https://rpubs.com/graceHUA/837060

R Markdown

# import data

load("IPS_706_Midterm.rda")
load("IPS_706_Midterm2.rda")
#Describe ,summary, hist , plot
str(ips.706)
## Classes 'tbl_df', 'tbl' and 'data.frame':    142 obs. of  2 variables:
##  $ x: num  58.2 58.2 58.7 57.3 58.1 ...
##  $ y: num  91.9 92.2 90.3 89.9 92 ...
str(ips.706b)
## Classes 'tbl_df', 'tbl' and 'data.frame':    142 obs. of  2 variables:
##  $ x: num  55.4 51.5 46.2 42.8 40.8 ...
##  $ y: num  97.2 96 94.5 91.4 88.3 ...
xa <- ips.706$x
ya <- ips.706$y
xb <- ips.706b$x
yb <- ips.706b$y
##summary ,hist

summary(xa)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   27.02   41.03   56.53   54.27   68.71   86.44
hist(xa)

summary(ya)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   14.37   20.37   50.11   47.84   63.55   92.21
hist(ya)

summary(xb)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   22.31   44.10   53.33   54.26   64.74   98.21
hist(xb)

summary(yb)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.949  25.288  46.026  47.832  68.526  99.487
hist(yb)

## plot dataset ips.706
plot(x=xa, y=ya)

## plot dataset ips.706b
plot(x=xb, y=yb)

Note: annotation:

  1. The independent variables (x) and dependent variables (y) of the two data sets show star and dinosaur, which initially seem to be unrelated or non-linear.
  2. Therefore, in the next step, try to merge the two data sets.
# cbind 2 dataset

xyc <- cbind(xa, xb, ya, yb)

plot(x=xa, y=yb)

plot(x=xb, y=ya)

plot(x=ya, y=yb)

plot(x=xa, y=xb)

#correlation
cor(xa, xb)
## [1] 0.8523187
cor(ya, yb)
## [1] 0.9631865
cor(xa, yb)
## [1] -0.04150085
cor(xb, ya)
## [1] -0.0645828

Note: Found after merging

  1. Initially, xa, xb seem to be related or linear.
  2. The yb and ya also seem to be related or linear at first.
  3. Therefore, in the next step, try to merge the 4 variables into a new data set.
as.data.frame(xyc)
##           xa      xb       ya      yb
## 1   58.21361 55.3846 91.88189 97.1795
## 2   58.19605 51.5385 92.21499 96.0256
## 3   58.71823 46.1538 90.31053 94.4872
## 4   57.27837 42.8205 89.90761 91.4103
## 5   58.08202 40.7692 92.00815 88.3333
## 6   57.48945 38.7179 88.08529 84.8718
## 7   28.08874 35.6410 63.51079 79.8718
## 8   28.08547 33.0769 63.59020 77.5641
## 9   28.08727 28.9744 63.12328 74.4872
## 10  27.57803 26.1538 62.82104 71.4103
## 11  27.77992 23.0769 63.51815 66.4103
## 12  28.58900 22.3077 63.02408 61.7949
## 13  28.73914 22.3077 62.72086 57.1795
## 14  27.02460 23.3333 62.90186 52.9487
## 15  28.80134 25.8974 63.38904 51.0256
## 16  27.18646 29.4872 63.55873 51.0256
## 17  29.28515 32.8205 63.38361 51.0256
## 18  39.40295 35.3846 51.15086 51.4103
## 19  28.81133 40.2564 61.35785 51.4103
## 20  34.30396 44.1026 56.54213 52.9487
## 21  29.60276 46.6667 60.15735 54.1026
## 22  49.11616 50.0000 63.66000 55.2564
## 23  39.61755 53.0769 62.92519 55.6410
## 24  43.23308 56.6667 63.16522 56.0256
## 25  64.89279 59.2308 65.81418 57.9487
## 26  62.49015 61.2821 74.58429 62.1795
## 27  68.98808 61.5385 63.23215 66.4103
## 28  62.10562 61.7949 75.99087 69.1026
## 29  32.46185 57.4359 62.88190 55.2564
## 30  41.32720 54.8718 49.07025 49.8718
## 31  44.00715 52.5641 46.44967 46.0256
## 32  44.07406 48.2051 34.55320 38.3333
## 33  44.00132 49.4872 33.90421 42.1795
## 34  45.00630 51.0256 38.29902 44.1026
## 35  44.44384 45.3846 36.01908 36.4103
## 36  42.17871 42.8205 26.49212 32.5641
## 37  44.04457 38.7179 35.66224 31.4103
## 38  41.64045 35.1282 27.09310 30.2564
## 39  41.93833 32.5641 24.99152 32.1795
## 40  44.05393 30.0000 33.55639 36.7949
## 41  39.20672 33.5897 51.53372 41.4103
## 42  28.70445 36.6667 61.77753 45.6410
## 43  31.70866 38.2051 58.83775 49.1026
## 44  42.81171 29.7436 30.02045 36.0256
## 45  43.30061 29.7436 31.52643 32.1795
## 46  40.39863 30.0000 16.34701 29.1026
## 47  40.43569 32.0513 20.23267 26.7949
## 48  40.93655 35.8974 16.91300 25.2564
## 49  39.66157 41.0256 15.60936 25.2564
## 50  40.89926 44.1026 20.79853 25.6410
## 51  41.96862 47.1795 26.49707 28.7180
## 52  40.38341 49.4872 21.39123 31.4103
## 53  56.53813 51.5385 32.44425 34.8718
## 54  52.97069 53.5897 29.04020 37.5641
## 55  54.62095 55.1282 30.34452 40.6410
## 56  65.09904 56.6667 27.24156 42.1795
## 57  63.05599 59.2308 29.70910 44.4872
## 58  70.96014 62.3077 41.25950 46.0256
## 59  69.89582 64.8718 43.45376 46.7949
## 60  70.59589 67.9487 41.96474 47.9487
## 61  69.64702 70.5128 44.04445 53.7180
## 62  77.39298 71.5385 63.37146 60.6410
## 63  64.40079 71.5385 67.44872 64.4872
## 64  63.86896 69.4872 70.21374 69.4872
## 65  56.59442 46.9231 86.92701 79.8718
## 66  56.53134 48.2051 87.49981 84.1026
## 67  59.65216 50.0000 87.80946 85.2564
## 68  56.63651 53.0769 85.63750 85.2564
## 69  58.67229 55.3846 90.07716 86.0256
## 70  58.22161 56.6667 90.41102 86.0256
## 71  57.91466 56.1538 89.95380 82.9487
## 72  55.31551 53.8462 80.25186 80.6410
## 73  54.57573 51.2821 77.53629 78.7180
## 74  54.41309 50.0000 78.22909 78.7180
## 75  55.07451 47.9487 79.81755 77.5641
## 76  29.43296 29.7436 60.80178 59.8718
## 77  29.42269 29.7436 63.06846 62.1795
## 78  29.00561 31.2821 63.39075 62.5641
## 79  58.46184 57.9487 90.26533 99.4872
## 80  57.99780 61.7949 92.15991 99.1026
## 81  57.54947 64.8718 90.74891 97.5641
## 82  59.52993 68.4615 88.32727 94.1026
## 83  58.24939 70.7692 92.12968 91.0256
## 84  58.02451 72.0513 91.69442 86.4103
## 85  58.38212 73.8462 90.55348 83.3333
## 86  62.56676 75.1282 77.74393 79.1026
## 87  72.17582 76.6667 63.12893 75.2564
## 88  79.47276 77.6923 63.40869 71.4103
## 89  80.35770 79.7436 63.29544 66.7949
## 90  78.75724 81.7949 53.33262 60.2564
## 91  82.54024 83.3333 56.54105 55.2564
## 92  86.43590 85.1282 59.79276 51.4103
## 93  79.48868 86.4103 53.65167 47.5641
## 94  81.53042 87.9487 56.02536 46.0256
## 95  79.18679 89.4872 53.23479 42.5641
## 96  77.89906 93.3333 51.82246 39.8718
## 97  75.13071 95.3846 23.37244 36.7949
## 98  76.05801 98.2051 16.38375 33.7180
## 99  57.61467 56.6667 33.82245 40.6410
## 100 56.17140 59.2308 32.11799 38.3333
## 101 66.28789 60.7692 26.11711 33.7180
## 102 67.88172 63.0769 24.23602 29.1026
## 103 64.02808 64.1026 27.67269 25.2564
## 104 77.49665 64.3590 14.94852 24.1026
## 105 77.63465 74.3590 14.46185 22.9487
## 106 77.86373 71.2821 14.61068 22.9487
## 107 77.33816 67.9487 15.89005 22.1795
## 108 76.18042 65.8974 15.91257 20.2564
## 109 77.25265 63.0769 15.15152 19.1026
## 110 77.41338 61.2821 15.22193 19.1026
## 111 76.73185 58.7179 16.21685 18.3333
## 112 49.47111 55.1282 25.06302 18.3333
## 113 42.47654 52.3077 18.33847 18.3333
## 114 43.59512 49.7436 19.99420 17.5641
## 115 50.33997 47.4359 26.47140 16.0256
## 116 40.74898 44.8718 16.18214 13.7180
## 117 38.38653 48.7179 14.58022 14.8718
## 118 38.40402 51.2821 14.45195 14.8718
## 119 38.76428 54.1026 14.36559 14.8718
## 120 41.47014 56.1538 17.27803 14.1026
## 121 47.15540 52.0513 22.37793 12.5641
## 122 39.58257 48.7179 17.64845 11.0256
## 123 41.74024 47.1795 17.82932  9.8718
## 124 39.31187 46.1538 15.64072  6.0256
## 125 41.67985 50.5128 17.74592  9.4872
## 126 39.08746 53.8462 15.12230 10.2564
## 127 41.48150 57.4359 18.04744 10.2564
## 128 77.60609 60.0000 15.16287 10.6410
## 129 75.98266 64.1026 16.30692 10.6410
## 130 76.94576 66.9231 15.85848 10.6410
## 131 77.54372 71.2821 15.25395 10.6410
## 132 77.58474 74.3590 15.83004 10.6410
## 133 76.82230 78.2051 15.59517 10.6410
## 134 77.34857 67.9487 15.77453  8.7180
## 135 77.57315 68.4615 14.78065  5.2564
## 136 77.97261 68.2051 14.95570  2.9487
## 137 41.52892 37.6923 24.91643 25.7692
## 138 43.72255 39.4872 19.07733 25.3846
## 139 79.32608 91.2821 52.90039 41.5385
## 140 56.66397 50.0000 87.94013 95.7692
## 141 57.82179 47.9487 90.69317 95.0000
## 142 58.24317 44.1026 92.10433 92.6923
library(tibble)
xyc <- xyc %>%
  as_tibble()%>%
  setNames(c("xa","xb","ya","yb"))

save(xyc,file = "xyc.rda")
load("xyc.rda")
#lm analysis & plot
library(stargazer)
## 
## Please cite as:
##  Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
m1 <- lm(ya~yb,data = xyc)
summary(m1)
## 
## Call:
## lm(formula = ya ~ yb, data = xyc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.8637  -5.6448   0.4982   5.7511  16.0482 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.77694    1.24595   1.426    0.156    
## yb           0.96300    0.02272  42.393   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.266 on 140 degrees of freedom
## Multiple R-squared:  0.9277, Adjusted R-squared:  0.9272 
## F-statistic:  1797 on 1 and 140 DF,  p-value: < 2.2e-16
plot(ya ~ yb, data=xyc)+abline(m1)

## integer(0)
m1.1 <- lm(ya~yb+xa+xb, data = xyc)
plot(ya~yb+xa+xb, data = xyc)+abline(m1.1)

## Warning in abline(m1.1): only using the first two of 4 regression coefficients

## integer(0)
summary(m1.1)
## 
## Call:
## lm(formula = ya ~ yb + xa + xb, data = xyc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.6011  -5.3804   0.3701   5.7419  14.6866 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.92862    2.45040   1.195    0.234    
## yb           0.96387    0.02268  42.498   <2e-16 ***
## xa          -0.12259    0.06951  -1.764    0.080 .  
## xb           0.10061    0.06961   1.445    0.151    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.237 on 138 degrees of freedom
## Multiple R-squared:  0.9293, Adjusted R-squared:  0.9278 
## F-statistic: 604.9 on 3 and 138 DF,  p-value: < 2.2e-16
m1.2 <- lm(yb~ya+xa+xb, data = xyc)
plot(yb~ya+xa+xb, data = xyc)+abline(m1.2)

## Warning in abline(m1.2): only using the first two of 4 regression coefficients

## integer(0)
summary(m1.2)
## 
## Call:
## lm(formula = yb ~ ya + xa + xb, data = xyc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.6017  -5.6610   0.4094   4.9404  18.3013 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.92675    2.46174   0.376   0.7072    
## ya           0.96384    0.02268  42.498   <2e-16 ***
## xa           0.12377    0.06949   1.781   0.0771 .  
## xb          -0.10911    0.06952  -1.570   0.1188    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.236 on 138 degrees of freedom
## Multiple R-squared:  0.9294, Adjusted R-squared:  0.9278 
## F-statistic: 605.2 on 3 and 138 DF,  p-value: < 2.2e-16
# 
m2 <- lm(xa~xb,data = xyc)
plot(xa~xb,data = xyc)+abline(m2)

## integer(0)
summary(m2)
## 
## Call:
## lm(formula = xa ~ xb, data = xyc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.510  -6.431   1.335   6.224  18.667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.00721    2.51030    3.19  0.00176 ** 
## xb           0.85251    0.04421   19.28  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.802 on 140 degrees of freedom
## Multiple R-squared:  0.7264, Adjusted R-squared:  0.7245 
## F-statistic: 371.8 on 1 and 140 DF,  p-value: < 2.2e-16
m2.1 <- lm(xa~xb+ya+yb, data = xyc)
plot(xa~xb+ya+yb, data = xyc)+abline(m2.1)

## Warning in abline(m2.1): only using the first two of 4 regression coefficients

## integer(0)
summary(m2.1)
## 
## Call:
## lm(formula = xa ~ xb + ya + yb, data = xyc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -23.1536  -6.3082   0.9232   5.4255  19.3233 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.91777    2.90583   2.725  0.00727 ** 
## xb           0.85266    0.04412  19.327  < 2e-16 ***
## ya          -0.17981    0.10195  -1.764  0.07999 .  
## yb           0.18154    0.10193   1.781  0.07711 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.764 on 138 degrees of freedom
## Multiple R-squared:  0.7327, Adjusted R-squared:  0.7268 
## F-statistic: 126.1 on 3 and 138 DF,  p-value: < 2.2e-16
m2.2 <- lm(xb~xa+ya+yb, data = xyc)
plot(xb~xa+ya+yb, data = xyc)+abline(m2.2)

## Warning in abline(m2.2): only using the first two of 4 regression coefficients

## integer(0)
summary(m2.2)
## 
## Call:
## lm(formula = xb ~ xa + ya + yb, data = xyc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.3163  -6.0470  -0.8473   5.5690  27.6740 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.38661    2.90300   2.889  0.00449 ** 
## xa           0.85640    0.04431  19.327  < 2e-16 ***
## ya           0.14822    0.10255   1.445  0.15062    
## yb          -0.16074    0.10241  -1.570  0.11882    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.783 on 138 degrees of freedom
## Multiple R-squared:  0.7314, Adjusted R-squared:  0.7255 
## F-statistic: 125.2 on 3 and 138 DF,  p-value: < 2.2e-16
# stargazer(m1,m1.1,m1.2,m2,m2.1,m2.2 ,type = "html", out = "xyc.html")

Note: analysis

Through regression analysis,

it is found :

  1. When “ya” is a dependent variable:

“yb” and”xa” are statistically significant for “ya” (“yb” is positively correlated, “xa” is negatively correlated).

  1. When “yb” is a dependent variable:

“ya” and “xa” are statistically significant for “yb” (both “ya” and “xa” are positively correlated). >

  1. When “xa” is a dependent variable:

“ya”, “yb” and “xb” are all statistically significant for “xa” (“yb” and”xb” are positively correlated, and “ya” are negatively correlated).

  1. When “xb” is a dependent variable:

Only “xa” is statistically significant (positive correlation) to “xb”.

  1. comparative analysis:

When comparing regression models from “ad r2”, the explanatory power of “m1.1” and “m1.2” much more better. In other words, the model with “ya” or “yb” as the dependent variable better than others, but the explanatory nature of “xa” is in the opposite direction. It shows a positive effect in the “ya” model and a negative effect in the “yb” model.