0.1 Research Problem
“What is more important for student achievement nowadays: books or computers?”
Perhaps the only thing I learned from the sociology of education lessons is that the number of books at home was a good predictor of success in school. Lord for God’s sake, I do not remember what this article is for. However, the debate about the use of technology for learning is long (The impact of using multimedia on students’ academic achievement in the College of Education at King Saud University, Sara Aloraini 2012). And what is more important for this study, even home use of technology has an impact on educational success (Schacter, J., & Fagnano, C. (1999). Does Computer Technology Improve Student Learning and Achievement? How, When, and under What Conditions? Journal of Educational Computing Research, 20(4), 329–343).
On the other hand, it is obvious that the better the student reads and things like that, the better he will cope with the school, because the school (not the higher school of economics) teaches to study through reading (Students’ self-perception of reading ability, enjoyment of reading and reading achievement Jeffrey K.Smith, 2012, Learning and Individual Differences Volume 22, Issue 2, April 2012, Pages 202-206). And success in reading, in turn, depends on the student’s motivation (WANG, J. H. and GUTHRIE, J. T. (2004), Modeling the effects of intrinsic motivation, extrinsic motivation, amount of reading, and past reading achievement on text comprehension between U.S. and Chinese students. Reading Research Quarterly, 39: 162-186. doi:10.1598/RRQ.39.2.2).
Taking the above into account, and the fact that I could not find the article that answered the research question. It would be very interesting to find out whether it is necessary to set up an experiment on younger brothers, or regression and factor analysis will provide a convincing answer.
0.2 Preparation packages and data
library(foreign)
library(dplyr)
library(psych)
library(formattable)
library(ggplot2)
library(jtools)
library(ggthemes)
library(gridExtra)
library(polycor)
library(QuantPsyc)
library(stargazer)
library(sjPlot)
library(stats)
library(car)data <- read.spss("~/datanal/3year/hw/BSGRUSM6.sav", to.data.frame=TRUE)
data_reg <- data %>% dplyr::select(BSMMAT01, BSBG04, BSBG06A, BSBG06B, ITSEX, BSBG09B) %>% na.omit()
data_reg$BSMMAT01 <- as.numeric(data_reg$BSMMAT01)
data_reg$BSBG04 <- factor(data_reg$BSBG04, ordered = TRUE)
colnames(data_reg) <- c("math", "books", "table", "pc", "gender", "migrant")
data_reg$computers <- as.factor(ifelse(data_reg$table == "Yes" | data_reg$pc == "Yes", "Yes", "No"))Index for computers was created, for fun Amount of books were ordered.
| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| math | 1 | 4695 | 2398.314377 | 1376.6991372 | 2400 | 2400.327921 | 1765.7766 | 1 | 4775 | 4774 | -0.009533691 | -1.1985640 | 20.091910824 |
| books* | 2 | 4695 | 2.922045 | 1.0420912 | 3 | 2.863455 | 1.4826 | 1 | 5 | 4 | 0.321907912 | -0.3794799 | 0.015208554 |
| table* | 3 | 4695 | 1.151864 | 0.3589269 | 1 | 1.064945 | 0.0000 | 1 | 2 | 1 | 1.939459704 | 1.7618793 | 0.005238275 |
| pc* | 4 | 4695 | 1.162513 | 0.3689603 | 1 | 1.078254 | 0.0000 | 1 | 2 | 1 | 1.829003130 | 1.3455392 | 0.005384705 |
| gender* | 5 | 4695 | 1.518637 | 0.4997058 | 2 | 1.523290 | 0.0000 | 1 | 2 | 1 | -0.074575398 | -1.9948633 | 0.007292838 |
| migrant* | 6 | 4695 | 1.177210 | 0.4671942 | 1 | 1.051371 | 0.0000 | 1 | 3 | 2 | 2.675987115 | 6.4160230 | 0.006818356 |
| computers* | 7 | 4695 | 1.979766 | 0.1408158 | 2 | 2.000000 | 0.0000 | 1 | 2 | 1 | -6.812637956 | 44.4214975 | 0.002055103 |
Math score distributed not normally, but since there are more than 2000 observations, we happily violate this assumption. Most of students have 26-50 books, and PC or table at home. Boys and girls equally distributed in this sample. Most of students are not from migrant families.
ggplot(data = data_reg, aes(x = math))+
geom_density(fill = "#D0104C")+
labs(x = "Math ability",
y = "Density",
title = "Math abilities in Russia")+
theme_wsj()
##
## Two-sample Kolmogorov-Smirnov test
##
## data: rnorm(10^4) and data_reg$math
## D = 0.99936, p-value < 2.2e-16
## alternative hypothesis: two-sidedAs we see, our distribution is not really normal, as p-value < 2.2e-16 and given null hypothesis of normality. However we are okay with this violation, because there are more than 2000 observations.
0.3 Regression
Lets start our forwards approach to construction of regression.
0.3.1 Model
Obviously we will start from the books.
model1 <- lm(math ~ books, data = data_reg)
stargazer(model1, type = "text", title = "Books and math", style = "ajs")##
## Books and math
##
## ============================================
## MATH
## --------------------------------------------
## books.L 606.088***
## (66.833)
##
## books.Q -84.602
## (58.984)
##
## books.C -133.278**
## (50.681)
##
## books4 -31.685
## (39.373)
##
## Constant 2,408.523***
## (24.561)
##
## Observations 4,695
## R2 .026
## Adjusted R2 .026
## Residual Std. Error 1,358.957 (df = 4690)
## F Statistic 31.842*** (df = 4; 4690)
## --------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001Only books explains 2% of the model, so we won`t really discuss results. There is positive linear relation between amount of books at home and math scores, as well as negative cubic.
model2 <- update(model1, ~.+computers)
stargazer(model2, type = "text", title = "Books and math and devices", style = "ajs")##
## Books and math and devices
##
## ============================================
## MATH
## --------------------------------------------
## books.L 601.451***
## (66.947)
##
## books.Q -82.384
## (59.012)
##
## books.C -132.636**
## (50.682)
##
## books4 -30.669
## (39.381)
##
## computersYes 166.068
## (141.213)
##
## Constant 2,246.092***
## (140.287)
##
## Observations 4,695
## R2 .027
## Adjusted R2 .026
## Residual Std. Error 1,358.901 (df = 4689)
## F Statistic 25.753*** (df = 5; 4689)
## --------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001No changes in model, so let`s add tables and pc separatelly
model2 <- update(model1, ~.+pc+table)
stargazer(model2, type = "text", title = "Books and math and pc and tablets", style = "ajs")##
## Books and math and pc and tablets
##
## ============================================
## MATH
## --------------------------------------------
## books.L 586.373***
## (66.628)
##
## books.Q -83.268
## (58.657)
##
## books.C -129.333*
## (50.398)
##
## books4 -35.179
## (39.151)
##
## pcNo -349.642***
## (53.609)
##
## tableNo 205.942***
## (55.028)
##
## Constant 2,433.808***
## (27.481)
##
## Observations 4,695
## R2 .038
## Adjusted R2 .037
## Residual Std. Error 1,350.866 (df = 4688)
## F Statistic 31.208*** (df = 6; 4688)
## --------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001Saparatelly they improve the model, but owning a PC increase match scores, hence owning a tablet decrease them. R^2 = 0.037…
Control variables should be added
model3 <- update(model2, ~.+gender+migrant)
stargazer(model3, type = "text", title = "Books and pc + controls", style = "ajs")##
## Books and pc + controls
##
## ============================================
## MATH
## --------------------------------------------
## books.L 600.232***
## (66.648)
##
## books.Q -81.540
## (58.604)
##
## books.C -130.625**
## (50.352)
##
## books4 -30.046
## (39.128)
##
## pcNo -359.420***
## (53.623)
##
## tableNo 221.543***
## (55.126)
##
## genderMale 149.084***
## (39.717)
##
## migrantNo -35.770
## (64.538)
##
## migrantI don't know -102.465
## (105.800)
##
## Constant 2,363.628***
## (35.364)
##
## Observations 4,695
## R2 .042
## Adjusted R2 .040
## Residual Std. Error 1,349.068 (df = 4685)
## F Statistic 22.584*** (df = 9; 4685)
## --------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001Being male increase math scores for 150, migration of parents does not effect match scores. R^2 = 0.04%, only 4% of observations are explained. Very poor model. Let`s add interaction
0.3.2 interaction
model4 <- lm(math ~ books + gender+ table*pc*gender + migrant , data = data_reg)
stargazer(model4, type = "text", title = "Books and pc + controls", style = "ajs")##
## Books and pc + controls
##
## =================================================
## MATH
## -------------------------------------------------
## books.L 600.739***
## (66.684)
##
## books.Q -82.939
## (58.623)
##
## books.C -128.807*
## (50.360)
##
## books4 -32.002
## (39.132)
##
## genderMale 146.181**
## (47.086)
##
## tableNo 189.358*
## (80.202)
##
## pcNo -371.084***
## (89.556)
##
## migrantNo -36.818
## (64.552)
##
## migrantI don't know -108.879
## (105.830)
##
## tableNo:pcNo 310.526
## (221.471)
##
## genderMale:tableNo 88.621
## (119.007)
##
## genderMale:pcNo 30.502
## (116.582)
##
## genderMale:tableNo:pcNo -774.169*
## (320.429)
##
## Constant 2,363.999***
## (37.898)
##
## Observations 4,695
## R2 .043
## Adjusted R2 .040
## Residual Std. Error 1,348.722 (df = 4681)
## F Statistic 16.135*** (df = 13; 4681)
## -------------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001By the method of conscious scientific enumeration, a single significant interaction effect was chosen, which shows a unique effect when Men have neither a computer nor a tablet, their educational achievements in mathematics fall significantly, although the usual addition of these parameters in the regression did not give such a result.
While men as a whole do better with math, but the absence of any technique breaks their lives
##
## Books and pc + controls
##
## ==========================================================================
## MATH
## 1 2
## --------------------------------------------------------------------------
## books.L 600.739*** 600.232***
## (66.684) (66.648)
##
## books.Q -82.939 -81.540
## (58.623) (58.604)
##
## books.C -128.807* -130.625**
## (50.360) (50.352)
##
## books4 -32.002 -30.046
## (39.132) (39.128)
##
## genderMale 146.181** 149.084***
## (47.086) (39.717)
##
## tableNo 189.358* 221.543***
## (80.202) (55.126)
##
## pcNo -371.084*** -359.420***
## (89.556) (53.623)
##
## migrantNo -36.818 -35.770
## (64.552) (64.538)
##
## migrantI don't know -108.879 -102.465
## (105.830) (105.800)
##
## tableNo:pcNo 310.526
## (221.471)
##
## genderMale:tableNo 88.621
## (119.007)
##
## genderMale:pcNo 30.502
## (116.582)
##
## genderMale:tableNo:pcNo -774.169*
## (320.429)
##
## Constant 2,363.999*** 2,363.628***
## (37.898) (35.364)
##
## Observations 4,695 4,695
## R2 .043 .042
## Adjusted R2 .040 .040
## Residual Std. Error 1,348.722 (df = 4681) 1,349.068 (df = 4685)
## F Statistic 16.135*** (df = 13; 4681) 22.584*** (df = 9; 4685)
## --------------------------------------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001R^2 is same for all models, so we need anova or bic to compare them
## [1] 81011.14## [1] 81012.73They are the same
## Analysis of Variance Table
##
## Model 1: math ~ books + gender + table * pc * gender + migrant
## Model 2: math ~ books + pc + table + gender + migrant
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 4681 8514982777
## 2 4685 8526622397 -4 -11639620 1.5997 0.1715First model uses less term for same poor result. That is our best model.
0.3.3 diagnostics
Let’s check model for multicollinearity.
## GVIF Df GVIF^(1/(2*Df))
## books 1.017277 4 1.002143
## pc 1.009589 1 1.004783
## table 1.009702 1 1.004839
## gender 1.015926 1 1.007931
## migrant 1.006517 2 1.001625Coefficients are less than 5, everything’s OK!
## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 1146 2.204854 0.027513 NANo problems with outliers, exept for 1146. I will add this student to my list
## 1146 2759
## 1121 2709Residuals distributed not so normally, there are some outliers: 2759 and 1146
Model explain data OK in each set, graphs looks fine, due to data structure they are funny. (Variables are no integer in general) There are outliers 2759, 1146, 2759, 1138, 1163, 114
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.5022577, Df = 1, p = 0.47851strong indicator of heteroscedasticity
library(MASS)
sresid <- studres(model3)
hist(sresid, freq=FALSE,
main="Distribution of Studentized Residuals")
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
not so normal…
Model shows not a really good(really bad) fit
moving on!
0.4 EFA
data_EFA <- data %>% dplyr::select(BSBG06A, BSBG06B, BSBG06C, BSBG06D, BSBG06E, BSBG06F, BSBG06G, BSBG06H, BSBG06I, BSBG06J, BSBG06K, BSMMAT01, BSBG04, ITSEX, BSBG09B) %>% na.omit()
corrr<- hetcor(data_EFA[,-12:-15])
corrr <- corrr$correlations
cor.mtest <- function(mat, ...) {
mat <- as.matrix(mat)
n <- ncol(mat)
p.mat<- matrix(NA, n, n)
diag(p.mat) <- 0
for (i in 1:(n - 1)) {
for (j in (i + 1):n) {
tmp <- cor.test(mat[, i], mat[, j], ...)
p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
}
}
colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
p.mat
}
# matrix of the p-value of the correlation
p.mat <- cor.mtest(corrr)
corrplot::corrplot(corrr, type="upper", order="hclust",
p.mat = p.mat, sig.level = 0.05, insig = "blank")
For a some reason there is only one one sighnificant correlation in this data. Could I did something totally wrong? Yes, sure.
## Parallel analysis suggests that the number of factors = 5 and the number of components = 45 factors are recommended
one of factors explains only one variable, we need to reduce them to 4
only two variable for factor is still not so good.
Looks better, but some of factors poorly (0.4) correlate with variables
we need to try different rotation
It does not improve anyrhing, but making it only worse, by introducing intercorrelation
BSBG06E,BSBG06F, BSBG06B – ML2 BSBG06H not explainde BSBG06C, BSBG06D, BSBG06A – ML1 BSBG06K, BSBG06G, BSBG06I, BSBG06J – ML3
ML2 – Internet connection, Your own mobile phone, A computer or tablet that is shared with other people at home Minimal needs, civilization
ML1 – Study desk/table for your use, Your own room, A computer or tablet of your own – Personal things
ML3 – indicators of wealth
data_num <- sapply( data_EFA, as.numeric )
data_num <- as.data.frame(data_num)
fa_num_model <- fa(data_num[,-12:-15], nfactors=3, rotate="varimax", fm="ml", n.obs = 4579, cor = "mixed") ##
## mixed.cor is deprecated, please use mixedCor.##
## Loadings:
## ML2 ML1 ML3
## BSBG06A 0.373
## BSBG06B 0.554
## BSBG06C 0.912
## BSBG06D 0.535
## BSBG06E 0.729
## BSBG06F 0.660
## BSBG06G 0.571
## BSBG06H
## BSBG06I 0.425
## BSBG06J 0.382
## BSBG06K 0.616
##
## ML2 ML1 ML3
## SS loadings 1.507 1.487 1.274
## Proportion Var 0.137 0.135 0.116
## Cumulative Var 0.137 0.272 0.388all variables located only on one factor
##
## Factor analysis with Call: fa(r = data_num[, -12:-15], nfactors = 3, n.obs = 4579, rotate = "varimax",
## fm = "ml", cor = "mixed")
##
## Test of the hypothesis that 3 factors are sufficient.
## The degrees of freedom for the model is 25 and the objective function was 0.31
## The number of observations was 4579 with Chi Square = 1426.67 with prob < 7.7e-286
##
## The root mean square of the residuals (RMSA) is 0.05
## The df corrected root mean square of the residuals is 0.08
##
## Tucker Lewis Index of factoring reliability = 0.716
## RMSEA index = 0.111 and the 10 % confidence intervals are 0.106 0.116
## BIC = 1215.93RMSA is on 0.05 border, that will be considered as good, while as RMSR more then 0.05, border is less then 0.1, both of them does show ok model fit. Tucker Lewis Index 0.716 does not cross 0.9 border. Not a good model
0.4.1 Loadings
##
## Reliability analysis
## Call: psych::alpha(x = data_num[c("BSBG06A", "BSBG06B", "BSBG06C",
## "BSBG06D", "BSBG06E", "BSBG06F", "BSBG06G", "BSBG06H", "BSBG06I",
## "BSBG06J", "BSBG06K")], check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.49 0.51 0.51 0.087 1 0.011 1.3 0.16 0.073
##
## lower alpha upper 95% confidence boundaries
## 0.47 0.49 0.51
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## BSBG06A 0.47 0.49 0.48 0.087 0.95 0.011 0.0040 0.069
## BSBG06B 0.50 0.52 0.51 0.097 1.08 0.011 0.0034 0.079
## BSBG06C 0.46 0.48 0.47 0.084 0.91 0.011 0.0037 0.069
## BSBG06D 0.45 0.48 0.47 0.083 0.91 0.012 0.0035 0.073
## BSBG06E 0.48 0.48 0.47 0.084 0.92 0.011 0.0041 0.073
## BSBG06F 0.48 0.49 0.48 0.088 0.97 0.011 0.0042 0.079
## BSBG06G 0.47 0.49 0.48 0.088 0.97 0.011 0.0038 0.078
## BSBG06H 0.49 0.50 0.50 0.092 1.01 0.011 0.0044 0.083
## BSBG06I 0.43 0.46 0.46 0.079 0.86 0.012 0.0041 0.067
## BSBG06J 0.45 0.48 0.48 0.086 0.94 0.012 0.0037 0.078
## BSBG06K 0.44 0.47 0.47 0.082 0.90 0.012 0.0039 0.069
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## BSBG06A 4579 0.38 0.41 0.28 0.181 1.2 0.36
## BSBG06B 4579 0.28 0.31 0.13 0.066 1.2 0.37
## BSBG06C 4579 0.37 0.44 0.34 0.223 1.1 0.28
## BSBG06D 4579 0.49 0.44 0.35 0.241 1.3 0.47
## BSBG06E 4579 0.29 0.43 0.33 0.192 1.0 0.18
## BSBG06F 4579 0.23 0.39 0.26 0.156 1.0 0.14
## BSBG06G 4579 0.43 0.39 0.26 0.194 1.7 0.44
## BSBG06H 4579 0.41 0.36 0.21 0.145 1.6 0.48
## BSBG06I 4579 0.54 0.48 0.40 0.300 1.3 0.47
## BSBG06J 4579 0.50 0.42 0.30 0.238 1.5 0.50
## BSBG06K 4579 0.48 0.45 0.36 0.273 1.8 0.40
##
## Non missing response frequency for each item
## 1 2 miss
## BSBG06A 0.85 0.15 0
## BSBG06B 0.84 0.16 0
## BSBG06C 0.92 0.08 0
## BSBG06D 0.68 0.32 0
## BSBG06E 0.97 0.03 0
## BSBG06F 0.98 0.02 0
## BSBG06G 0.26 0.74 0
## BSBG06H 0.37 0.63 0
## BSBG06I 0.68 0.32 0
## BSBG06J 0.51 0.49 0
## BSBG06K 0.21 0.79 0Cronbach’s Alpha shows low inter-item reliability, because value is near 0.49, (expected 0.9 or more, for exellent, or 0.7 for good) SD is nice but, who cares.
0.5 Regression 2
data_reg2$BSMMAT01 <- as.numeric(data_reg2$BSMMAT01)
data_reg2$BSBG04 <- factor(data_reg2$BSBG04, ordered = TRUE)
data_reg2 <- data_reg2 %>% dplyr::select(BSMMAT01, BSBG04, BSBG06A, BSBG06B, ITSEX, BSBG09B, ML1, ML2, ML3)
colnames(data_reg2) <- c("math", "books", "table", "pc", "gender", "migrant", "moie", "minimum", "wealth")
model_final <- lm(math ~ books + gender+ table+ pc +gender + migrant + moie + minimum + wealth, data = data_reg2)
stargazer(model_final, type = "text", title = "Books and pc + controls", style = "ajs")##
## Books and pc + controls
##
## =============================================
## MATH
## ---------------------------------------------
## books.L 560.433***
## (67.722)
##
## books.Q -80.059
## (58.919)
##
## books.C -129.143*
## (50.634)
##
## books4 -37.934
## (39.413)
##
## genderMale 168.029***
## (40.425)
##
## tableNo 307.775***
## (61.431)
##
## pcNo -162.217*
## (69.166)
##
## migrantNo -22.974
## (65.081)
##
## migrantI don't know -106.517
## (106.605)
##
## moie -5.009
## (22.720)
##
## minimum -141.056***
## (26.777)
##
## wealth 20.696
## (25.518)
##
## Constant 2,314.450***
## (36.590)
##
## Observations 4,579
## R2 .050
## Adjusted R2 .048
## Residual Std. Error 1,342.038 (df = 4566)
## F Statistic 20.042*** (df = 12; 4566)
## ---------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001only minimal techinal equipment shows sighnificant and negative resuls, e.t. not having at mobilre phone and internet decrease math scores.
0.5.1 compare
##
## Books and pc + controls
##
## ======================================================================
## MATH
## 1 2
## ----------------------------------------------------------------------
## books.L 560.433*** 600.232***
## (67.722) (66.648)
##
## books.Q -80.059 -81.540
## (58.919) (58.604)
##
## books.C -129.143* -130.625**
## (50.634) (50.352)
##
## books4 -37.934 -30.046
## (39.413) (39.128)
##
## genderMale 168.029*** 149.084***
## (40.425) (39.717)
##
## tableNo 307.775*** 221.543***
## (61.431) (55.126)
##
## pcNo -162.217* -359.420***
## (69.166) (53.623)
##
## migrantNo -22.974 -35.770
## (65.081) (64.538)
##
## migrantI don't know -106.517 -102.465
## (106.605) (105.800)
##
## moie -5.009
## (22.720)
##
## minimum -141.056***
## (26.777)
##
## wealth 20.696
## (25.518)
##
## Constant 2,314.450*** 2,363.628***
## (36.590) (35.364)
##
## Observations 4,579 4,695
## R2 .050 .042
## Adjusted R2 .048 .040
## Residual Std. Error 1,342.038 (df = 4566) 1,349.068 (df = 4685)
## F Statistic 20.042*** (df = 12; 4566) 22.584*** (df = 9; 4685)
## ----------------------------------------------------------------------
## Notes: *P < .05
## **P < .01
## ***P < .001Median math points near 2300 for both models Each additional level of owning a books increase math scores at 560 points for model with components and for 600 points for a base model equal negative relation between each additional qubic point for level of books, that decreases math score for 130 points Being male increase math scores for 170 and 150 recpectively Not having a tablet increases math scores for 300 and 220 And having a PC increases them for 160 and 360 points Each step on minimal equipment supplies increases math points on 140 Adding factors increases R^2 from 4% to 4.8%
model_scaled <- lm(scale(math) ~ books + gender+ table+ pc +gender + migrant + moie + minimum + wealth, data = data_reg2)
summary(model_scaled)##
## Call:
## lm(formula = scale(math) ~ books + gender + table + pc + gender +
## migrant + moie + minimum + wealth, data = data_reg2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.14036 -0.84544 0.00178 0.83172 2.38561
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.066159 0.026608 -2.486 0.0129 *
## books.L 0.407551 0.049248 8.276 < 2e-16 ***
## books.Q -0.058220 0.042846 -1.359 0.1743
## books.C -0.093914 0.036822 -2.550 0.0108 *
## books^4 -0.027586 0.028661 -0.962 0.3359
## genderMale 0.122192 0.029397 4.157 3.29e-05 ***
## tableNo 0.223817 0.044673 5.010 5.65e-07 ***
## pcNo -0.117965 0.050298 -2.345 0.0191 *
## migrantNo -0.016707 0.047328 -0.353 0.7241
## migrantI don't know -0.077460 0.077524 -0.999 0.3178
## moie -0.003643 0.016522 -0.220 0.8255
## minimum -0.102577 0.019473 -5.268 1.45e-07 ***
## wealth 0.015050 0.018557 0.811 0.4174
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9759 on 4566 degrees of freedom
## Multiple R-squared: 0.05004, Adjusted R-squared: 0.04754
## F-statistic: 20.04 on 12 and 4566 DF, p-value: < 2.2e-16as we see Books still are mostly correlated with an education in terms of msth scores
0.6 Plots
We could see ralation of each variables in base regression
models are diffrerently distributed, and superinteraction is really platocurtosys, , distribution of model without interaction is more normall
library(jtools)
#plot_summs(model_scaled, scale = TRUE, plot.distributions = TRUE)
# no reason for this plot stop workingcomponents distributed equally and normally
## # A tibble: 2 x 4
## BSBG06A moi min wealth
## <fct> <dbl> <dbl> <dbl>
## 1 Yes 1.12 0.725 -0.177
## 2 No 1.49 1.47 0.466Table output of distribution of Factors across conditions.
0.7 conclusion
I will throw out the computer, as the analysis made it clear that books are more important than computers, no matter how measured. here. take it, please.