# The estimated regression equation - Expert Work

The estimated regression equation is not explaining about 67 percent of the variation of sales price (dependent variable). The search continues for additional statistically significant explanatory variables. The distance of homes for sale from the city center may be relevant in explaining the variation in the sales price of homes. A potential fourth explanatory variable (x4) has been included in the Real Estate Data workbook to make it easy to put together a scatterplot, simple regression equation and multiple regression equation. On the Computer (Insert (Scatterplot) & Tools/Data Analysis/Regression)

(a) What is your expectation about the direction of the relationship between sales price and distance from the center of the city?
(b) Construct and evaluate the scatterplot between sales price and distance from the city center.
(c) Estimate a simple regression between daily sales (y) and distance from the city center (x4). Using all the tests (including a hypothesis test on the slope coefficient), provide a written evaluation of the estimated simple regression equation.
(d) Estimate the multiple regression equation (include square footage, number of bedrooms, number of bathrooms, distance from the center of the city).
(e) Conduct individual hypothesis tests (alpha=.05) to determine if any of the explanatory variables can be dropped from the estimated multiple regression equation.
(f) Conduct a global hypothesis test (F-Test) to verify the overall statistical significance (p-value =.05) of the estimated multiple regression equation in part d.

(g) If any variables should be dropped from the multiple regression equation, re-run and repeat parts e and f.
(h) Provide an overall written evaluation of your final multiple regression equation justifying your decision. Is the explanatory variable distance from the city center a worthwhile addition to the multiple regression equation?
(i) Based on the final regression equation (you decide), forecast the sales price for a home which is 3,950 square feet has 4 bedrooms and 3 bathrooms, and is located 21 miles from the center of the city.