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? GPAs, 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. Score GPA Hours Absences
68 2.53 3 0
69 2.26 4 3
70 2.6 2.5 1
72 3.09 0.5 0
74 3.08 6 4
76 2.74 3.5 5
77 3.35 1.5 0
78 2.99 3 3
79 2.99 2 3
78 2.84 2.5 2
79 2.8 4.5 0
81 3.43 7 1
82 3.26 3 1
85 3.15 3 4
83 3.19 5.5 0
84 2.96 2 0
84 2.7 4 1
84 3.21 4.5 3
85 3.75 2 0
84 3.57 3.5 2
86 2.92 6 1
86 3.03 6.5 1
85 3.17 5 3
88 3.88 7.5 4
87 3.55 4 0
88 3.34 6.5 1
90 3.65 5 0
89 2.87 3.5 1
91 3.39 6 1
91 3.2 4.5 2
91 3.81 7 0
92 3.93 6 2
93 3.99 5 0
92 3.59 6.5 1
93 2.98 4 2
93 3.26 6.5 0
98 2.89 3.5 0
98 3.71 5 1
101 3.48 6.5 1
99 3 7 0
a. Construct a regression model using all three independent variables. Let y be the final exam? scores, x1 be the? GPAs, x2 be the number of hours spent? studying, and x3 be the number of absences during the semester.
= ( )+( )x_{1}+( )x_{2}+( )x_{3}
?(Round to three decimal places as? needed.)
b. Calculate the multiple coefficient of determination.
R^{2}=
?(Round to three decimal places as? needed.)
c. Test the significance of the overall regression model using alpha=0.05
State the null and alternative hypotheses. Choose the correct answer below.
A. H0?: At least one betainot equals0 ?(Relationship exists between the? variables)
H1?: beta1equalsbeta2equalsbeta3equals0 ?(No relationship between the? variables)
B. H0?: beta1equalsbeta2equalsbeta3 (No relationship between the? variables)
H1?: beta1not equalsbeta2not equalsbeta3 ? (Relationship exists between the? variables)
C. H0?: beta1equalsbeta2equalsbeta3equals0 ?(No relationship between the? variables)
H1?: At least one beta inot equals0 ?(Relationship exists between the? variables)
D. H0?: beta 1not equalsbeta2not equalsbeta3 (Relationship exists between the? variables)
H1?: beta 1equalsbeta2equalsbeta 3 (No relationship between the? variables)
Identify the value of the test statistic.
F= ?(Round to one decimal place as? needed.)
Calculate the? p-value.
The? p-value is ?(Round to three decimal places as? needed.)
State the conclusion. Choose the correct answer below.
A. Since the? p-value is less than alpha?, reject the null hypothesis. The overall regression model is significant at the alpha= 0.05 significance level.
B. Since the? p-value is greater than alpha?, do not reject the null hypothesis. The overall regression model is not significant at the alpha=0.05
significance level.
C. Since the? p-value is greater than alpha ?, do not reject the null hypothesis. The overall regression model is significant at the alpha=0.05 significance level.
D. Since the? p-value is less than alpha?, reject the null hypothesis. The overall regression model is not significant at the alpha=0.05 significance level.
d. Calculate the adjusted multiple coefficient of determination. R^{2}_{A}= (Round to three decimal places as? needed.)