## mother_ISCO 0.0873357203 0.008453903
## stat_affect 0.0839230764 0.053409115
## stat_cognitivecomp -0.0116732417 -0.133089641
## stat_difficulty -0.0270903996 -0.112489113
## stat_value -0.0861946654 -0.112381313
## efficacy 0.0264562878 0.099657882
## extrgoal 0.0188051588 -0.057142789
## intrgoal 0.0001241272 -0.117438120
## testanxiety 0.0552634845 -0.091988386
## mathanxiety 0.0472796919 -0.052767832
## interest 0.0107073489 0.046834696
## course -0.0840393535 -0.014617822
## certificate_mathgrade
## math_scores 0.272272283
## social_studies_scores 0.373012807
## russian_language_scores 0.347400796
## foreign_language_scores 0.379777902
## certificate_mathgrade 1.000000000
## certificate_social_studiesgrade 0.525399537
## certificate_russianlanggrade 0.628299631
## certificate_foreign_langgrade 0.498284640
## gpa 0.442735729
## subject_mark 0.242680206
## gender -0.438517343
## father_ISCO 0.154887669
## mother_ISCO 0.005202136
## stat_affect 0.037917029
## stat_cognitivecomp -0.045608957
## stat_difficulty 0.023980111
## stat_value -0.014001819
## efficacy 0.095729787
## extrgoal 0.010094366
## intrgoal -0.064134628
## testanxiety -0.022944634
## mathanxiety -0.023254805
## interest 0.054564167
## course 0.153095698
## certificate_social_studiesgrade
## math_scores 0.071559641
## social_studies_scores 0.271478846
## russian_language_scores 0.176806382
## foreign_language_scores 0.216928181
## certificate_mathgrade 0.525399537
## certificate_social_studiesgrade 1.000000000
## certificate_russianlanggrade 0.488838172
## certificate_foreign_langgrade 0.467877902
## gpa 0.267007084
## subject_mark 0.074224882
## gender -0.332739691
## father_ISCO 0.101509834
## mother_ISCO 0.045637275
## stat_affect 0.032495187
## stat_cognitivecomp 0.001571909
## stat_difficulty 0.064889609
## stat_value -0.041065281
## efficacy 0.011240682
## extrgoal -0.018137106
## intrgoal 0.039594975
## testanxiety 0.063261876
## mathanxiety 0.032790097
## interest -0.056984503
## course 0.044305478
## certificate_russianlanggrade
## math_scores 0.12216889
## social_studies_scores 0.30667361
## russian_language_scores 0.30017206
## foreign_language_scores 0.31602555
## certificate_mathgrade 0.62829963
## certificate_social_studiesgrade 0.48883817
## certificate_russianlanggrade 1.00000000
## certificate_foreign_langgrade 0.52134613
## gpa 0.40422486
## subject_mark 0.17195549
## gender -0.43607037
## father_ISCO 0.15447927
## mother_ISCO 0.12458614
## stat_affect 0.06258597
## stat_cognitivecomp -0.01666650
## stat_difficulty 0.09180853
## stat_value -0.05732558
## efficacy -0.01138230
## extrgoal -0.04498487
## intrgoal 0.01406144
## testanxiety 0.08158489
## mathanxiety 0.07087570
## interest -0.06623677
## course 0.14806940
## certificate_foreign_langgrade gpa
## math_scores 0.027618482 0.42578919
## social_studies_scores 0.264999465 0.46996764
## russian_language_scores 0.285141039 0.36838440
## foreign_language_scores 0.305181109 0.46890419
## certificate_mathgrade 0.498284640 0.44273573
## certificate_social_studiesgrade 0.467877902 0.26700708
## certificate_russianlanggrade 0.521346126 0.40422486
## certificate_foreign_langgrade 1.000000000 0.28507351
## gpa 0.285073510 1.00000000
## subject_mark 0.108331373 0.61366468
## gender -0.430774161 -0.23738074
## father_ISCO 0.085878926 0.08180342
## mother_ISCO 0.013238875 0.06455866
## stat_affect -0.009050429 0.23639481
## stat_cognitivecomp 0.058506110 -0.17263675
## stat_difficulty 0.036706123 -0.08603657
## stat_value -0.034976368 -0.21375725
## efficacy 0.001648678 0.33855523
## extrgoal -0.100210369 0.11751354
## intrgoal 0.032475900 -0.04408093
## testanxiety 0.068240689 -0.07438839
## mathanxiety 0.116524802 -0.07841520
## interest -0.057168045 0.19211190
## course 0.120485972 0.05161812
## subject_mark gender father_ISCO
## math_scores 0.233764237 0.06851771 0.12076766
## social_studies_scores 0.308346718 -0.28173006 0.12488349
## russian_language_scores 0.183408212 -0.30431906 0.11631694
## foreign_language_scores 0.184988308 -0.16509654 0.14975194
## certificate_mathgrade 0.242680206 -0.43851734 0.15488767
## certificate_social_studiesgrade 0.074224882 -0.33273969 0.10150983
## certificate_russianlanggrade 0.171955486 -0.43607037 0.15447927
## certificate_foreign_langgrade 0.108331373 -0.43077416 0.08587893
## gpa 0.613664678 -0.23738074 0.08180342
## subject_mark 1.000000000 -0.13037432 -0.03953584
## gender -0.130374323 1.00000000 -0.09590236
## father_ISCO -0.039535845 -0.09590236 1.00000000
## mother_ISCO 0.048254456 0.02542340 0.09997725
## stat_affect 0.160946617 0.07553418 0.01931649
## stat_cognitivecomp -0.035464550 -0.18643381 -0.02319954
## stat_difficulty 0.014186818 -0.18327079 -0.03685497
## stat_value -0.109365270 -0.06879662 0.03228279
## efficacy 0.389094480 0.14351317 -0.02604902
## extrgoal 0.184238422 0.26527072 -0.07009105
## intrgoal -0.129005953 -0.12979057 -0.11069757
## testanxiety -0.109512208 -0.28348584 -0.10694320
## mathanxiety -0.001112895 -0.25134357 -0.04004357
## interest 0.203617424 0.18789659 -0.01666801
## course 0.251836503 -0.19031277 0.02656832
## mother_ISCO stat_affect stat_cognitivecomp
## math_scores 0.025019155 0.140892730 -0.329684372
## social_studies_scores 0.051257475 0.037435695 -0.015940253
## russian_language_scores 0.087335720 0.083923076 -0.011673242
## foreign_language_scores 0.008453903 0.053409115 -0.133089641
## certificate_mathgrade 0.005202136 0.037917029 -0.045608957
## certificate_social_studiesgrade 0.045637275 0.032495187 0.001571909
## certificate_russianlanggrade 0.124586142 0.062585973 -0.016666495
## certificate_foreign_langgrade 0.013238875 -0.009050429 0.058506110
## gpa 0.064558660 0.236394815 -0.172636749
## subject_mark 0.048254456 0.160946617 -0.035464550
## gender 0.025423404 0.075534176 -0.186433806
## father_ISCO 0.099977246 0.019316491 -0.023199541
## mother_ISCO 1.000000000 0.034265985 -0.110093409
## stat_affect 0.034265985 1.000000000 -0.378855835
## stat_cognitivecomp -0.110093409 -0.378855835 1.000000000
## stat_difficulty -0.029756007 -0.268428753 0.631088837
## stat_value -0.074694986 -0.651758207 0.313128877
## efficacy -0.102124331 0.355070912 -0.411798431
## extrgoal -0.093866430 0.352975290 -0.190601338
## intrgoal -0.110720249 0.071766081 0.209971001
## testanxiety -0.036959686 -0.063414836 0.455056380
## mathanxiety -0.047689285 -0.086447877 0.475444207
## interest -0.054391629 0.394764461 -0.199739678
## course 0.023851480 -0.034172936 0.041111951
## stat_difficulty stat_value efficacy
## math_scores -0.215155145 -0.10605834 0.303241268
## social_studies_scores -0.001475602 -0.11004951 0.120022659
## russian_language_scores -0.027090400 -0.08619467 0.026456288
## foreign_language_scores -0.112489113 -0.11238131 0.099657882
## certificate_mathgrade 0.023980111 -0.01400182 0.095729787
## certificate_social_studiesgrade 0.064889609 -0.04106528 0.011240682
## certificate_russianlanggrade 0.091808532 -0.05732558 -0.011382297
## certificate_foreign_langgrade 0.036706123 -0.03497637 0.001648678
## gpa -0.086036569 -0.21375725 0.338555233
## subject_mark 0.014186818 -0.10936527 0.389094480
## gender -0.183270785 -0.06879662 0.143513168
## father_ISCO -0.036854974 0.03228279 -0.026049016
## mother_ISCO -0.029756007 -0.07469499 -0.102124331
## stat_affect -0.268428753 -0.65175821 0.355070912
## stat_cognitivecomp 0.631088837 0.31312888 -0.411798431
## stat_difficulty 1.000000000 0.20997479 -0.322758773
## stat_value 0.209974787 1.00000000 -0.265824022
## efficacy -0.322758773 -0.26582402 1.000000000
## extrgoal -0.070325832 -0.28243474 0.600829413
## intrgoal 0.281992290 0.02817709 -0.025566348
## testanxiety 0.489843786 0.13048589 -0.342588799
## mathanxiety 0.411240563 0.18497722 -0.379012534
## interest -0.154394875 -0.36688530 0.644978388
## course 0.191141331 0.12853089 0.002406911
## extrgoal intrgoal testanxiety
## math_scores 0.221043474 -0.0976674290 -0.250576749
## social_studies_scores -0.003693572 -0.0754503730 -0.030548788
## russian_language_scores 0.018805159 0.0001241272 0.055263485
## foreign_language_scores -0.057142789 -0.1174381197 -0.091988386
## certificate_mathgrade 0.010094366 -0.0641346281 -0.022944634
## certificate_social_studiesgrade -0.018137106 0.0395949745 0.063261876
## certificate_russianlanggrade -0.044984868 0.0140614440 0.081584886
## certificate_foreign_langgrade -0.100210369 0.0324758997 0.068240689
## gpa 0.117513535 -0.0440809344 -0.074388393
## subject_mark 0.184238422 -0.1290059529 -0.109512208
## gender 0.265270723 -0.1297905714 -0.283485840
## father_ISCO -0.070091050 -0.1106975713 -0.106943204
## mother_ISCO -0.093866430 -0.1107202486 -0.036959686
## stat_affect 0.352975290 0.0717660812 -0.063414836
## stat_cognitivecomp -0.190601338 0.2099710010 0.455056380
## stat_difficulty -0.070325832 0.2819922903 0.489843786
## stat_value -0.282434736 0.0281770917 0.130485888
## efficacy 0.600829413 -0.0255663479 -0.342588799
## extrgoal 1.000000000 0.2066146701 0.001397036
## intrgoal 0.206614670 1.0000000000 0.547747406
## testanxiety 0.001397036 0.5477474060 1.000000000
## mathanxiety -0.136183499 0.3651534709 0.603877188
## interest 0.710018920 0.1339214778 -0.064338242
## course -0.145016300 -0.2543210132 -0.063924831
## mathanxiety interest course
## math_scores -0.201859899 0.27471106 -0.171214255
## social_studies_scores 0.009554514 0.05847632 -0.073175646
## russian_language_scores 0.047279692 0.01070735 -0.084039354
## foreign_language_scores -0.052767832 0.04683470 -0.014617822
## certificate_mathgrade -0.023254805 0.05456417 0.153095698
## certificate_social_studiesgrade 0.032790097 -0.05698450 0.044305478
## certificate_russianlanggrade 0.070875698 -0.06623677 0.148069404
## certificate_foreign_langgrade 0.116524802 -0.05716804 0.120485972
## gpa -0.078415204 0.19211190 0.051618119
## subject_mark -0.001112895 0.20361742 0.251836503
## gender -0.251343566 0.18789659 -0.190312767
## father_ISCO -0.040043574 -0.01666801 0.026568322
## mother_ISCO -0.047689285 -0.05439163 0.023851480
## stat_affect -0.086447877 0.39476446 -0.034172936
## stat_cognitivecomp 0.475444207 -0.19973968 0.041111951
## stat_difficulty 0.411240563 -0.15439487 0.191141331
## stat_value 0.184977219 -0.36688530 0.128530892
## efficacy -0.379012534 0.64497839 0.002406911
## extrgoal -0.136183499 0.71001892 -0.145016300
## intrgoal 0.365153471 0.13392148 -0.254321013
## testanxiety 0.603877188 -0.06433824 -0.063924831
## mathanxiety 1.000000000 -0.24948765 0.012440510
## interest -0.249487653 1.00000000 -0.147356099
## course 0.012440510 -0.14735610 1.000000000
Correlation coefficients
Math USE scores and math school grade: ~ 0.27
Social sciences USE scores and Social sciences school grade: ~ 0.26
Russian language USE scores and Russian language school grade: ~ 0.30
Foreign language USE scores and Foreign language school grade: ~ 0.31
##
## Call:
## lm(formula = math_scores ~ certificate_mathgrade, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.243 -5.085 -1.085 2.915 24.757
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 59.8720 3.5032 17.091 < 2e-16 ***
## certificate_mathgrade 3.8426 0.7464 5.148 4.52e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.172 on 331 degrees of freedom
## Multiple R-squared: 0.07413, Adjusted R-squared: 0.07134
## F-statistic: 26.5 on 1 and 331 DF, p-value: 4.524e-07model22<-lm(social_studies_scores~certificate_social_studiesgrade, data = final_reg)
summary(model22)##
## Call:
## lm(formula = social_studies_scores ~ certificate_social_studiesgrade,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.564 -5.564 1.435 7.436 21.250
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51.493 6.446 7.989 2.28e-14 ***
## certificate_social_studiesgrade 6.814 1.328 5.132 4.90e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.689 on 331 degrees of freedom
## Multiple R-squared: 0.0737, Adjusted R-squared: 0.0709
## F-statistic: 26.34 on 1 and 331 DF, p-value: 4.9e-07model23<-lm(russian_language_scores~certificate_russianlanggrade, data = final_reg)
summary(model23)##
## Call:
## lm(formula = russian_language_scores ~ certificate_russianlanggrade,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.406 -4.406 2.594 4.594 13.819
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 65.2790 4.3066 15.158 < 2e-16 ***
## certificate_russianlanggrade 5.2254 0.9127 5.725 2.32e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.52 on 331 degrees of freedom
## Multiple R-squared: 0.0901, Adjusted R-squared: 0.08735
## F-statistic: 32.78 on 1 and 331 DF, p-value: 2.319e-08model24<-lm(foreign_language_scores~certificate_foreign_langgrade, data = final_reg)
summary(model24)##
## Call:
## lm(formula = foreign_language_scores ~ certificate_foreign_langgrade,
## data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30.626 -4.626 2.374 5.374 20.105
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.973 5.589 9.477 < 2e-16 ***
## certificate_foreign_langgrade 6.731 1.154 5.830 1.31e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.316 on 331 degrees of freedom
## Multiple R-squared: 0.09314, Adjusted R-squared: 0.0904
## F-statistic: 33.99 on 1 and 331 DF, p-value: 1.314e-08Cheking H5: performance goal orientation will positively predict anxiety while self-efficacy beliefs will have negative correlation with it.
Correlation
library(polycor)
library(corrplot)
dat.cor <- hetcor(final_reg)
dat.cor<- dat.cor$correlations
dat.cor## math_scores social_studies_scores
## math_scores 1.00000000 0.327192422
## social_studies_scores 0.32719242 1.000000000
## russian_language_scores 0.23984168 0.394356726
## foreign_language_scores 0.35776048 0.512822092
## certificate_mathgrade 0.27227228 0.373012807
## certificate_social_studiesgrade 0.07155964 0.271478846
## certificate_russianlanggrade 0.12216889 0.306673614
## certificate_foreign_langgrade 0.02761848 0.264999465
## gpa 0.42578919 0.469967643
## subject_mark 0.23376424 0.308346718
## gender 0.06851771 -0.281730060
## father_ISCO 0.12076766 0.124883489
## mother_ISCO 0.02501915 0.051257475
## stat_affect 0.14089273 0.037435695
## stat_cognitivecomp -0.32968437 -0.015940253
## stat_difficulty -0.21515514 -0.001475602
## stat_value -0.10605834 -0.110049510
## efficacy 0.30324127 0.120022659
## extrgoal 0.22104347 -0.003693572
## intrgoal -0.09766743 -0.075450373
## testanxiety -0.25057675 -0.030548788
## mathanxiety -0.20185990 0.009554514
## interest 0.27471106 0.058476316
## course -0.17121426 -0.073175646
## russian_language_scores foreign_language_scores
## math_scores 0.2398416849 0.357760475
## social_studies_scores 0.3943567262 0.512822092
## russian_language_scores 1.0000000000 0.380804573
## foreign_language_scores 0.3808045734 1.000000000
## certificate_mathgrade 0.3474007961 0.379777902
## certificate_social_studiesgrade 0.1768063822 0.216928181
## certificate_russianlanggrade 0.3001720599 0.316025547
## certificate_foreign_langgrade 0.2851410394 0.305181109
## gpa 0.3683844021 0.468904187
## subject_mark 0.1834082120 0.184988308
## gender -0.3043190630 -0.165096545
## father_ISCO 0.1163169421 0.149751939
## mother_ISCO 0.0873357203 0.008453903
## stat_affect 0.0839230764 0.053409115
## stat_cognitivecomp -0.0116732417 -0.133089641
## stat_difficulty -0.0270903996 -0.112489113
## stat_value -0.0861946654 -0.112381313
## efficacy 0.0264562878 0.099657882
## extrgoal 0.0188051588 -0.057142789
## intrgoal 0.0001241272 -0.117438120
## testanxiety 0.0552634845 -0.091988386
## mathanxiety 0.0472796919 -0.052767832
## interest 0.0107073489 0.046834696
## course -0.0840393535 -0.014617822
## certificate_mathgrade
## math_scores 0.272272283
## social_studies_scores 0.373012807
## russian_language_scores 0.347400796
## foreign_language_scores 0.379777902
## certificate_mathgrade 1.000000000
## certificate_social_studiesgrade 0.525399537
## certificate_russianlanggrade 0.628299631
## certificate_foreign_langgrade 0.498284640
## gpa 0.442735729
## subject_mark 0.242680206
## gender -0.438517343
## father_ISCO 0.154887669
## mother_ISCO 0.005202136
## stat_affect 0.037917029
## stat_cognitivecomp -0.045608957
## stat_difficulty 0.023980111
## stat_value -0.014001819
## efficacy 0.095729787
## extrgoal 0.010094366
## intrgoal -0.064134628
## testanxiety -0.022944634
## mathanxiety -0.023254805
## interest 0.054564167
## course 0.153095698
## certificate_social_studiesgrade
## math_scores 0.071559641
## social_studies_scores 0.271478846
## russian_language_scores 0.176806382
## foreign_language_scores 0.216928181
## certificate_mathgrade 0.525399537
## certificate_social_studiesgrade 1.000000000
## certificate_russianlanggrade 0.488838172
## certificate_foreign_langgrade 0.467877902
## gpa 0.267007084
## subject_mark 0.074224882
## gender -0.332739691
## father_ISCO 0.101509834
## mother_ISCO 0.045637275
## stat_affect 0.032495187
## stat_cognitivecomp 0.001571909
## stat_difficulty 0.064889609
## stat_value -0.041065281
## efficacy 0.011240682
## extrgoal -0.018137106
## intrgoal 0.039594975
## testanxiety 0.063261876
## mathanxiety 0.032790097
## interest -0.056984503
## course 0.044305478
## certificate_russianlanggrade
## math_scores 0.12216889
## social_studies_scores 0.30667361
## russian_language_scores 0.30017206
## foreign_language_scores 0.31602555
## certificate_mathgrade 0.62829963
## certificate_social_studiesgrade 0.48883817
## certificate_russianlanggrade 1.00000000
## certificate_foreign_langgrade 0.52134613
## gpa 0.40422486
## subject_mark 0.17195549
## gender -0.43607037
## father_ISCO 0.15447927
## mother_ISCO 0.12458614
## stat_affect 0.06258597
## stat_cognitivecomp -0.01666650
## stat_difficulty 0.09180853
## stat_value -0.05732558
## efficacy -0.01138230
## extrgoal -0.04498487
## intrgoal 0.01406144
## testanxiety 0.08158489
## mathanxiety 0.07087570
## interest -0.06623677
## course 0.14806940
## certificate_foreign_langgrade gpa
## math_scores 0.027618482 0.42578919
## social_studies_scores 0.264999465 0.46996764
## russian_language_scores 0.285141039 0.36838440
## foreign_language_scores 0.305181109 0.46890419
## certificate_mathgrade 0.498284640 0.44273573
## certificate_social_studiesgrade 0.467877902 0.26700708
## certificate_russianlanggrade 0.521346126 0.40422486
## certificate_foreign_langgrade 1.000000000 0.28507351
## gpa 0.285073510 1.00000000
## subject_mark 0.108331373 0.61366468
## gender -0.430774161 -0.23738074
## father_ISCO 0.085878926 0.08180342
## mother_ISCO 0.013238875 0.06455866
## stat_affect -0.009050429 0.23639481
## stat_cognitivecomp 0.058506110 -0.17263675
## stat_difficulty 0.036706123 -0.08603657
## stat_value -0.034976368 -0.21375725
## efficacy 0.001648678 0.33855523
## extrgoal -0.100210369 0.11751354
## intrgoal 0.032475900 -0.04408093
## testanxiety 0.068240689 -0.07438839
## mathanxiety 0.116524802 -0.07841520
## interest -0.057168045 0.19211190
## course 0.120485972 0.05161812
## subject_mark gender father_ISCO
## math_scores 0.233764237 0.06851771 0.12076766
## social_studies_scores 0.308346718 -0.28173006 0.12488349
## russian_language_scores 0.183408212 -0.30431906 0.11631694
## foreign_language_scores 0.184988308 -0.16509654 0.14975194
## certificate_mathgrade 0.242680206 -0.43851734 0.15488767
## certificate_social_studiesgrade 0.074224882 -0.33273969 0.10150983
## certificate_russianlanggrade 0.171955486 -0.43607037 0.15447927
## certificate_foreign_langgrade 0.108331373 -0.43077416 0.08587893
## gpa 0.613664678 -0.23738074 0.08180342
## subject_mark 1.000000000 -0.13037432 -0.03953584
## gender -0.130374323 1.00000000 -0.09590236
## father_ISCO -0.039535845 -0.09590236 1.00000000
## mother_ISCO 0.048254456 0.02542340 0.09997725
## stat_affect 0.160946617 0.07553418 0.01931649
## stat_cognitivecomp -0.035464550 -0.18643381 -0.02319954
## stat_difficulty 0.014186818 -0.18327079 -0.03685497
## stat_value -0.109365270 -0.06879662 0.03228279
## efficacy 0.389094480 0.14351317 -0.02604902
## extrgoal 0.184238422 0.26527072 -0.07009105
## intrgoal -0.129005953 -0.12979057 -0.11069757
## testanxiety -0.109512208 -0.28348584 -0.10694320
## mathanxiety -0.001112895 -0.25134357 -0.04004357
## interest 0.203617424 0.18789659 -0.01666801
## course 0.251836503 -0.19031277 0.02656832
## mother_ISCO stat_affect stat_cognitivecomp
## math_scores 0.025019155 0.140892730 -0.329684372
## social_studies_scores 0.051257475 0.037435695 -0.015940253
## russian_language_scores 0.087335720 0.083923076 -0.011673242
## foreign_language_scores 0.008453903 0.053409115 -0.133089641
## certificate_mathgrade 0.005202136 0.037917029 -0.045608957
## certificate_social_studiesgrade 0.045637275 0.032495187 0.001571909
## certificate_russianlanggrade 0.124586142 0.062585973 -0.016666495
## certificate_foreign_langgrade 0.013238875 -0.009050429 0.058506110
## gpa 0.064558660 0.236394815 -0.172636749
## subject_mark 0.048254456 0.160946617 -0.035464550
## gender 0.025423404 0.075534176 -0.186433806
## father_ISCO 0.099977246 0.019316491 -0.023199541
## mother_ISCO 1.000000000 0.034265985 -0.110093409
## stat_affect 0.034265985 1.000000000 -0.378855835
## stat_cognitivecomp -0.110093409 -0.378855835 1.000000000
## stat_difficulty -0.029756007 -0.268428753 0.631088837
## stat_value -0.074694986 -0.651758207 0.313128877
## efficacy -0.102124331 0.355070912 -0.411798431
## extrgoal -0.093866430 0.352975290 -0.190601338
## intrgoal -0.110720249 0.071766081 0.209971001
## testanxiety -0.036959686 -0.063414836 0.455056380
## mathanxiety -0.047689285 -0.086447877 0.475444207
## interest -0.054391629 0.394764461 -0.199739678
## course 0.023851480 -0.034172936 0.041111951
## stat_difficulty stat_value efficacy
## math_scores -0.215155145 -0.10605834 0.303241268
## social_studies_scores -0.001475602 -0.11004951 0.120022659
## russian_language_scores -0.027090400 -0.08619467 0.026456288
## foreign_language_scores -0.112489113 -0.11238131 0.099657882
## certificate_mathgrade 0.023980111 -0.01400182 0.095729787
## certificate_social_studiesgrade 0.064889609 -0.04106528 0.011240682
## certificate_russianlanggrade 0.091808532 -0.05732558 -0.011382297
## certificate_foreign_langgrade 0.036706123 -0.03497637 0.001648678
## gpa -0.086036569 -0.21375725 0.338555233
## subject_mark 0.014186818 -0.10936527 0.389094480
## gender -0.183270785 -0.06879662 0.143513168
## father_ISCO -0.036854974 0.03228279 -0.026049016
## mother_ISCO -0.029756007 -0.07469499 -0.102124331
## stat_affect -0.268428753 -0.65175821 0.355070912
## stat_cognitivecomp 0.631088837 0.31312888 -0.411798431
## stat_difficulty 1.000000000 0.20997479 -0.322758773
## stat_value 0.209974787 1.00000000 -0.265824022
## efficacy -0.322758773 -0.26582402 1.000000000
## extrgoal -0.070325832 -0.28243474 0.600829413
## intrgoal 0.281992290 0.02817709 -0.025566348
## testanxiety 0.489843786 0.13048589 -0.342588799
## mathanxiety 0.411240563 0.18497722 -0.379012534
## interest -0.154394875 -0.36688530 0.644978388
## course 0.191141331 0.12853089 0.002406911
## extrgoal intrgoal testanxiety
## math_scores 0.221043474 -0.0976674290 -0.250576749
## social_studies_scores -0.003693572 -0.0754503730 -0.030548788
## russian_language_scores 0.018805159 0.0001241272 0.055263485
## foreign_language_scores -0.057142789 -0.1174381197 -0.091988386
## certificate_mathgrade 0.010094366 -0.0641346281 -0.022944634
## certificate_social_studiesgrade -0.018137106 0.0395949745 0.063261876
## certificate_russianlanggrade -0.044984868 0.0140614440 0.081584886
## certificate_foreign_langgrade -0.100210369 0.0324758997 0.068240689
## gpa 0.117513535 -0.0440809344 -0.074388393
## subject_mark 0.184238422 -0.1290059529 -0.109512208
## gender 0.265270723 -0.1297905714 -0.283485840
## father_ISCO -0.070091050 -0.1106975713 -0.106943204
## mother_ISCO -0.093866430 -0.1107202486 -0.036959686
## stat_affect 0.352975290 0.0717660812 -0.063414836
## stat_cognitivecomp -0.190601338 0.2099710010 0.455056380
## stat_difficulty -0.070325832 0.2819922903 0.489843786
## stat_value -0.282434736 0.0281770917 0.130485888
## efficacy 0.600829413 -0.0255663479 -0.342588799
## extrgoal 1.000000000 0.2066146701 0.001397036
## intrgoal 0.206614670 1.0000000000 0.547747406
## testanxiety 0.001397036 0.5477474060 1.000000000
## mathanxiety -0.136183499 0.3651534709 0.603877188
## interest 0.710018920 0.1339214778 -0.064338242
## course -0.145016300 -0.2543210132 -0.063924831
## mathanxiety interest course
## math_scores -0.201859899 0.27471106 -0.171214255
## social_studies_scores 0.009554514 0.05847632 -0.073175646
## russian_language_scores 0.047279692 0.01070735 -0.084039354
## foreign_language_scores -0.052767832 0.04683470 -0.014617822
## certificate_mathgrade -0.023254805 0.05456417 0.153095698
## certificate_social_studiesgrade 0.032790097 -0.05698450 0.044305478
## certificate_russianlanggrade 0.070875698 -0.06623677 0.148069404
## certificate_foreign_langgrade 0.116524802 -0.05716804 0.120485972
## gpa -0.078415204 0.19211190 0.051618119
## subject_mark -0.001112895 0.20361742 0.251836503
## gender -0.251343566 0.18789659 -0.190312767
## father_ISCO -0.040043574 -0.01666801 0.026568322
## mother_ISCO -0.047689285 -0.05439163 0.023851480
## stat_affect -0.086447877 0.39476446 -0.034172936
## stat_cognitivecomp 0.475444207 -0.19973968 0.041111951
## stat_difficulty 0.411240563 -0.15439487 0.191141331
## stat_value 0.184977219 -0.36688530 0.128530892
## efficacy -0.379012534 0.64497839 0.002406911
## extrgoal -0.136183499 0.71001892 -0.145016300
## intrgoal 0.365153471 0.13392148 -0.254321013
## testanxiety 0.603877188 -0.06433824 -0.063924831
## mathanxiety 1.000000000 -0.24948765 0.012440510
## interest -0.249487653 1.00000000 -0.147356099
## course 0.012440510 -0.14735610 1.000000000
Correlation coefficients
Test anxiety and extrinsic goal orientation: 0.545
Test anxiety and self-efficacy: -0.34
Math anxiety and extrinsic goal orientation: 0.36
Math anxiety and self-efficacy: -0.37
Hypothesis is supported
Regression with outcome: test anxiety
##
## Call:
## lm(formula = testanxiety ~ extrgoal + efficacy, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0411 -0.5743 0.1295 0.7039 1.7785
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.497e-17 4.872e-02 0.000 1
## extrgoal 3.228e-01 6.190e-02 5.215 3.25e-07 ***
## efficacy -5.240e-01 6.063e-02 -8.643 2.41e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8891 on 330 degrees of freedom
## Multiple R-squared: 0.1846, Adjusted R-squared: 0.1796
## F-statistic: 37.35 on 2 and 330 DF, p-value: 2.39e-15The hypothesis seem to be supported by the regression model since the coefficients are statistically significant and indicate that:
extrgoal: students whose main goal is to get better grades (high performance goal orientation) have higher test anxiety
efficacy: students who are confident in their ability to perform a task have lower test anxiety
Regression with outcome: math anxiety
##
## Call:
## lm(formula = mathanxiety ~ extrgoal + efficacy, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8968 -0.6750 -0.1177 0.5578 2.8162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.543e-16 5.242e-02 0.000 1.0000
## extrgoal 1.509e-01 6.659e-02 2.265 0.0241 *
## efficacy -4.798e-01 6.523e-02 -7.355 1.53e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9565 on 330 degrees of freedom
## Multiple R-squared: 0.1568, Adjusted R-squared: 0.1517
## F-statistic: 30.67 on 2 and 330 DF, p-value: 6.049e-13The proportion of the explained variance in this case is almost twice lower, but the trend is the same as with test anxiety
Cheking H6: interest will predict adoption of learning goal orientation which in turn will end up in the increased self-efficacy beliefs
## math_scores social_studies_scores
## math_scores 1.00000000 0.327192422
## social_studies_scores 0.32719242 1.000000000
## russian_language_scores 0.23984168 0.394356726
## foreign_language_scores 0.35776048 0.512822092
## certificate_mathgrade 0.27227228 0.373012807
## certificate_social_studiesgrade 0.07155964 0.271478846
## certificate_russianlanggrade 0.12216889 0.306673614
## certificate_foreign_langgrade 0.02761848 0.264999465
## gpa 0.42578919 0.469967643
## subject_mark 0.23376424 0.308346718
## gender 0.06851771 -0.281730060
## father_ISCO 0.12076766 0.124883489
## mother_ISCO 0.02501915 0.051257475
## stat_affect 0.14089273 0.037435695
## stat_cognitivecomp -0.32968437 -0.015940253
## stat_difficulty -0.21515514 -0.001475602
## stat_value -0.10605834 -0.110049510
## efficacy 0.30324127 0.120022659
## extrgoal 0.22104347 -0.003693572
## intrgoal -0.09766743 -0.075450373
## testanxiety -0.25057675 -0.030548788
## mathanxiety -0.20185990 0.009554514
## interest 0.27471106 0.058476316
## course -0.17121426 -0.073175646
## russian_language_scores foreign_language_scores
## math_scores 0.2398416849 0.357760475
## social_studies_scores 0.3943567262 0.512822092
## russian_language_scores 1.0000000000 0.380804573
## foreign_language_scores 0.3808045734 1.000000000
## certificate_mathgrade 0.3474007961 0.379777902
## certificate_social_studiesgrade 0.1768063822 0.216928181
## certificate_russianlanggrade 0.3001720599 0.316025547
## certificate_foreign_langgrade 0.2851410394 0.305181109
## gpa 0.3683844021 0.468904187
## subject_mark 0.1834082120 0.184988308
## gender -0.3043190630 -0.165096545
## father_ISCO 0.1163169421 0.149751939
## mother_ISCO 0.0873357203 0.008453903
## stat_affect 0.0839230764 0.053409115
## stat_cognitivecomp -0.0116732417 -0.133089641
## stat_difficulty -0.0270903996 -0.112489113
## stat_value -0.0861946654 -0.112381313
## efficacy 0.0264562878 0.099657882
## extrgoal 0.0188051588 -0.057142789
## intrgoal 0.0001241272 -0.117438120
## testanxiety 0.0552634845 -0.091988386
## mathanxiety 0.0472796919 -0.052767832
## interest 0.0107073489 0.046834696
## course -0.0840393535 -0.014617822
## certificate_mathgrade
## math_scores 0.272272283
## social_studies_scores 0.373012807
## russian_language_scores 0.347400796
## foreign_language_scores 0.379777902
## certificate_mathgrade 1.000000000
## certificate_social_studiesgrade 0.525399537
## certificate_russianlanggrade 0.628299631
## certificate_foreign_langgrade 0.498284640
## gpa 0.442735729
## subject_mark 0.242680206
## gender -0.438517343
## father_ISCO 0.154887669
## mother_ISCO 0.005202136
## stat_affect 0.037917029
## stat_cognitivecomp -0.045608957
## stat_difficulty 0.023980111
## stat_value -0.014001819
## efficacy 0.095729787
## extrgoal 0.010094366
## intrgoal -0.064134628
## testanxiety -0.022944634
## mathanxiety -0.023254805
## interest 0.054564167
## course 0.153095698
## certificate_social_studiesgrade
## math_scores 0.071559641
## social_studies_scores 0.271478846
## russian_language_scores 0.176806382
## foreign_language_scores 0.216928181
## certificate_mathgrade 0.525399537
## certificate_social_studiesgrade 1.000000000
## certificate_russianlanggrade 0.488838172
## certificate_foreign_langgrade 0.467877902
## gpa 0.267007084
## subject_mark 0.074224882
## gender -0.332739691
## father_ISCO 0.101509834
## mother_ISCO 0.045637275
## stat_affect 0.032495187
## stat_cognitivecomp 0.001571909
## stat_difficulty 0.064889609
## stat_value -0.041065281
## efficacy 0.011240682
## extrgoal -0.018137106
## intrgoal 0.039594975
## testanxiety 0.063261876
## mathanxiety 0.032790097
## interest -0.056984503
## course 0.044305478
## certificate_russianlanggrade
## math_scores 0.12216889
## social_studies_scores 0.30667361
## russian_language_scores 0.30017206
## foreign_language_scores 0.31602555
## certificate_mathgrade 0.62829963
## certificate_social_studiesgrade 0.48883817
## certificate_russianlanggrade 1.00000000
## certificate_foreign_langgrade 0.52134613
## gpa 0.40422486
## subject_mark 0.17195549
## gender -0.43607037
## father_ISCO 0.15447927
## mother_ISCO 0.12458614
## stat_affect 0.06258597
## stat_cognitivecomp -0.01666650
## stat_difficulty 0.09180853
## stat_value -0.05732558
## efficacy -0.01138230
## extrgoal -0.04498487
## intrgoal 0.01406144
## testanxiety 0.08158489
## mathanxiety 0.07087570
## interest -0.06623677
## course 0.14806940
## certificate_foreign_langgrade gpa
## math_scores 0.027618482 0.42578919
## social_studies_scores 0.264999465 0.46996764
## russian_language_scores 0.285141039 0.36838440
## foreign_language_scores 0.305181109 0.46890419
## certificate_mathgrade 0.498284640 0.44273573
## certificate_social_studiesgrade 0.467877902 0.26700708
## certificate_russianlanggrade 0.521346126 0.40422486
## certificate_foreign_langgrade 1.000000000 0.28507351
## gpa 0.285073510 1.00000000
## subject_mark 0.108331373 0.61366468
## gender -0.430774161 -0.23738074
## father_ISCO 0.085878926 0.08180342
## mother_ISCO 0.013238875 0.06455866
## stat_affect -0.009050429 0.23639481
## stat_cognitivecomp 0.058506110 -0.17263675
## stat_difficulty 0.036706123 -0.08603657
## stat_value -0.034976368 -0.21375725
## efficacy 0.001648678 0.33855523
## extrgoal -0.100210369 0.11751354
## intrgoal 0.032475900 -0.04408093
## testanxiety 0.068240689 -0.07438839
## mathanxiety 0.116524802 -0.07841520
## interest -0.057168045 0.19211190
## course 0.120485972 0.05161812
## subject_mark gender father_ISCO
## math_scores 0.233764237 0.06851771 0.12076766
## social_studies_scores 0.308346718 -0.28173006 0.12488349
## russian_language_scores 0.183408212 -0.30431906 0.11631694
## foreign_language_scores 0.184988308 -0.16509654 0.14975194
## certificate_mathgrade 0.242680206 -0.43851734 0.15488767
## certificate_social_studiesgrade 0.074224882 -0.33273969 0.10150983
## certificate_russianlanggrade 0.171955486 -0.43607037 0.15447927
## certificate_foreign_langgrade 0.108331373 -0.43077416 0.08587893
## gpa 0.613664678 -0.23738074 0.08180342
## subject_mark 1.000000000 -0.13037432 -0.03953584
## gender -0.130374323 1.00000000 -0.09590236
## father_ISCO -0.039535845 -0.09590236 1.00000000
## mother_ISCO 0.048254456 0.02542340 0.09997725
## stat_affect 0.160946617 0.07553418 0.01931649
## stat_cognitivecomp -0.035464550 -0.18643381 -0.02319954
## stat_difficulty 0.014186818 -0.18327079 -0.03685497
## stat_value -0.109365270 -0.06879662 0.03228279
## efficacy 0.389094480 0.14351317 -0.02604902
## extrgoal 0.184238422 0.26527072 -0.07009105
## intrgoal -0.129005953 -0.12979057 -0.11069757
## testanxiety -0.109512208 -0.28348584 -0.10694320
## mathanxiety -0.001112895 -0.25134357 -0.04004357
## interest 0.203617424 0.18789659 -0.01666801
## course 0.251836503 -0.19031277 0.02656832
## mother_ISCO stat_affect stat_cognitivecomp
## math_scores 0.025019155 0.140892730 -0.329684372
## social_studies_scores 0.051257475 0.037435695 -0.015940253
## russian_language_scores 0.087335720 0.083923076 -0.011673242
## foreign_language_scores 0.008453903 0.053409115 -0.133089641
## certificate_mathgrade 0.005202136 0.037917029 -0.045608957
## certificate_social_studiesgrade 0.045637275 0.032495187 0.001571909
## certificate_russianlanggrade 0.124586142 0.062585973 -0.016666495
## certificate_foreign_langgrade 0.013238875 -0.009050429 0.058506110
## gpa 0.064558660 0.236394815 -0.172636749
## subject_mark 0.048254456 0.160946617 -0.035464550
## gender 0.025423404 0.075534176 -0.186433806
## father_ISCO 0.099977246 0.019316491 -0.023199541
## mother_ISCO 1.000000000 0.034265985 -0.110093409
## stat_affect 0.034265985 1.000000000 -0.378855835
## stat_cognitivecomp -0.110093409 -0.378855835 1.000000000
## stat_difficulty -0.029756007 -0.268428753 0.631088837
## stat_value -0.074694986 -0.651758207 0.313128877
## efficacy -0.102124331 0.355070912 -0.411798431
## extrgoal -0.093866430 0.352975290 -0.190601338
## intrgoal -0.110720249 0.071766081 0.209971001
## testanxiety -0.036959686 -0.063414836 0.455056380
## mathanxiety -0.047689285 -0.086447877 0.475444207
## interest -0.054391629 0.394764461 -0.199739678
## course 0.023851480 -0.034172936 0.041111951
## stat_difficulty stat_value efficacy
## math_scores -0.215155145 -0.10605834 0.303241268
## social_studies_scores -0.001475602 -0.11004951 0.120022659
## russian_language_scores -0.027090400 -0.08619467 0.026456288
## foreign_language_scores -0.112489113 -0.11238131 0.099657882
## certificate_mathgrade 0.023980111 -0.01400182 0.095729787
## certificate_social_studiesgrade 0.064889609 -0.04106528 0.011240682
## certificate_russianlanggrade 0.091808532 -0.05732558 -0.011382297
## certificate_foreign_langgrade 0.036706123 -0.03497637 0.001648678
## gpa -0.086036569 -0.21375725 0.338555233
## subject_mark 0.014186818 -0.10936527 0.389094480
## gender -0.183270785 -0.06879662 0.143513168
## father_ISCO -0.036854974 0.03228279 -0.026049016
## mother_ISCO -0.029756007 -0.07469499 -0.102124331
## stat_affect -0.268428753 -0.65175821 0.355070912
## stat_cognitivecomp 0.631088837 0.31312888 -0.411798431
## stat_difficulty 1.000000000 0.20997479 -0.322758773
## stat_value 0.209974787 1.00000000 -0.265824022
## efficacy -0.322758773 -0.26582402 1.000000000
## extrgoal -0.070325832 -0.28243474 0.600829413
## intrgoal 0.281992290 0.02817709 -0.025566348
## testanxiety 0.489843786 0.13048589 -0.342588799
## mathanxiety 0.411240563 0.18497722 -0.379012534
## interest -0.154394875 -0.36688530 0.644978388
## course 0.191141331 0.12853089 0.002406911
## extrgoal intrgoal testanxiety
## math_scores 0.221043474 -0.0976674290 -0.250576749
## social_studies_scores -0.003693572 -0.0754503730 -0.030548788
## russian_language_scores 0.018805159 0.0001241272 0.055263485
## foreign_language_scores -0.057142789 -0.1174381197 -0.091988386
## certificate_mathgrade 0.010094366 -0.0641346281 -0.022944634
## certificate_social_studiesgrade -0.018137106 0.0395949745 0.063261876
## certificate_russianlanggrade -0.044984868 0.0140614440 0.081584886
## certificate_foreign_langgrade -0.100210369 0.0324758997 0.068240689
## gpa 0.117513535 -0.0440809344 -0.074388393
## subject_mark 0.184238422 -0.1290059529 -0.109512208
## gender 0.265270723 -0.1297905714 -0.283485840
## father_ISCO -0.070091050 -0.1106975713 -0.106943204
## mother_ISCO -0.093866430 -0.1107202486 -0.036959686
## stat_affect 0.352975290 0.0717660812 -0.063414836
## stat_cognitivecomp -0.190601338 0.2099710010 0.455056380
## stat_difficulty -0.070325832 0.2819922903 0.489843786
## stat_value -0.282434736 0.0281770917 0.130485888
## efficacy 0.600829413 -0.0255663479 -0.342588799
## extrgoal 1.000000000 0.2066146701 0.001397036
## intrgoal 0.206614670 1.0000000000 0.547747406
## testanxiety 0.001397036 0.5477474060 1.000000000
## mathanxiety -0.136183499 0.3651534709 0.603877188
## interest 0.710018920 0.1339214778 -0.064338242
## course -0.145016300 -0.2543210132 -0.063924831
## mathanxiety interest course
## math_scores -0.201859899 0.27471106 -0.171214255
## social_studies_scores 0.009554514 0.05847632 -0.073175646
## russian_language_scores 0.047279692 0.01070735 -0.084039354
## foreign_language_scores -0.052767832 0.04683470 -0.014617822
## certificate_mathgrade -0.023254805 0.05456417 0.153095698
## certificate_social_studiesgrade 0.032790097 -0.05698450 0.044305478
## certificate_russianlanggrade 0.070875698 -0.06623677 0.148069404
## certificate_foreign_langgrade 0.116524802 -0.05716804 0.120485972
## gpa -0.078415204 0.19211190 0.051618119
## subject_mark -0.001112895 0.20361742 0.251836503
## gender -0.251343566 0.18789659 -0.190312767
## father_ISCO -0.040043574 -0.01666801 0.026568322
## mother_ISCO -0.047689285 -0.05439163 0.023851480
## stat_affect -0.086447877 0.39476446 -0.034172936
## stat_cognitivecomp 0.475444207 -0.19973968 0.041111951
## stat_difficulty 0.411240563 -0.15439487 0.191141331
## stat_value 0.184977219 -0.36688530 0.128530892
## efficacy -0.379012534 0.64497839 0.002406911
## extrgoal -0.136183499 0.71001892 -0.145016300
## intrgoal 0.365153471 0.13392148 -0.254321013
## testanxiety 0.603877188 -0.06433824 -0.063924831
## mathanxiety 1.000000000 -0.24948765 0.012440510
## interest -0.249487653 1.00000000 -0.147356099
## course 0.012440510 -0.14735610 1.000000000Correlation coefficients:
Interest and learning goal orientation: ~0.71
Learning goal orientation and self-efficacy beliefs: ~0.6
##
## Call:
## lm(formula = intrgoal ~ interest, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.48477 -0.51602 -0.00628 0.79478 1.76534
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.443e-16 5.264e-02 0.000 1.0000
## interest 1.269e-01 5.160e-02 2.459 0.0145 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9607 on 331 degrees of freedom
## Multiple R-squared: 0.01793, Adjusted R-squared: 0.01497
## F-statistic: 6.045 on 1 and 331 DF, p-value: 0.01446##
## Call:
## lm(formula = efficacy ~ intrgoal, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.38767 -0.62803 0.00452 0.68146 2.16999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.854e-17 5.524e-02 0.000 1.000
## intrgoal -2.659e-02 5.715e-02 -0.465 0.642
##
## Residual standard error: 1.008 on 331 degrees of freedom
## Multiple R-squared: 0.0006536, Adjusted R-squared: -0.002366
## F-statistic: 0.2165 on 1 and 331 DF, p-value: 0.642Sem model
library(lavaan)
myModel <- '
subject_mark ~ certificate_mathgrade+efficacy + mathanxiety+intrgoal
math_scores ~ certificate_mathgrade+extrgoal
mathanxiety ~ efficacy+extrgoal
intrgoal ~ interest+efficacy
efficacy ~ interest+math_scores+extrgoal'
fit <- sem(model = myModel,
data = final_reg)
summary(fit, fit.measures = TRUE)## lavaan 0.6-6 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 18
##
## Number of observations 333
##
## Model Test User Model:
##
## Test statistic 87.905
## Degrees of freedom 12
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 510.317
## Degrees of freedom 25
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.844
## Tucker-Lewis Index (TLI) 0.674
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3005.479
## Loglikelihood unrestricted model (H1) -2961.527
##
## Akaike (AIC) 6046.959
## Bayesian (BIC) 6115.505
## Sample-size adjusted Bayesian (BIC) 6058.408
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.138
## 90 Percent confidence interval - lower 0.112
## 90 Percent confidence interval - upper 0.166
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.075
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## subject_mark ~
## certfct_mthgrd 0.633 0.157 4.037 0.000
## efficacy 0.795 0.089 8.923 0.000
## mathanxiety 0.418 0.086 4.863 0.000
## intrgoal -0.352 0.085 -4.131 0.000
## math_scores ~
## certfct_mthgrd 3.812 0.725 5.259 0.000
## extrgoal 1.648 0.388 4.251 0.000
## mathanxiety ~
## efficacy -0.480 0.066 -7.324 0.000
## extrgoal 0.151 0.067 2.268 0.023
## intrgoal ~
## interest 0.244 0.066 3.704 0.000
## efficacy -0.184 0.067 -2.742 0.006
## efficacy ~
## interest 0.404 0.056 7.250 0.000
## math_scores 0.017 0.006 3.146 0.002
## extrgoal 0.287 0.058 4.926 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .subject_mark 2.260 0.175 12.903 0.000
## .math_scores 48.501 3.759 12.903 0.000
## .mathanxiety 0.907 0.070 12.903 0.000
## .intrgoal 0.897 0.070 12.903 0.000
## .efficacy 0.533 0.041 12.903 0.000## [,1] [,2] [,3] [,4]
## [1,] NA NA "certificate_mathgrade" NA
## [2,] "extrgoal" NA "interest" "math_scores"
## [3,] "efficacy" "mathanxiety" "intrgoal" NA
## [,5]
## [1,] NA
## [2,] "subject_mark"
## [3,] NA
## attr(,"class")
## [1] "layout_matrix" "matrix" "array"lay <- get_layout("", "math_scores", "","certificate_mathgrade","",
"", "","","","",
"mathanxiety","","subject_mark","","intrgoal",
"extrgoal","","efficacy","","interest", rows = 4)
Subsetting courses
firstcourse <- subset(final_reg, course == 1)
firstcourse$father_ISCO <- as.numeric(firstcourse$father_ISCO)
secondcourse <- subset(final_reg, course == 2)
secondcourse$father_ISCO <- as.numeric(secondcourse$father_ISCO)
thirdcourse <- subset(final_reg, course == 3)
thirdcourse$father_ISCO <- as.numeric(thirdcourse$father_ISCO)For the first course
##
## Call:
## lm(formula = subject_mark ~ math_scores, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0684 -0.8807 -0.0684 0.7439 3.9316
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.44058 0.94261 -1.528 0.128
## math_scores 0.09386 0.01192 7.871 4.31e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.245 on 166 degrees of freedom
## Multiple R-squared: 0.2718, Adjusted R-squared: 0.2674
## F-statistic: 61.96 on 1 and 166 DF, p-value: 4.307e-13firstmodel1 <-lm(subject_mark ~ math_scores+social_studies_scores, data = firstcourse)
summary(firstmodel1)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1823 -0.7683 0.0062 0.6431 3.6365
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.42770 1.09493 -3.131 0.00206 **
## math_scores 0.08255 0.01208 6.836 1.51e-10 ***
## social_studies_scores 0.03355 0.01014 3.309 0.00115 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.209 on 165 degrees of freedom
## Multiple R-squared: 0.3171, Adjusted R-squared: 0.3088
## F-statistic: 38.31 on 2 and 165 DF, p-value: 2.155e-14firstmodel2 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores, data = firstcourse)
summary(firstmodel2)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3281 -0.6783 -0.0400 0.6536 3.6619
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.70217 1.20931 -3.888 0.000146 ***
## math_scores 0.07375 0.01249 5.904 1.99e-08 ***
## social_studies_scores 0.02337 0.01091 2.143 0.033618 *
## foreign_language_scores 0.03319 0.01415 2.345 0.020228 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.193 on 164 degrees of freedom
## Multiple R-squared: 0.3393, Adjusted R-squared: 0.3272
## F-statistic: 28.07 on 3 and 164 DF, p-value: 1.055e-14firstmodel3 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+russian_language_scores, data = firstcourse)
summary(firstmodel3)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + russian_language_scores, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2884 -0.7668 -0.0128 0.6751 3.6100
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.41528 1.29737 -4.174 4.86e-05 ***
## math_scores 0.06957 0.01276 5.452 1.81e-07 ***
## social_studies_scores 0.01897 0.01126 1.685 0.0939 .
## foreign_language_scores 0.02726 0.01466 1.860 0.0647 .
## russian_language_scores 0.02123 0.01432 1.483 0.1401
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.189 on 163 degrees of freedom
## Multiple R-squared: 0.3481, Adjusted R-squared: 0.3321
## F-statistic: 21.76 on 4 and 163 DF, p-value: 2.116e-14firstmodel4 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade, data = firstcourse)
summary(firstmodel4)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0066 -0.7404 -0.0847 0.6878 3.5710
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.44461 1.24167 -4.385 2.07e-05 ***
## math_scores 0.07032 0.01244 5.650 6.99e-08 ***
## social_studies_scores 0.01737 0.01112 1.563 0.1200
## foreign_language_scores 0.02942 0.01409 2.087 0.0384 *
## certificate_mathgrade 0.40190 0.18202 2.208 0.0286 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.179 on 163 degrees of freedom
## Multiple R-squared: 0.3585, Adjusted R-squared: 0.3427
## F-statistic: 22.77 on 4 and 163 DF, p-value: 5.873e-15firstmodel5 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+certificate_social_studiesgrade, data = firstcourse)
summary(firstmodel5)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + certificate_social_studiesgrade,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0024 -0.7477 -0.0843 0.6835 3.5701
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.33812 1.46297 -3.649 0.000355 ***
## math_scores 0.07005 0.01263 5.549 1.15e-07 ***
## social_studies_scores 0.01756 0.01123 1.563 0.119908
## foreign_language_scores 0.02945 0.01414 2.083 0.038799 *
## certificate_mathgrade 0.41647 0.21064 1.977 0.049720 *
## certificate_social_studiesgrade -0.03572 0.25753 -0.139 0.889841
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.183 on 162 degrees of freedom
## Multiple R-squared: 0.3585, Adjusted R-squared: 0.3387
## F-statistic: 18.11 on 5 and 162 DF, p-value: 2.991e-14firstmodel6 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+certificate_foreign_langgrade, data = firstcourse)
summary(firstmodel6)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + certificate_foreign_langgrade,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9865 -0.7271 -0.0763 0.6973 3.5746
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.98854 1.44450 -3.453 0.000706 ***
## math_scores 0.06874 0.01272 5.403 2.3e-07 ***
## social_studies_scores 0.01769 0.01115 1.587 0.114458
## foreign_language_scores 0.03036 0.01420 2.138 0.034046 *
## certificate_mathgrade 0.46915 0.21208 2.212 0.028354 *
## certificate_foreign_langgrade -0.15669 0.25225 -0.621 0.535347
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.182 on 162 degrees of freedom
## Multiple R-squared: 0.36, Adjusted R-squared: 0.3402
## F-statistic: 18.22 on 5 and 162 DF, p-value: 2.505e-14firstmodel7 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+certificate_russianlanggrade, data = firstcourse)
summary(firstmodel7)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + certificate_russianlanggrade,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0111 -0.7446 -0.0800 0.6826 3.5695
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.47436 1.28249 -4.269 3.34e-05 ***
## math_scores 0.07049 0.01260 5.593 9.32e-08 ***
## social_studies_scores 0.01724 0.01124 1.534 0.1270
## foreign_language_scores 0.02926 0.01422 2.058 0.0412 *
## certificate_mathgrade 0.38974 0.22126 1.761 0.0800 .
## certificate_russianlanggrade 0.02093 0.21530 0.097 0.9227
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.183 on 162 degrees of freedom
## Multiple R-squared: 0.3585, Adjusted R-squared: 0.3387
## F-statistic: 18.11 on 5 and 162 DF, p-value: 3.005e-14firstmodel8 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy, data = firstcourse)
summary(firstmodel8)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.43920 -0.66142 -0.08868 0.63209 2.88725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.55800 1.18605 -3.000 0.003128 **
## math_scores 0.04390 0.01233 3.561 0.000485 ***
## social_studies_scores 0.01962 0.01020 1.924 0.056123 .
## foreign_language_scores 0.02688 0.01293 2.079 0.039174 *
## certificate_mathgrade 0.44207 0.16700 2.647 0.008918 **
## efficacy 0.49648 0.08778 5.656 6.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.081 on 162 degrees of freedom
## Multiple R-squared: 0.4643, Adjusted R-squared: 0.4477
## F-statistic: 28.08 on 5 and 162 DF, p-value: < 2.2e-16firstmodel9 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+extrgoal, data = firstcourse)
summary(firstmodel9)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## extrgoal, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.41644 -0.65072 -0.08417 0.62269 2.95836
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.51071 1.18603 -2.960 0.003541 **
## math_scores 0.04630 0.01251 3.701 0.000294 ***
## social_studies_scores 0.01899 0.01021 1.861 0.064587 .
## foreign_language_scores 0.02511 0.01302 1.929 0.055474 .
## certificate_mathgrade 0.43924 0.16691 2.632 0.009323 **
## efficacy 0.57538 0.11318 5.084 1.02e-06 ***
## extrgoal -0.13108 0.11881 -1.103 0.271565
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.08 on 161 degrees of freedom
## Multiple R-squared: 0.4683, Adjusted R-squared: 0.4485
## F-statistic: 23.63 on 6 and 161 DF, p-value: < 2.2e-16firstmodel10 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+intrgoal, data = firstcourse)
summary(firstmodel10)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## intrgoal, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.35803 -0.70090 -0.07449 0.65516 2.91066
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.43561 1.19967 -2.864 0.004744 **
## math_scores 0.04255 0.01248 3.409 0.000824 ***
## social_studies_scores 0.01969 0.01021 1.928 0.055556 .
## foreign_language_scores 0.02634 0.01297 2.031 0.043862 *
## certificate_mathgrade 0.44992 0.16759 2.685 0.008020 **
## efficacy 0.49759 0.08792 5.659 6.8e-08 ***
## intrgoal -0.07027 0.09671 -0.727 0.468568
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.083 on 161 degrees of freedom
## Multiple R-squared: 0.466, Adjusted R-squared: 0.4461
## F-statistic: 23.42 on 6 and 161 DF, p-value: < 2.2e-16firstmodel11 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+mathanxiety, data = firstcourse)
summary(firstmodel11)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## mathanxiety, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.30378 -0.67225 -0.09858 0.63817 2.94061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.61085 1.19082 -3.032 0.002830 **
## math_scores 0.04390 0.01235 3.555 0.000496 ***
## social_studies_scores 0.02009 0.01024 1.962 0.051464 .
## foreign_language_scores 0.02681 0.01295 2.070 0.040006 *
## certificate_mathgrade 0.44690 0.16745 2.669 0.008390 **
## efficacy 0.46513 0.09993 4.655 6.74e-06 ***
## mathanxiety -0.06422 0.09726 -0.660 0.510000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.083 on 161 degrees of freedom
## Multiple R-squared: 0.4657, Adjusted R-squared: 0.4458
## F-statistic: 23.39 on 6 and 161 DF, p-value: < 2.2e-16firstmodel12 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+testanxiety, data = firstcourse)
summary(firstmodel12)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## testanxiety, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.41300 -0.67078 -0.08601 0.63437 2.86274
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.53667 1.19263 -2.965 0.003483 **
## math_scores 0.04348 0.01248 3.484 0.000636 ***
## social_studies_scores 0.01964 0.01023 1.921 0.056525 .
## foreign_language_scores 0.02683 0.01297 2.070 0.040094 *
## certificate_mathgrade 0.44541 0.16803 2.651 0.008832 **
## efficacy 0.48994 0.09193 5.329 3.28e-07 ***
## testanxiety -0.02488 0.10073 -0.247 0.805206
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.084 on 161 degrees of freedom
## Multiple R-squared: 0.4645, Adjusted R-squared: 0.4445
## F-statistic: 23.27 on 6 and 161 DF, p-value: < 2.2e-16firstmodel13 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+interest, data = firstcourse)
summary(firstmodel13)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## interest, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.46221 -0.63957 -0.08184 0.63483 2.90523
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.56471 1.19004 -2.995 0.003174 **
## math_scores 0.04410 0.01240 3.556 0.000495 ***
## social_studies_scores 0.01957 0.01023 1.913 0.057504 .
## foreign_language_scores 0.02681 0.01297 2.067 0.040314 *
## certificate_mathgrade 0.44270 0.16752 2.643 0.009039 **
## efficacy 0.51088 0.11300 4.521 1.19e-05 ***
## interest -0.02170 0.10667 -0.203 0.839088
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.084 on 161 degrees of freedom
## Multiple R-squared: 0.4644, Adjusted R-squared: 0.4444
## F-statistic: 23.27 on 6 and 161 DF, p-value: < 2.2e-16firstmodel14 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores+certificate_mathgrade+efficacy+stat_difficulty, data = firstcourse)
summary(firstmodel14)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy +
## stat_difficulty, data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.52506 -0.66705 -0.08934 0.66450 2.93810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.52015 1.19224 -2.953 0.003623 **
## math_scores 0.04441 0.01241 3.577 0.000459 ***
## social_studies_scores 0.01895 0.01034 1.833 0.068654 .
## foreign_language_scores 0.02711 0.01297 2.091 0.038143 *
## certificate_mathgrade 0.43437 0.16836 2.580 0.010773 *
## efficacy 0.50962 0.09309 5.475 1.65e-07 ***
## stat_difficulty 0.04593 0.10604 0.433 0.665458
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.084 on 161 degrees of freedom
## Multiple R-squared: 0.4649, Adjusted R-squared: 0.4449
## F-statistic: 23.31 on 6 and 161 DF, p-value: < 2.2e-16FINAL:
##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.43920 -0.66142 -0.08868 0.63209 2.88725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.55800 1.18605 -3.000 0.003128 **
## math_scores 0.04390 0.01233 3.561 0.000485 ***
## social_studies_scores 0.01962 0.01020 1.924 0.056123 .
## foreign_language_scores 0.02688 0.01293 2.079 0.039174 *
## certificate_mathgrade 0.44207 0.16700 2.647 0.008918 **
## efficacy 0.49648 0.08778 5.656 6.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.081 on 162 degrees of freedom
## Multiple R-squared: 0.4643, Adjusted R-squared: 0.4477
## F-statistic: 28.08 on 5 and 162 DF, p-value: < 2.2e-16## [1] "math_scores" "social_studies_scores"
## [3] "russian_language_scores" "foreign_language_scores"
## [5] "certificate_mathgrade" "certificate_social_studiesgrade"
## [7] "certificate_russianlanggrade" "certificate_foreign_langgrade"
## [9] "gpa" "subject_mark"
## [11] "gender" "father_ISCO"
## [13] "mother_ISCO" "stat_affect"
## [15] "stat_cognitivecomp" "stat_difficulty"
## [17] "stat_value" "efficacy"
## [19] "extrgoal" "intrgoal"
## [21] "testanxiety" "mathanxiety"
## [23] "interest" "course"For the second course
##
## Call:
## lm(formula = subject_mark ~ math_scores, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7975 -0.5400 -0.2430 0.3016 2.8660
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.25137 1.06131 -1.179 0.241
## math_scores 0.07425 0.01351 5.498 3.17e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.917 on 96 degrees of freedom
## Multiple R-squared: 0.2395, Adjusted R-squared: 0.2315
## F-statistic: 30.23 on 1 and 96 DF, p-value: 3.169e-07secondmodel1 <-lm(subject_mark ~ math_scores+social_studies_scores, data = secondcourse)
summary(secondmodel1)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores,
## data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73232 -0.69547 -0.03864 0.27085 3.01489
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.725069 1.062213 -1.624 0.107682
## math_scores 0.059041 0.014917 3.958 0.000146 ***
## social_studies_scores 0.020293 0.009172 2.213 0.029323 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8989 on 95 degrees of freedom
## Multiple R-squared: 0.2767, Adjusted R-squared: 0.2615
## F-statistic: 18.17 on 2 and 95 DF, p-value: 2.074e-07secondmodel2 <-lm(subject_mark ~ math_scores+social_studies_scores+foreign_language_scores, data = secondcourse)
summary(secondmodel2)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.74576 -0.67992 -0.04446 0.29453 3.00682
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.576873 1.115185 -1.414 0.160665
## math_scores 0.060540 0.015337 3.947 0.000152 ***
## social_studies_scores 0.023162 0.011159 2.076 0.040651 *
## foreign_language_scores -0.005864 0.012874 -0.455 0.649800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9027 on 94 degrees of freedom
## Multiple R-squared: 0.2783, Adjusted R-squared: 0.2553
## F-statistic: 12.08 on 3 and 94 DF, p-value: 9.283e-07secondmodel3 <-lm(subject_mark ~ math_scores+social_studies_scores+russian_language_scores, data = secondcourse)
summary(secondmodel3)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## russian_language_scores, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73439 -0.66004 -0.09576 0.31214 2.82621
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.99002 1.31143 -0.755 0.452184
## math_scores 0.05913 0.01492 3.962 0.000145 ***
## social_studies_scores 0.02487 0.01035 2.403 0.018218 *
## russian_language_scores -0.01260 0.01318 -0.957 0.341268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8993 on 94 degrees of freedom
## Multiple R-squared: 0.2837, Adjusted R-squared: 0.2608
## F-statistic: 12.41 on 3 and 94 DF, p-value: 6.589e-07secondmodel4 <-lm(subject_mark ~ math_scores+social_studies_scores+interest, data = secondcourse)
summary(secondmodel4)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## interest, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.42793 -0.59349 -0.09622 0.30080 2.81585
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.24120 1.06836 -1.162 0.248267
## math_scores 0.05180 0.01505 3.442 0.000865 ***
## social_studies_scores 0.02156 0.00903 2.388 0.018941 *
## interest 0.19443 0.09218 2.109 0.037588 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.883 on 94 degrees of freedom
## Multiple R-squared: 0.3094, Adjusted R-squared: 0.2874
## F-statistic: 14.04 on 3 and 94 DF, p-value: 1.231e-07secondmodel5 <-lm(subject_mark ~ math_scores+social_studies_scores+interest+mother_ISCO, data = secondcourse)
summary(secondmodel5)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## interest + mother_ISCO, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3327 -0.6557 -0.1173 0.3532 2.7139
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.356e+00 1.051e+00 -1.290 0.20027
## math_scores 4.979e-02 1.482e-02 3.360 0.00113 **
## social_studies_scores 1.969e-02 8.918e-03 2.208 0.02970 *
## interest 2.116e-01 9.095e-02 2.326 0.02219 *
## mother_ISCO 1.541e-04 7.385e-05 2.087 0.03961 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8677 on 93 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.3119
## F-statistic: 11.99 on 4 and 93 DF, p-value: 6.686e-08FINAL:
##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## interest + mother_ISCO, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3327 -0.6557 -0.1173 0.3532 2.7139
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.356e+00 1.051e+00 -1.290 0.20027
## math_scores 4.979e-02 1.482e-02 3.360 0.00113 **
## social_studies_scores 1.969e-02 8.918e-03 2.208 0.02970 *
## interest 2.116e-01 9.095e-02 2.326 0.02219 *
## mother_ISCO 1.541e-04 7.385e-05 2.087 0.03961 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8677 on 93 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.3119
## F-statistic: 11.99 on 4 and 93 DF, p-value: 6.686e-08For the third course
##
## Call:
## lm(formula = subject_mark ~ efficacy, data = thirdcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4918 -1.2880 0.2723 1.1571 2.5665
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.6491 0.1802 42.455 <2e-16 ***
## efficacy 0.4111 0.1862 2.208 0.0308 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.453 on 65 degrees of freedom
## Multiple R-squared: 0.06974, Adjusted R-squared: 0.05543
## F-statistic: 4.873 on 1 and 65 DF, p-value: 0.03081##
## Call:
## lm(formula = subject_mark ~ efficacy + mathanxiety, data = thirdcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5445 -1.2109 0.1307 1.1429 2.5045
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.5702 0.1772 42.719 < 2e-16 ***
## efficacy 0.5105 0.1847 2.763 0.00746 **
## mathanxiety 0.3879 0.1634 2.375 0.02057 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.404 on 64 degrees of freedom
## Multiple R-squared: 0.1451, Adjusted R-squared: 0.1184
## F-statistic: 5.43 on 2 and 64 DF, p-value: 0.006634thirdmodel2 <-lm(subject_mark ~ efficacy+mathanxiety+father_ISCO, data = thirdcourse)
summary(thirdmodel2)##
## Call:
## lm(formula = subject_mark ~ efficacy + mathanxiety + father_ISCO,
## data = thirdcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.52570 -1.13408 0.03359 1.01670 2.65986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.020e+00 2.738e-01 29.295 < 2e-16 ***
## efficacy 4.784e-01 1.805e-01 2.650 0.01016 *
## mathanxiety 4.365e-01 1.607e-01 2.716 0.00852 **
## father_ISCO -2.115e-04 9.986e-05 -2.118 0.03810 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.367 on 63 degrees of freedom
## Multiple R-squared: 0.2019, Adjusted R-squared: 0.1639
## F-statistic: 5.313 on 3 and 63 DF, p-value: 0.002502FINAL
##
## Call:
## lm(formula = subject_mark ~ efficacy + mathanxiety + father_ISCO,
## data = thirdcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.52570 -1.13408 0.03359 1.01670 2.65986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.020e+00 2.738e-01 29.295 < 2e-16 ***
## efficacy 4.784e-01 1.805e-01 2.650 0.01016 *
## mathanxiety 4.365e-01 1.607e-01 2.716 0.00852 **
## father_ISCO -2.115e-04 9.986e-05 -2.118 0.03810 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.367 on 63 degrees of freedom
## Multiple R-squared: 0.2019, Adjusted R-squared: 0.1639
## F-statistic: 5.313 on 3 and 63 DF, p-value: 0.002502Final regression models
All courses
allmodel10 <-lm(subject_mark ~ math_scores+social_studies_scores+efficacy+mathanxiety*gender+intrgoal+course+father_ISCO+mother_ISCO, data = final_reg)
summary(allmodel10)##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## efficacy + mathanxiety * gender + intrgoal + course + father_ISCO +
## mother_ISCO, data = final_reg)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8132 -0.9505 -0.0618 0.9347 3.8595
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.622e-01 1.067e+00 -0.621 0.5352
## math_scores 2.807e-02 1.188e-02 2.363 0.0187 *
## social_studies_scores 4.003e-02 8.616e-03 4.646 4.94e-06 ***
## efficacy 6.878e-01 8.925e-02 7.707 1.61e-13 ***
## mathanxiety 4.974e-01 1.116e-01 4.459 1.14e-05 ***
## gendermale -1.882e-01 1.744e-01 -1.079 0.2814
## intrgoal -1.849e-01 9.283e-02 -1.992 0.0472 *
## course 5.432e-01 1.078e-01 5.041 7.74e-07 ***
## father_ISCO -9.234e-05 4.154e-05 -2.223 0.0269 *
## mother_ISCO 1.109e-04 7.065e-05 1.570 0.1173
## mathanxiety:gendermale -3.689e-01 1.554e-01 -2.373 0.0182 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.416 on 322 degrees of freedom
## Multiple R-squared: 0.3574, Adjusted R-squared: 0.3375
## F-statistic: 17.91 on 10 and 322 DF, p-value: < 2.2e-16
## math_scores social_studies_scores efficacy
## 1.294967 1.242882 1.337638
## mathanxiety gender intrgoal
## 2.224140 1.169720 1.337651
## course father_ISCO mother_ISCO
## 1.184290 1.056549 1.042306
## mathanxiety:gender
## 1.955272FIRST
##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## foreign_language_scores + certificate_mathgrade + efficacy,
## data = firstcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.43920 -0.66142 -0.08868 0.63209 2.88725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.55800 1.18605 -3.000 0.003128 **
## math_scores 0.04390 0.01233 3.561 0.000485 ***
## social_studies_scores 0.01962 0.01020 1.924 0.056123 .
## foreign_language_scores 0.02688 0.01293 2.079 0.039174 *
## certificate_mathgrade 0.44207 0.16700 2.647 0.008918 **
## efficacy 0.49648 0.08778 5.656 6.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.081 on 162 degrees of freedom
## Multiple R-squared: 0.4643, Adjusted R-squared: 0.4477
## F-statistic: 28.08 on 5 and 162 DF, p-value: < 2.2e-16## math_scores social_studies_scores foreign_language_scores
## 1.417459 1.376110 1.419524
## certificate_mathgrade efficacy
## 1.199764 1.200318SECOND
##
## Call:
## lm(formula = subject_mark ~ math_scores + social_studies_scores +
## interest + mother_ISCO, data = secondcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3327 -0.6557 -0.1173 0.3532 2.7139
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.356e+00 1.051e+00 -1.290 0.20027
## math_scores 4.979e-02 1.482e-02 3.360 0.00113 **
## social_studies_scores 1.969e-02 8.918e-03 2.208 0.02970 *
## interest 2.116e-01 9.095e-02 2.326 0.02219 *
## mother_ISCO 1.541e-04 7.385e-05 2.087 0.03961 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8677 on 93 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.3119
## F-statistic: 11.99 on 4 and 93 DF, p-value: 6.686e-08## math_scores social_studies_scores interest
## 1.344906 1.288200 1.065761
## mother_ISCO
## 1.031168THIRD
##
## Call:
## lm(formula = subject_mark ~ efficacy + mathanxiety + father_ISCO,
## data = thirdcourse)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.52570 -1.13408 0.03359 1.01670 2.65986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.020e+00 2.738e-01 29.295 < 2e-16 ***
## efficacy 4.784e-01 1.805e-01 2.650 0.01016 *
## mathanxiety 4.365e-01 1.607e-01 2.716 0.00852 **
## father_ISCO -2.115e-04 9.986e-05 -2.118 0.03810 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.367 on 63 degrees of freedom
## Multiple R-squared: 0.2019, Adjusted R-squared: 0.1639
## F-statistic: 5.313 on 3 and 63 DF, p-value: 0.002502## efficacy mathanxiety father_ISCO
## 1.061549 1.076023 1.035212