Question 5 (24 points):

In a multiple linear regression study, we want to test whether scores on a performance test (y) are related to scores on a test of manual dexterity (X1), visual perception (x2), mechanical ability (x3), physical efficiency (), and reaction time (X5) to a stimulus. A portion of the analysis of variance table for the results of the experiment appears below.

Source of variation

Regression

Degrees of freedom

Sum of squares

Means of squares

Residuals

10

145,22

Total

522,23

Complete the analysis of variance table by indicating the missing values. Based on the results of the ANOVA table, does the hypothesis H hold at the 5% significance level? Explain. Note: your explanation should provide H1, the value of F, the decision rule, and your decision/conclusion. What percentage of variation in the performance test scores is explained by all five explanatory variables? What is the name of this measure? What is the standard deviation of the residuals?