Residential real estate prices depend, in part, on property size and number of b
ID: 2931881 • Letter: R
Question
Residential real estate prices depend, in part, on property size and number of bedrooms. The house size X1 (in hundreds of square feet), number of bedrooms X2, and house price Y (in thousands of dollars) of a random sample of houses in a certain county were observed. The data are listed in the following table ( = 0.05) House House size (X) Number of bedrooms (%) House price (Y) 2 20 95 18 25 17 3 89 19 80 104 110 175 85 PLease provide SAS codes and SAS outputs with the answer. If using another computer program, PLease include those codes and outputs. b) Perform the overall F test for the regression of Y on both independent variables. Interpret your result.Explanation / Answer
## By using Minitab:
MTB > Regress 'Y' 2 'X1' 'X2';
SUBC> Constant;
SUBC> Brief 2.
Regression Analysis: Y versus X1, X2
The regression equation is
Y = - 16.1 + 5.72 X1 - 1.2 X2
Predictor Coef SE Coef T P
Constant -16.09 24.65 -0.65 0.549
X1 5.722 1.828 3.13 0.035
X2 -1.17 13.39 -0.09 0.934
S = 11.9624 R-Sq = 90.9% R-Sq(adj) = 86.4%
Analysis of Variance
Source DF SS MS F P
Regression 2 5733.3 2866.7 20.03 0.008
Residual Error 4 572.4 143.1
Total 6 6305.7
From the Above Ananlysis of variance table
The P value is 0.008<0.05 hence we reject the null hypothesis that the model is not signifiacant.
That is the model is significant. Which means the coeficients are are not both equal to zero.
Both the P values for the coefficints X1 is 0.035<0.05 indicated that the House Size significantly related to House of Price.
Here R-Sq = 90.9% which indicates that the 90.9% variability in the response is explins by predictors.
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