A sample of 30 recently sold single-family houses in a small city is selected. Develop a model to predict the selling price (in thousands of dollars), using the assessed value (in thousands of dollars) as well as time (in months since reassessment). The houses in the city had been reassessed at full value one year prior to the study. The results are stored in House1.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the selling price for a house that has an assessed value of $$\$ 170,000$$ and was sold 12 months after reassessment.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Determine whether there is a significant relationship between selling price and the two independent variables (assessed value and time period) at the 0.05 level of significance.
f. Determine the $p$-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted $r^2$.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the $p$-values in (i) and interpret their meaning.
k. Construct a $95 \%$ confidence interval estimate of the population slope between selling price and assessed value. How does the interpretation of the slope here differ from that in Problem 13.76 on page 565 ?
1. Compute and interpret the coefficients of partial determination.