Unless otherwise specified, round all your answers to three decimal places.

(a) Let y be the sales per sq. ft, x1 be the median income (in thousands of dollars), and x2 be the number of competitors. Here we will assume the population model:

y = 0 + 1x1+ 2x2

Use Fit Model to find the fitted model. In lab 4 you already wrote the fitted model and saved the output.

(b) Check all four assumptions for the model in part 2a. For each assumption indicate which graph is used

to check this assumption. Also indicate whether the assumption has been met. Finally, provide an

the explanation for why the assumption is met or not met. For multiple regression, we check the same set of

assumptions as in simple linear regression. (Hint: To create these plots we must first save the residuals and the predicted values from the multiple regression model.)

(i) Independence: Graph used to check assumption:

Determine if there are any concerns with this assumption. Provide explanation:

(ii) Form of the model: Graph used to check assumption:

Determine if there are any concerns with this assumption. Provide explanation:

(iii) Constant Variance: Graph used to check assumption:

Determine if there are any concerns with this assumption. Provide explanation:

(iv) Normality: Graph: Graph used to check assumption:

Determine if there are any concerns with this assumption. Provide explanation:

(c) Create and interpret a 98% confidence interval for the slope associated with the median income.

(d) Find the RMSE for this fitted multiple regression model. Interpret this value using a 99.7% level. Be sure to include the context of the data.

(e) Based on the multiple regression model, interpret the estimate for the slope associated with median income.

(f) (Model 3) Conduct a hypothesis test to determine if there is evidence of a negative linear relationship between the number of competitors and annual sales per square foot even after accounting for the median income. Record all steps in the space below (null and alternative hypothesis, test statistic, p-value, and conclusion in the context of the example).

(g) (Model 2 and Model 3) Provide a statistical explanation for the observed differences in p-values and the conclusions reached Hint: be careful about the subscript on the parameter tested in the null and alternative hypothesis.

(h) (Model 1, Model 2, and Model 3) Comment on the R2 values for the two simple linear regression models

4. In the multiple regression model we explain percent more of the variability in the sales per square foot in the women's retail store using both explanatory variables median income and number of competitors, compared to the percent of the variability in the sales per square foot explain when using the simple linear regression model with explanatory variable Median income.

(j) (Model 3) Based on the multiple regression model, report the predicted value for 2 different locations the first location is in a community with a median income of with other competitors.

The data is here below. ($464.00 is under sales, 60 : income and 1: competitors; that's the format)

Sales ($/sq. ft),Income ($000),Competitors

$464.00, 60 ,1

$552.00,61,1

$377.00,52,1

$674.00,67,1

$560.00,63,1

$523.00,61,1

$546.00,60,1

$569.00,61,0

$579.00,58,0

$502.00,56,1

$615.00,62,0

$551.00,52,1

$400.00,54,1

$434.00,58,1

$534.00,54,0

$500.00,51,0

$475.00,58,0

$521.00,71,0

$490.00,60,3

$455.00,72,2

$486.00,61,3

$551.00,77,3

$577.00,69,3

$514.00,70,3

$509.00,48,2

$609.00,71,2

$531.00,57,3

$359.00,55,3

$503.00,59,3

$521.00,58,2

$554.00,74,2

$475.00,54,3

$473.00,51,2

$834.00,86,2

$459.00,63,3

$346.00,59,2

$709.00,83,3

$310.00,54,2

$477.00,77,3

$587.00,76,3

$430.00,54,3

$504.00,53,2

$559.00,62,3

$464.00,64,2

$457.00,50,2

$475.00,63,2

$534.00,66,3

$377.00,61,3

$400.00,62,2

$609.00,86,4

$611.00,83,4

$504.00,61,4

$458.00,59,5

$304.00,52,5

$640.00,90,5

$485.00,66,4

$538.00,83,4

$437.00,62,4

$767.00,91,5

$358.00,64,5

$486.00,70,5

$404.00,54,4

$562.00,69,4

$487.00,68,4

$839.00,105,6