A real estate agency collects data concerning y = the sales price of a house (in

Question

A real estate agency collects data concerning y = the sales price of a house (in thousands of dollars), and x = the home size (in hundreds of square feet). The MINITAB output of a simple linear regression analysis of the data set for this case is given in table (below). MINITAB Output of a Simple Linear Regression Analysis of the Real Estate Sales Price Data The regression equation is SPrice = 48.0 + 5.70 HomeSize

Predictor Constant HomeSize 5.7003 0.7457 7.64 0.000 Coef SE Coef T 48.02 14.43.33 0.010 S = 10.5880 R-Sq 88.0% R-Sq(adj) = 86.5% Analysis of Variance Source Regression Residual Error 8896.8 MS 1 6550.7 6550.7 58.43 0.000 112.1 DF SS Total 9 7447.5 Values of Predictors for New Obs New Obs HomeSize 20.0 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% Pl 162.03 3.47 154.04, 170.02) (136.34, 187.72)

Explanation / Answer

Solution:

a) b0 = 48.02, b1=5.7003

b) SSE=896.8

   S=10.588

c) Sb1=0.7457

     t = 7.64

d) For alpha=0.05 and tcrit=2.30 (for 2-tailed test), we see t = 7.64 > tcrit. Hence, H0 is rejected and alternate hypothesis, Ha is true for alpha = 0.05.

e) For alpha=0.01 and tcrit=3.36 (for 2-tailed test), we see t = 7.64 > tcrit. Hence, H0 is rejected and alternate hypothesis, Ha is true for alpha = 0.01.

f) p-value is 0.010 in output.

For alpha = 0.10, it is less than alpha. Hence H0 is rejected.

For alpha = 0.05, it is less than alpha. Hence H0 is rejected.

For alpha = 0.01, it is equal to alpha. Hence H0 is rejected.

For alpha = 0.001, it is greater than alpha. Hence we fail to reject H0.

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