1)

b1 * Xbar = 244.4506

2) The relationship is linear. Below is the scatter plot.

(B) If the time spent playing with brick-based construction toys had been recorded in hours per day instead of minutes per day, then the correlation would have been 0.65/60.

(C) When time spent playing with brick-based construction toys (in minutes per day) increases by 1, the average increase in first grade math score is 0.65.

(D) If two childred are selected from those included in the study, then the one with the greater time spent playing with brick-based construction toys will have the higher first grade math score.

(E) Less than half of the variation in first grade math score can be explained by the regression line of first grade math score on time spent playing with brick-based construction toys in nursery school.

Since r=0.65

Hence R

Theefore the answer is E

3)

Please consider the data presented above for the monthly sales of Ever-cool brand of refrigerators in 1,000s of dollars and answer the following questions:

Independent variables are

Price (in dollars); Promotional Expenditure (in 1,000s of dollars); Quality of service (scale of 1-10); location (categorical variable: city area: 1; suburban area: 0).

**A. ** Based on the relevant residual plots, do you see any evidence of violation of assumptions (Linearity, Normality, Equal variance)?

**B. ** State the multiple regression equation and interpret the meaning of the slopes, b1, b2, b3, and b4.

**C. ** At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model. (Based on t - test results)

**D. ** Construct a 95% confidence interval estimate of the population slope between Quality and the monthly sales () (please note that Minitab can’t do this directly, however you may use the relevant information from Minitab output and then construct the confidence interval manually)

**E. ** Perform the overall F- test and comment on the significance of the model.

**Solution**

A)

b1: A unit increase in b1, sales decreases by -0.222, keeping all other variables constant.

b2: A unit increase in b2, sales increases by 2.841, keeping all other variables constant.

b3: A unit increase in b3, sales increases by 0.275, keeping all other variables constant.

b4: A unit increase in b4, sales increases by 3.738, keeping all other variables constant.