This exercise uses data on 850 houses sold in Baton Rouge, Louisiana during mid-2005. We will be concerned with the selling price in thousands of dollars (PRICE), the size of the house in hundreds of square feet (SQFT), the number of bathrooms (BATHS), and the number of bedrooms (BEDS). Consider the following conditional expectations

a. Express \(\alpha_{1}\) and \(\alpha_{2}\) in terms of the parameters \(\left(\beta_{1}, \beta_{2}, \beta_{3}, \gamma_{1}, \gamma_{2}\right)\).

b. Express \(\beta_{1}, \beta_{2}\), and \(\beta_{3}\) in terms of the parameters \(\left(\delta_{1}, \delta_{2}, \delta_{3}, \delta_{4}, \theta_{1}, \theta_{2}, \theta_{3}\right)\).

c. Use the information in Table 6.11 and a \(1 \%\) significance level to test whether

d. Show that the estimates in Table 6.11 satisfy the expressions you derived in parts (a) and (b).

e. Can you explain why the coefficient of BEDS changed sign when \(S Q F T\) was added to equation (XR6.12.1).

f. Suppose that \(E(B A T H S \mid B E D S)=\lambda_{1}+\lambda_{2} B E D S\). Use the results in Table 6.11 to find estimates for \(\lambda_{1}\) and \(\lambda_{2}\).

g. Use the estimates from part (f) and the estimates for equations (XR6.12.3) and (XR6.12.4) to find estimates of \(\alpha_{1}\) and \(\alpha_{2}\). Do they agree with the estimates in Table 6.11?

h. Would you view any of the parameter estimates as causal?

Transcribed Image Text:

E(PRICE|BEDS) = + BEDS (XR6.12.1) E(PRICE|BEDS, SQFT) = B + BBEDS + 3SQFT (XR6.12.2) E(SQFT BEDS) = Y+YBEDS (XR6.12.3) E(PRICE|BEDS, SQFT, BATHS) = 8 + 8BEDS + 83SQFT+8BATHS (XR6.12.4) E(BATHS BEDS, SQFT) = 0 +0BEDS +03SQFT (XR6.12.5)