The following data was collected to explore how the average number of hours a student studies per night and the student's gpa affect their act score. the dependent variable is the act score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's gpa. effects on act scoresstudy hours gpa act score6 2 313 4 285 2 192 4 292 4 20
1. find the p-value for the regression equation that fits the given data. round your answer to four decimal.

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 HoursGPAACT 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!

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1