Question

The following table was generated from the sample data of 10 college students regarding the number of parking tickets the student receives in a semester, the student's age, and the student's GPA. The dependent variable is the student's GPA, the first independent variable (x1) is the number of parking tickets, and the second independent variable (x2) is the student's age.

Intercept   2.120785   2.284291   0.928421   0.395800
Number of Parking Tickets   -0.337479   0.066991   -5.037686   0.003975
Student's Age   0.127003   0.116260   1.092403   0.324473

Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places.

Step 2 of 2: Indicate if any of the independent variables could be eliminated at the 0.05 level of significance.

Answer 1

## Q ) The following table was generated from the sample data of 10 college students regarding the number of parking tickets the student receives in a semester, the student's age, and the student's GPA. The dependent variable is the student's GPA, the first independent variable (x1) is the number of parking tickets, and the second independent variable (x2) is the student's age.

Answer :

We have given output of the multiple regression model :

y = dependent variable = student's GPA

x1 = first independent variable =  the number of parking tickets and

x2 = second independent variable = the student's age

Coefficient std error t stat p value

Intercept 2.120785 2.284291 0.928421 0.395800
Number of Parking Tickets   - 0.337479 0.066991 -5.037686 0.003975
Student's Age 0.127003 0.116260 1.092403 0.324473

Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places.

Answer : Estimated multiple  regression model :

ŷ = b0 + b1 *x1 + b2 * x2

where b0 = y intercept =  2.120785 ie 2.121

b1 = first slope =  - 0.337479 ie - 0.337

b2 = second slope =   0.127003 ie 0.127

ŷ = b0 + b1 *x1 + b2 * x2  

ŷ  =  2.121 - ( 0.337 * x1 ) + ( 0.127 * x2)

### Step 2 of 2: Indicate if any of the independent variables could be eliminated at the 0.05 level of significance.

Answer :

1 ) Test for first independent variable : or first slope : β1

To test :

Ho : β1 = 0 vs H1: β1 ≠ 0  

Test statistics : t = - 5.037686

p value = 0.003975

α = level of significance = 5 % = 0.05

Decision :

We reject Ho if p value is less than  α value using p value approach here p value is less than α value

we reject Ho at given level of significance .

Conclusion :

There is sufficient evidence to conclude that β1 is significant at given level of significance .

## 2 ) Test for second  independent variable : or second   slope : β2

To test :

Ho : β2 = 0 vs H1: β2 ≠ 0  

Test statistics : t = 1.092403   

p value = 0.324473

α = level of significance = 5 % = 0.05

Decision :

We reject Ho if p value is less than  α value using p value approach here p value is greater  than  α value

we fail to reject Ho at given level of significance .

Conclusion :

There is Insufficient evidence to conclude that β2 is significant at given level of significance .

# here variable second   Student's Age is not significant hence it should be eliminate .