Question

A business statistics professor at a college would like to develop a regression model to predict the final exam scores for students based on their current GPS, the number of hours they studied for the exam and the number of times they were absent during the semester. The data for these variables are in the accompanying table Complete parts a through d below. ERE Click the icon to view the table of data a. Constructa regression models independent variables. Let y be the final am scores, x, be the GPA , be the number of hours spent studying, and x, be the number of absences during the (Round to three decimal places as needed) b. Calculate the multicolor of determination R. (Round to the decimal places as needed.) c. Tout the cance of the overal regression modeling 0.10 Sunted have the Choose the correct ans DAHA how the ans ) erbs) OBH , he H Och H o the w the variable) Click to set your new

Answer 1

using R we have the following out put

Residuals:
Min 1Q Median 3Q Max
-11.1095 -4.0849 -0.5934 3.0743 16.2962

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 54.2128 8.7088 6.225 3.48e-07 ***
GPA 7.5710 2.8522 2.654 0.01175 *
Hours 1.8888 0.6360 2.970 0.00528 **
Absences -1.0837 0.7172 -1.511 0.13950
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.514 on 36 degrees of freedom
Multiple R-squared: 0.4571,   Adjusted R-squared: 0.4119
F-statistic: 10.11 on 3 and 36 DF, p-value: 5.707e-05

a) $\hat{y} = 54.213 +7.571 x_{1}+1.889 x_{2} -1.084 x_{3}$

b ) Multiple R-squared: 0.457

c ) option c is correct

F = 10.1

p value is 0.000

A ) p value is less than alpha , reject the null hypothesis . the overalll regression modal is significant  

d )  Adjusted R-squared: 0.412