Question
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
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?
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