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 1 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?