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Question: Correlations: PRICE, HOUSESIZE Pearson correlation of PRICE and HOUSESIZE = 0.971 P-Value = 0.000 Regression Analysis: PRICE versus...
Question:
Correlations: PRICE, HOUSESIZE
Pearson correlation of PRICE and HOUSESIZE = 0.971
P-Value = 0.000
Regression Analysis: PRICE versus HOUSESIZE
The regression equation is
PRICE = 11730 + 54.6 HOUSESIZE
Predictor Coef SECoef T P
Constant 11730 1098 1.06 0.321
HOUSESIZE 54.576 4.717 11.57 0.000
S = 6676.82 R-Sq = 94.4% R-Sq(adj) = 93.7%
Analysis of Variance
Sourc DF SS MS F P
Regression 1 5968960529 5968960529 33.89 0.000
Residual Error 8 356639471 4579934
Total 9 6325600000
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 120881 2568 (114959, 126804) (104385, 137378)
2 230033 8246 (211018, 249048) (205566, 254500)XX
XX denotes a point that is an extreme outlier in the predictors.
Values of Predictors for New Observations
New Obs HOUSESIZE
1 2000
2 4000
a. Analyze the above output to determine the regression equation.
b. Find and interpret β1 in 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) the house size can be used to predict the selling price? 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 mean selling price for homes that are 2000 square feet in size. Interpret this interval.
g. Find the 95% prediction interval for the selling price of a single home that is 2000 square feet in size. Interpret this interval.
h. What can we say about the selling price for a home that is 4,000 sq. ft in size?
