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The document details a series of linear regression analyses performed on a dataset named 'trixdataap', focusing on the relationships between GDP, GB, and education (ED). Multiple models are created, including simple linear regressions and a multiple linear regression, with significant coefficients and high R-squared values indicating strong relationships. Additionally, diagnostic tests for model assumptions are conducted, and various transformations of the data are applied.

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Vanshika Agrawal
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51 views22 pages

Apurvareport

The document details a series of linear regression analyses performed on a dataset named 'trixdataap', focusing on the relationships between GDP, GB, and education (ED). Multiple models are created, including simple linear regressions and a multiple linear regression, with significant coefficients and high R-squared values indicating strong relationships. Additionally, diagnostic tests for model assumptions are conducted, and various transformations of the data are applied.

Uploaded by

Vanshika Agrawal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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> View(trixdataap)

> attach(trixdataap)
> names(trixdataap)
[1] "gdp" "gb" "ed"
> plot(gb,ed,main="scatterplot")
> model<-lm(gb~gdp)
> summary(model)

Call:
lm(formula = gb ~ gdp)

Residuals:
Min 1Q Median 3Q Max
-58756 -21418 1015 20553 75134

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.389e+04 9.299e+03 3.645 0.00094 ***
gdp 1.401e+00 6.070e-02 23.079 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 32570 on 32 degrees of freedom


Multiple R-squared: 0.9433, Adjusted R-squared: 0.9416
F-statistic: 532.7 on 1 and 32 DF, p-value: < 2.2e-16
> attributes(model)
$names
[1] "coefficients" "residuals" "effects" "rank" "fitt
ed.values" "assign" "qr"
[8] "df.residual" "xlevels" "call" "terms" "mode
l"

$class
[1] "lm"

> model$coefficients
(Intercept) gdp
33889.196597 1.400879
> plot(gb,eb,main="scatterplot")
Error: object 'eb' not found
> plot(gb,ed,main="scatterplot")
> abline(model)
> abline(model,col=2)
> abline(model,col=3,lwd=5)
> confint(model,level=0.99)
0.5 % 99.5 %
(Intercept) 8424.975808 59353.4174
gdp 1.234658 1.5671

> anova(model)
Analysis of Variance Table

Response: gb
Df Sum Sq Mean Sq F value Pr(>F)
gdp 1 5.6509e+11 5.6509e+11 532.66 < 2.2e-16 ***
Residuals 32 3.3948e+10 1.0609e+09
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> plot(gdp,ed,main="scatterplot")

abline(model)
> abline(model,col=2)
> abline(model,col=3,lwd=5)
> confint(model,level=0.99)
0.5 % 99.5 %
(Intercept) 8424.975808 59353.4174
gdp 1.234658 1.5671
> anova(model)
Analysis of Variance Table

Response: gb
Df Sum Sq Mean Sq F value Pr(>F)
gdp 1 5.6509e+11 5.6509e+11 532.66 < 2.2e-16 ***
Residuals 32 3.3948e+10 1.0609e+09
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> modeltwo<-lm(gdp~ed)
> summary(modeltwo)

Call:
lm(formula = gdp ~ ed)

Residuals:
Min 1Q Median 3Q Max
-35405 -13536 -6295 8045 47072

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.800e+04 4.911e+03 5.701 2.59e-06 ***
ed 5.477e-02 2.061e-03 26.571 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19750 on 32 degrees of freedom


Multiple R-squared: 0.9566, Adjusted R-squared: 0.9553
F-statistic: 706 on 1 and 32 DF, p-value: < 2.2e-16
> attributes(modeltwo)
$names
[1] "coefficients" "residuals" "effects" "rank" "fitt
ed.values" "assign" "qr"
[8] "df.residual" "xlevels" "call" "terms" "mode
l"

$class
[1] "lm"

> model$coefficients
(Intercept) gdp
33889.196597 1.400879
> modeltwo$coefficients
(Intercept) ed
2.799590e+04 5.476692e-02
MULTILINEAR
> model<-lm(gdp+gb~ed)
> summary(model)

Call:
lm(formula = gdp + gb ~ ed)

Residuals:
Min 1Q Median 3Q Max
-75032 -28373 3886 26176 55714

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.651e+04 8.896e+03 10.85 2.98e-12 ***
ed 1.342e-01 3.734e-03 35.93 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 35780 on 32 degrees of freedom


Multiple R-squared: 0.9758, Adjusted R-squared: 0.9751
F-statistic: 1291 on 1 and 32 DF, p-value: < 2.2e-16

> confint(model,level=0.99)
0.5 % 99.5 %
(Intercept) 7.214898e+04 1.208745e+05
ed 1.239258e-01 1.443758e-01
> anova(model)
Analysis of Variance Table

Response: gdp + gb
Df Sum Sq Mean Sq F value Pr(>F)
ed 1 1.6528e+12 1.6528e+12 1290.9 < 2.2e-16 ***
Residuals 32 4.0972e+10 1.2804e+09
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> predicted_value<-predict(model)
> trixdataap$predicted_y<-predicted_value
> residuals<-residuals(model)
> trixdataap$residuals<-residuals
hist(residuals)
logy<-log(ed)
> trixdataap$logy<-logy
> logx1<-log(gdp)
> trixdataap$logx1<-logx1
> logx2<-log(gb)
> trixdataap$logx2<-logx2
> logmodel=lm(formula=logy~logx1+logx2,data=trixdataap)
> logmodel

Call:
lm(formula = logy ~ logx1 + logx2, data = trixdataap)

Coefficients:
(Intercept) logx1 logx2
-2.9611 0.6659 0.7662

> summary(logmodel)

Call:
lm(formula = logy ~ logx1 + logx2, data = trixdataap)

Residuals:
Min 1Q Median 3Q Max
-0.27240 -0.11768 -0.02842 0.14019 0.24657

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.9611 0.6765 -4.377 0.000127 ***
logx1 0.6659 0.1050 6.342 4.65e-07 ***
logx2 0.7662 0.1430 5.360 7.65e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1559 on 31 degrees of freedom


Multiple R-squared: 0.9805, Adjusted R-squared: 0.9793
F-statistic: 780.1 on 2 and 31 DF, p-value: < 2.2e-16

> attributes(logmodel)
$names
[1] "coefficients" "residuals" "effects" "rank" "fitt
ed.values" "assign" "qr"
[8] "df.residual" "xlevels" "call" "terms" "mode
l"

$class
[1] "lm"
> pred_y<-predict(model)
> trixdataap$pred_y
NULL
Warning message:
Unknown or uninitialised column: `pred_y`.
> trixdataap$haty<-pred_y
> pred_logy<-predict(logmodel)
> trixdataap$hatlny<-pred_logy
> trixdataap$ln_haty<-log(trixdataap$haty)
> trixdataap$z1<-trixdataap$ln_haty-trixdataap$hatlny
> model2<-lm(ed~gdp+gb+trixdataap$z1)
> summary(model2)

Call:
lm(formula = ed ~ gdp + gb + trixdataap$z1)

Residuals:
Min 1Q Median 3Q Max
-422202 -90940 7833 31899 535105

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -48859.243 132588.636 -0.369 0.715
gdp 11.479 1.714 6.699 2.01e-07 ***
gb 6.378 1.072 5.951 1.60e-06 ***
trixdataap$z1 700167.518 131882.671 5.309 9.73e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 195400 on 30 degrees of freedom


Multiple R-squared: 0.9875, Adjusted R-squared: 0.9863
F-statistic: 791.8 on 3 and 30 DF, p-value: < 2.2e-16
> trixdataap$antilog_hatlny<-exp(trixdataap$hatlny)
> trixdataap$z2<-trixdataap$antilog_hatlny-trixdataap$haty
> model3<-lm(trixdataap$logy~trixdataap$logx1+trixdataap$logx2+trixdataap$
z2)
> summary(model3)

Call:
lm(formula = trixdataap$logy ~ trixdataap$logx1 + trixdataap$logx2 +
trixdataap$z2)
Residuals:
Min 1Q Median 3Q Max
-0.26135 -0.10803 -0.03487 0.13318 0.27059

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.804e+00 1.280e+00 -1.409 0.168992
trixdataap$logx1 6.665e-01 1.048e-01 6.361 5.1e-07 ***
trixdataap$logx2 6.638e-01 1.721e-01 3.857 0.000565 ***
trixdataap$z2 5.058e-08 4.756e-08 1.064 0.295999
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1556 on 30 degrees of freedom


Multiple R-squared: 0.9812, Adjusted R-squared: 0.9793
F-statistic: 522.7 on 3 and 30 DF, p-value: < 2.2e-16
> install.packages("lmtest")
WARNING: Rtools is required to build R packages but is not currently insta
lled. Please download and install the appropriate version of Rtools before
proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/HP/AppData/Local/R/win-library/4.4’
(as ‘lib’ is unspecified)
trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/lmtest_0.9-40
.zip'
Content type 'application/zip' length 411446 bytes (401 KB)
downloaded 401 KB

package ‘lmtest’ successfully unpacked and MD5 sums checked

The downloaded binary packages are in


C:\Users\HP\AppData\Local\Temp\RtmpOuWpqe\downloaded_packages
> library(lmtest)
Loading required package: zoo

Attaching package: ‘zoo’

The following objects are masked from ‘package:base’:

as.Date, as.Date.numeric

Warning message:
package ‘lmtest’ was built under R version 4.4.3
> bptest(model)

studentized Breusch-Pagan test

data: model
BP = 2.5669, df = 1, p-value = 0.1091
dwtest(model)

Durbin-Watson test

data: model
DW = 0.48078, p-value = 6.115e-09
alternative hypothesis: true autocorrelation is greater than 0

> install.packages("car")
WARNING: Rtools is required to build R packages but is not currently insta
lled. Please download and install the appropriate version of Rtools before
proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/HP/AppData/Local/R/win-library/4.4’
(as ‘lib’ is unspecified)
also installing the dependencies ‘rbibutils’, ‘cowplot’, ‘Deriv’, ‘microbe
nchmark’, ‘Rdpack’, ‘numDeriv’, ‘doBy’, ‘SparseM’, ‘MatrixModels’, ‘minqa’
, ‘nloptr’, ‘reformulas’, ‘RcppEigen’, ‘carData’, ‘abind’, ‘Formula’, ‘pbk
rtest’, ‘quantreg’, ‘lme4’

trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/rbibutils_2.3


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Content type 'application/zip' length 1032620 bytes (1008 KB)
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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/RcppEigen_0.3


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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/carData_3.0-5


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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/Formula_1.2-5


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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/pbkrtest_0.5.


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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/quantreg_6.1.


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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/lme4_1.1-37.z


ip'
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trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.4/car_3.1-3.zip


'
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The downloaded binary packages are in


C:\Users\HP\AppData\Local\Temp\RtmpOuWpqe\downloaded_packages
> library(car)
Loading required package: carData
Warning messages:
1: package ‘car’ was built under R version 4.4.3
2: package ‘carData’ was built under R version 4.4.3
>vif(model)
gdp gb
22.144629 18.023133

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