You want to develop a model to predict the taxes of houses, based on assessed value. A sample of 30 single family houses listed for sale in Silver Spring, Maryland, a suburb of Washington, DC, is selected. The taxes (in $) and the assessed value of the houses (in $ thousands) are recorded and stored in SilverSpring.
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 mean taxes for a house whose assessed value is $ 400,000.
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 taxes and assessed value?