McCave Development Enterprises is considering whether to build a shopping mall in Statesville. The manager wants you to analyze the relationship between mall size and the rate of return on invested capital. You select a random sample of 16 cities similar to Statesville in demographic and economic characteristics and collect the following data onFOOTAGE(in 10,000 square feet) andRETURN(rate of return as a %).

RETURN	FOOTAGE	PREDICT
18.3	12.8	15.0
11.7	18.6	7.5
19.5	10.3
17.5	14.3
15.4	14.2
9.8	21.4
11.4	18.6
14.5	16.7
16.3	15.5
19.0	9.8
17.0	14.2
15.1	16.2
19.5	12.8
10.9	19.4
16.3	15.0
16.3	15.4

Regression Analysis: RETURN versus FOOTAGE

The regression equation is

RETURN = 30.0 - 0.943 FOOTAGE

Predictor Coef SE Coef T P

Constant 29.976 1.238 24.22 0.000

FOOTAGE -0.94257 0.07921 -11.90 0.000

S = 0.969721 R-Sq = 91.0% R-Sq(adj) = 90.4%

Analysis of Variance

Source DF SS MS F P

Regression 1 133.15 133.15 141.59 0.000

Residual Error 14 13.17 0.94

Total 15 146.31

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI

1 15.838 0.244 (15.315, 16.360) (13.693, 17.982)

2 22.907 0.666 (21.479, 24.334) (20.384, 25.429)X

X denotes a point that is an outlier in the predictors.

Values of Predictors for New Observations

New Obs FOOTAGE

1 15.0

2 7.5

Correlations: RETURN, FOOTAGE

Pearson correlation of RETURN and FOOTAGE = -0.954

P-Value = 0.000

a. Analyze the above output to determine the regression equation.

b. Find and interpretin the context of this problem.

c. Find and interpret the coefficient of determination (r-squared).

d. Find and interpret coefficient of correlation.

e. Does the data provide significant evidence (a= .05) that Footage can be used to predict Return? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.

f. Find the 95% confidence interval for the mean rate of return on capital investment for malls that have square footage of 150,000. Interpret this interval.

g. Find the 95% prediction interval for the rate of return on capital investment for a mall that has square footage of 150,000. Interpret this interval.

h. What can we say about the rate of return on capital investment for a mall that has square footage of 75,000?