Answer:
Step-by-step explanation:
Hello!
The given data is for multiple regression with two independent variables:
Y= α + β₁X₁ + β₂X₂
Y: ACT score of a student
X₁: Number of hours spent studying.
X₂: Student's GPA
Effects on ACT Scores
Study Hours GPA ACT Score
6 2 31
3 4 28
5 2 19
2 4 29
2 4 20
Using a statistical software I've estimated the regression line:
Y= -37.57 + 7.14X₁ + 11.64X₂
1)Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
The p-value for the multiple regression (One-Tailed F-test-ANOVA-) is 0.5045
2)Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, it indicates that there is not enough evidence to show that the relationship is statistically significant.
The hypotheses for the multiple regression is:
H₀: β₁ = β₂ = 0
H₁: At least one βi≠0 ∀ i=1, 2
α: 0.01
Since the p-value= 0.5045 is greater than α: 0.0, the decision is to not reject the null hypothesis, this means that there is no significant evidence to say that there is a relationship between the ACT scores and the student's GPA and hours that the student spent studying.
The individual tests are:
(remember to have validity the individual tests should be made at the same α level)
H₀: β₁ = 0
H₁: β₁ ≠ 0
α: 0.01
ANOVA: p-value: 0.2977
The decision is to not reject the null hypothesis.
At a level of 1%, there is no evidence to support the hypothesis that the number of hours spent by studying doesn't modify the average ACT of students.
H₀: β₂ = 0
H₁: β₂ ≠ 0
α: 0.01
ANOVA: p-value: 0.3038
The decision is to not reject the null hypothesis.
At a level of 1%, there is no evidence to support the hypothesis that the student's GPA doesn't modify the average ACT of students.
None of the independent variables, together or individually, are effective to explain the variability of the ACT scores of the students in the study.
I hope this helps!
