Table Q6 Data contains data on sale prices of the 37 recent sales (within the last six months) in a mid-sized town. In addition to the log of sale price, you have data on the home size (square feet), the number of bedrooms, whether the home has a garage ("yes" is coded as 1), and whether the home is in the northern, allegedly more expensive, part of town ("yes" is coded as 1).

(a) Find the OLS line for predicting the sale price from the assessed value using all 37 properties. Report the regression results in tab Q6a Results and test the variables for significance. How many degrees of freedom do you use for these hypothesis tests? Be sure to include an interpretation of the coefficients of the significant variables in the space below.

(b) Test the model as a whole with the null hypothesis that none of the included explanatory variables are significant. In your test, write out both the null and alternative hypotheses as well as the results of your test. Report your results in the space below.

Property Log of Sale Price Log of Square Feet # Bedrooms Garage North 1 12.395 7.114769448 3 1 0 2 12.181 6.895682698 4 0 0 3 12.666 7.192934221 4 1 1 4 12.958 7.35436233 4 1 1 5 12.926 7.424761762 5 1 0 6 12.810 7.062191632 5 0 0 7 12.606 7.177018766 5 0 0 8 12.762 7.184629153 5 1 1 9 12.111 7.089243155 4 0 0 10 12.716 7.291656209 5 1 0 11 12.731 7.349230825 4 1 0 12 12.106 6.957497371 2 0 0 13 12.679 7.279318835 5 1 0 14 12.822 7.122866659 2 1 1 15 12.931 7.271703707 5 1 0 16 12.515 7.183111702 3 1 0 17 12.225 7.106606138 3 0 0 18 12.403 6.802394763 3 1 0 19 12.652 6.881411304 4 0 0 20 12.944 7.254177846 4 1 0 21 12.239 7.076653815 3 0 0 22 12.821 7.242082359 4 1 1 23 12.833 7.419979924 4 1 0 24 12.525 6.80461452 2 0 0 25 12.708 7.069023427 3 0 0 26 12.601 7.10824414 3 1 0 27 12.628 7.149916836 4 0 0 28 12.533 7.338888134 3 1 0 29 12.857 7.353081921 6 0 0 30 13.027 7.273092596 5 1 0 31 12.433 6.963189986 3 0 0 32 12.975 7.22329568 4 0 0 33 12.950 7.363279587 4 1 0 34 12.553 7.0800265 3 0 0 35 12.901 7.255591274 5 1 0 36 12.417 6.931471806 3 0 1 37 12.641 7.049254841 3 0 0