The data in the table give the square footages and sales prices of n = 12 houses randomly selected from those sold in a small city. Use the MINITAB printout to answer the questions.

Plot of data for Exercise 12.42

MINITAB output for Exercise 12.42
Regression Analysis: y versus x
The regression equation is
y = 251206 + 27.4 x
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a. Can you see any pattern other than a linear relationship in the original plot?
b. The value of r 2 for these data is .957. What does this tell you about the fit of the regression line?
c. Look at the accompanying diagnostic plots for these data. Do you see any pattern in the residuals? Does this suggest that the relationship between price and square feet is something other than linear?
Diagnostic plots for Exercise 12.42

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Square Feet, x Price,y Square Feet, x Price, y 1460 2108 1743 1499 1864 2391 $288,700 309,300 301,400 291,100 302,400 314,900 1977 1610 1530 1759 1821 2216 $305,400 297,000 292,400 298,200 304,300 311,700 315,000 310,.000 305,000 300,000- 295,000 290,000 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 x (Square Feet) Predictor Constant Coef 251206 27.406 SE Coef 3389 1.828 74.13 14.99 0.000 0.000 S1792.72 R-Sq 95.7% R-Sq (adj ) -95 . 3% Predicted Values for New Observations Fit SE Fit New Obs 2 Values of Predictors for New Observations 95.0% CI 95 . 0% pi 299989 306018 526 (299817, 30111) (295826, 304151) 602 (304676, 307360) (301804, 310232) New Obs 1780 2000 2 Normal Probability Plot of the Residuals (response is y) 95- 90 80 70 60 30 10 50004000 3000 20001000 01000 2000 3000 4000 Residual Residuals versus the Fitted Values (response is y) 3000 2000 1000 0 -1000 -2000- -3000 290,000 295,00O 300,000 305,000 310,000 315,000 320,000 Fitted Value