Please see the attached file.
You want to develop a model to predict the assessed value of houses, based on heating area. A sample of 15 single-family houses is selected in a city. The assessed value (in thousand of dollars) and the heating area of the houses (in thousands of square feet) are recorded, with the following results, stored in the file HOUSE2.xls(see attached file):
House Assessed Value Heating Area of Dwelling
($000) (Thousands of Square Feet)
1 184.4 2.00
2 177.4 1.71
3 175.7 1.45
4 185.9 1.76
5 179.1 1.93
6 170.4 1.20
7 175.8 1.55
8 185.9 1.93
9 178.5 1.59
10 179.2 1.50
11 186.7 1.90
12 179.3 1.39
13 174.5 1.54
14 183.8 1.89
15 176.8 1.59
(Hint: first,determine which are the independent and dependent variables.)
a) Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients B0 and B1.
b) Interpret the meaning of the Y intercept, B0, and the slope, B1, in this problem.
c) Use the prediction line developed in (a) to predict the assessed value for a house whose heating area is 1,750 square feet.
d) Determine the coefficient of determination, r square(r*r), and interpret its meaning in this problem.
e) Perform a residual analysis on your results and determine the adequacy of the fit of the model.
Using Excel, we obtain the scatterplot and ANOVA table and determine the regression equation. We can then interpret the meaning of the Y intercept, B0, and the slope in this problem. We can then predict the assessed value for a house whose heating area is 1,750 square feet. We also find the coefficient of determination, the percentage of variability in the assessed values of houses explained by the different heating areas. In Excel, we get the residual output as a table and plot.