Question 2
In a town, a sample of 24 recently sold houses is collected. We would like to predict the sale
price in ($)/(10000) (Y) using the size of the home in sq. ft./1000 (x_(1)) and the number of
rooms (x_(2)) as predictor variables.
a) Fit the model Y=eta _(0)+eta _(1)x_(1)+eta _(2)x_(2)+epsi lon to the house price data and give the least
squares function.
b) Find the value of SSE that is minimized by the least squares method.
c) Estimate the standard deviation of epsi lon
d) Conduct the ANOVA F-test for model usefulness at the alpha =0.05 significance level
(be sure to specify the null and alternative hypotheses).
e ) Conduct the individual t-tests for eta _(1) and eta _(2) at the alpha =0.05 significance level (be
sure to specify the null and alternative hypotheses).
f ) Find and interpret the coefficient of determination R^(2), and the adjusted
coefficient of determination R^(2).
g ) Which model do you think would be best: a simple linear regression with x_(1) as
the predictor variable, a simple linear regression with x_(2) as the predictor variable,
or the first-order multiple regression model with both x_(1) and x_(2) ?
h) Using the chosen model from part g ), predict the sale price for a 1000 square foot
house with 6 rooms. Give a 95% prediction interval for this estimate.
Question 2
In a town,a sample of 24 recently sold houses is collected. We would like to predict the sale price in $/10000 (Y) using the size of the home in sq.ft./1000(X) and the number of rooms (X) as predictor variables.
) Fit the model Y = o + X + X + to the house price data and give the least squares function. b) Find the value of SSE that is minimized by the least squares method. c) Estimate the standard deviation of d) Conduct the ANOVA F-test for model usefulness at the = 0.05 significance level (be sure to specify the null and alternative hypotheses) e) Conduct the individual t-tests for and 2 at the = 0.05 significance level (be sure to specify the null and alternative hypotheses) f) Find and interpret the coefficient of determination R2, and the adjusted coefficient of determination R2. g) Which model do you think would be best: a simple linear regression with X as the predictor variable, a simple linear regression with X2 as the predictor variable, or the first-order multiple regression model with both X and X2? h) Using the chosen model from part g), predict the sale price for a 1000 square foot house with 6 rooms. Give a 95% prediction interval for this estimate.
Prize 29.5 27.9 25.9 29.9 29.9 30.9 28.9 35.9 31.5 31 30.9 30
Size 1.5 1.175 1.232 1.121 0.988 1.24 1.501 1.225 1.552 0.975 1.121 1.02
Rooms
6 6 6 6 7 6 6 6 5 6 5
36.9 41.9 40.5 43.9 37.5 37.9 44.5 37.9 38.9 36.9 45.8 25.9
1.664 1.488 1.376 1.5 1.256 1.69 1.82 1.652 1.777 1.504 1.831 0.998
8 7 6 7 6 6 8 6 8 7 8 7
