Suppose we have 4 observations for the total construction cost of new houses: $1
ID: 3153947 • Letter: S
Question
Suppose we have 4 observations for the total construction cost of new houses: $10K for one house, $25K for 3 houses, $42K for 5 houses, and $51K for 7 houses.
(a) Please give the least squares regression line for the housing construction costs. Let y be the total construction cost and x be the number of houses.
(b) What is R^2 ?
(c) Consider another regression line: y = $4K + $6K * x. What is R^2 for this regression line?
(d) What conclusion can you make by comparing the results in parts (b) and (c)?
Explanation / Answer
Th regression equation is
y=a+bx
From Excel
The fitted regression is
y=4+7(Number of houses)
b) r2 =0.9859
SUMMARY OUTPUT Regression Statistics Multiple R 0.992933 R Square 0.985915 Adjusted R Square 0.978873 Standard Error 2.645751 Observations 4 ANOVA df SS MS F Significance F Regression 1 980 980 140 0.007067 Residual 2 14 7 Total 3 994 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4 2.711088 1.475422 0.278077 -7.66487 15.66487 -7.66487 15.66487 Number 7 0.591608 11.83216 0.007067 4.454516 9.545484 4.454516 9.545484