2. Estimate the following population model using the data set in the chart below

Question

2. Estimate the following population model using the data set in the chart below.

colGPA=?_0+?_1 age+?_2hsGPA+?_3 skipped+?_4 alcohol+u

where “colGPA” is a student’s college GPA

“age” is the student’s age

“hsGPA” is the student’s high school GPA

“skipped” is average lectures skipped per week

“alcohol” is average days per week the student drinks alcohol

(i) Report your estimated model and briefly discuss (no need to formally conduct a “four step” hypothesis test) the sign, significance and magnitude of the estimated coefficients.

(ii) Conduct a four-step F-test for the joint significance of alcohol and age.

(iii) Estimate the model (using the same data):

colGPA=?_0+?_1 age+?_2hsGPA+u

and then

colGPA=?_0+?_1 age+u

(a) Report your two estimated equations.

age colGPA hsGPA skipped alcohol 21 3 3 2 1 21 3.4 3.2 0 1 20 3 3.6 0 1 19 3.5 3.5 0 0 20 3.6 3.9 0 1.5 20 3 3.4 0 0 22 2.7 3.5 0 2 22 2.7 3 3 3 22 2.7 3 2 2.5 19 3.8 4 0.5 0.75 21 2.8 3 2 1 22 2.9 3.1 1 1 21 3 3.5 0 1 20 2.9 3.8 3 2.5 20 3.3 3.7 1 4 22 2.6 3 3 3.5 19 2.5 3.5 4 3 22 2.5 3 5 5 20 2.4 3 2 4 21 3.6 3.5 1 5 20 2.6 3.5 3 2 22 2.7 3 1 1 20 2.9 3.6 1 1 21 3 4 0 0 20 3.3 3.6 2 5 20 3.1 3.3 1 1 20 3 3.6 2 1 20 3.2 3.1 1 2 20 3 3.4 0 2 20 3.4 3.7 0.5 2 21 2.9 3.7 1 2 21 3.5 3.3 1 0 22 3.7 3.3 0 1 20 3.5 3.5 0 1 21 2.8 3.2 1 3 21 2.5 3.3 1 1 21 3.1 3.4 0.5 1 20 3.5 3.5 1 3 20 3.4 3.4 0.5 0 21 3.5 3.7 0 2 21 2.6 2.5 1 1 21 2.8 3.7 0 2 21 2.6 3 2 3 20 3.5 3 1 3 22 4 4 0 0.5 20 3.8 3.8 1 3 19 2.8 3 4 2 21 3.5 3.7 1 2 21 3 3.4 2 1 21 2.6 2.4 1 2 21 3 3.8 1 2 22 3.7 4 1 2 19 3 3.5 0 2 19 3 3.5 0 2 20 2.9 3.4 1 3 20 2.6 3.6 1 0 22 3 3.2 2 5 21 3.3 3.8 0.5 1 22 2.7 3.3 2 3 21 3 3.4 0 1 21 3.2 3 0 0 20 2.7 3.6 1 3 21 3.6 3.9 1 2 21 2.4 3 2 3 21 2.9 3 1 2 21 3.3 3.3 1 1 20 3.5 3.3 0.5 1.5 21 3 3.2 2 3 21 3 3.4 2 3 21 2.8 3.7 0 1 21 2.9 3.4 0 2 22 3.8 3.9 2 7 20 2.5 3.6 2 1 21 3 4 1 4 20 3.2 3.6 1 2 21 2.2 3 0 1 30 3.4 2.8 0 0 22 2.9 3.2 0 3 22 3.7 2.9 1 5 20 2.9 2.9 1 0.5 23 2.8 3.6 0.5 1 22 3.2 3.4 1 2 21 3.4 3.6 0.5 2 22 3 3.2 2 1 22 2.5 3.2 2 1 21 3.5 3.2 1 3 21 3.1 3.7 1 4 21 2.8 2.9 0 7 21 2.9 3.3 1 2 21 2.9 3.1 2 3 19 3.4 3.5 0 1 20 3.4 3.5 0 1.5 22 3.6 3.7 3 3 26 3.2 3 0.25 0.5 20 3.2 3.8 1 2 21 2.8 3.3 0 0.5 20 3.1 3.6 0 1 20 2.8 3.2 1 2 21 2.7 3.5 0 3 20 3 3.7 0 2

Explanation / Answer

First copy data in Excel then copy it in Excel
then run following command:(In R-console)

a=read.table("clipboard",header=T)
attach(a)
l1=lm(colGPA~age+hsGPA+skipped+alcohol)
l2=lm(colGPA~age+hsGPA+skipped+alcohol+age*alcohol)
l3=lm(colGPA~age+hsGPA)
l4=lm(colGPA~age)
summary(l1)
summary(l2)
summary(l3)
summary(l4)

The output is given by:

> summary(l1)

Call:
lm(formula = colGPA ~ age + hsGPA + skipped + alcohol)

Residuals:
Min 1Q Median 3Q Max
-0.75791 -0.21932 -0.00071 0.25609 0.73591

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.70631 0.72714 0.971 0.33384   
age 0.03830 0.02514 1.523 0.13105   
hsGPA 0.47250 0.10617 4.450 2.33e-05 ***
skipped -0.10436 0.03588 -2.909 0.00452 **
alcohol 0.02987 0.02514 1.188 0.23771   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3282 on 95 degrees of freedom
Multiple R-squared: 0.2764, Adjusted R-squared: 0.2459
F-statistic: 9.07 on 4 and 95 DF, p-value: 3.003e-06

> summary(l2)

Call:
lm(formula = colGPA ~ age + hsGPA + skipped + alcohol + age *
alcohol)

Residuals:
Min 1Q Median 3Q Max
-0.76168 -0.21234 -0.00877 0.26882 0.70961

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.850665 0.828078 1.027 0.30693   
age 0.031724 0.030877 1.027 0.30684   
hsGPA 0.472177 0.106664 4.427 2.58e-05 ***
skipped -0.105247 0.036122 -2.914 0.00446 **
alcohol -0.124566 0.418069 -0.298 0.76639   
age:alcohol 0.007278 0.019665 0.370 0.71215   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3297 on 94 degrees of freedom
Multiple R-squared: 0.2774, Adjusted R-squared: 0.239
F-statistic: 7.217 on 5 and 94 DF, p-value: 9.315e-06

> summary(l3)

Call:
lm(formula = colGPA ~ age + hsGPA)

Residuals:
Min 1Q Median 3Q Max
-0.65337 -0.22120 -0.02659 0.26047 0.85673

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.29249 0.73215 0.399 0.6904   
age 0.04427 0.02587 1.711 0.0902 .  
hsGPA 0.54373 0.10661 5.100 1.68e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3389 on 97 degrees of freedom
Multiple R-squared: 0.2119, Adjusted R-squared: 0.1956
F-statistic: 13.04 on 2 and 97 DF, p-value: 9.647e-06

> summary(l4)

Call:
lm(formula = colGPA ~ age)

Residuals:
Min 1Q Median 3Q Max
-0.86165 -0.26165 -0.06165 0.33835 0.93188

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 2.925765 0.581584 5.031 2.21e-06 ***
age 0.006471 0.027768 0.233 0.816   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3797 on 98 degrees of freedom
Multiple R-squared: 0.0005538, Adjusted R-squared: -0.009645
F-statistic: 0.0543 on 1 and 98 DF, p-value: 0.8162

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