A social scientist would like to predict perceived conflict resolution skill level from a set of fivepredictor variables for a sample of 36 teachers. A multiple linear regression analysis wasconducted. Complete the following ANOVA summary table for the test of significance of theoverall regression model. Except for the P-value, report all answers accurate to 3 decimal places;report the P-value accurate to 4 decimal places. Use a significance level of a = 0.02.SourcedfMSFP-valueRegression25Residual398TOTALWhat is your decision for the hypothesis test?O Reject the null hypothesis, Ho: B1 = B2 = ... = Bs = 0O Fail to reject HoWhat is your final conclusion?OThe evidence supports the claim that one or more of the regression coefficients is non-zeroOThe evidence supports the claim that all of the regression coefficients are zeroOThere is insufficient evidence to support the claim that at least one of the regressioncoefficients is non-zeroOThere is insufficient evidence to support the claim that all of the regression coefficients areequal to zero00

Answered: A social scientist would like to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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Question

A social scientist would like to predict perceived conflict resolution skill level from a set of five
predictor variables for a sample of 36 teachers. A multiple linear regression analysis was
conducted. Complete the following ANOVA summary table for the test of significance of the
overall regression model. Except for the P-value, report all answers accurate to 3 decimal places;
report the P-value accurate to 4 decimal places. Use a significance level of a = 0.02.
Source
df
MS
F
P-value
Regression
25
Residual
398
TOTAL
What is your decision for the hypothesis test?
O Reject the null hypothesis, Ho: B1 = B2 = ... = Bs = 0
O Fail to reject Ho
What is your final conclusion?
OThe evidence supports the claim that one or more of the regression coefficients is non-zero
OThe evidence supports the claim that all of the regression coefficients are zero
OThere is insufficient evidence to support the claim that at least one of the regression
coefficients is non-zero
OThere is insufficient evidence to support the claim that all of the regression coefficients are
equal to zero
00

Expert Solution

Step 1

Given:

Number of predictor variables k=5

sample size n=36

Degrees of freedom:

The degrees of freedom for regression is calculated below:

$\begin{array}{rcl} d f (R e g r e s s i o n) & = & k \\ = & 5 \end{array}$

Thus, the degrees of freedom for regression is 5

The degrees of freedom for residuals is calculated below:

$\begin{array}{rcl} d f (R e s i d u a l s) & = & n - (k + 1) \\ = & n - k - 1 \\ = & 36 - 5 - 1 \\ = & 30 \end{array}$

Thus, the degrees of freedom for residuals is 30

The degrees of freedom for total is calculated below:

$\begin{array}{rcl} d f (T o t a l) & = & n - 1 \\ = & 36 - 1 \\ = & 35 \end{array}$

Thus, the degrees of freedom for total is 35

Step 2

Sum of Squares:

The sum of squares for regression is calculated as below:

$\begin{array}{rcl} S S (R e g r e s si o n) & = & M S (R e g r e s s i o n) \times d f (R e g r e s s i o n) \\ = & 25 \times 5 \\ = & 125 \end{array}$

Thus, the sum of squares for regression is 125

The sum of squares of Total is calculated as below:

$\begin{array}{rcl} S S (T o t a l) & = & S S (R e g r e s s i o n) + S S (R e s i d u a l) \\ = & 125 + 398 \\ = & 523 \end{array}$

Thus, the sum of squares of Total is 523

Mean sum of squares:

The Mean sum of squares for residual is calculated as below:

$\begin{array}{rcl} M S (R e s i d u a l) & = & \frac{S S (R e s i d u a l)}{d f (R e s i d u a l)} \\ = & \frac{398}{30} \\ = & 13.267 \end{array}$

Thus, the Mean sum of squares for residual is 13.267.

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