You want to develop a model to predict the assessed value of houses, based on heating area. A sample of 15 single-family houses in a city is selected. The assessed value (in $thousands) and the heating area of the houses (in thousands of square feet) are recorded and stored in House2.
a. Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and bx.
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, r2, and interpret its meaning in this problem.
e. Perform a residual analysis on your results and evaluate the regression assumptions.
f. At the 0.05 level of significance, is there evidence of a linear relationship between assessed value and heating area?