(a) Start by making a scatter plot. Then plot the predicted values from your regression along with the raw data points, as we did in chapter 2. Does the regression line look like it's fitting the data well? (b) Now run a fourth-order polynomial regression (i.e., include schooling, schooling 2, schooling 3, and schooling 4. Do those predictions meaningfully differ from the predictions coming from the linear regression? (c) Now run different regressions for some different ranges of schooling. Do those lines look meaningfully different from the predictions you get from a single regression including all the data? (d) Does all this make you think the simple linear approach was reasonable or unreasonable? \begin{tabular}{|c|c|} \hline schooling & earnings \\ \hline 0 & 12.5572 \\ \hline 1 & 12.37059 \\ \hline 2 & 12.28345 \\ \hline 3 & 12.53942 \\ \hline 4 & 13.60204 \\ \hline 5 & 13.69685 \\ \hline 6 & 14.46392 \\ \hline 7 & 15.48792 \\ \hline 8 & 16.58223 \\ \hline 9 & 17.75331 \\ \hline 10 & 18.31583 \\ \hline 11 & 18.93581 \\ \hline 12 & 20.69255 \\ \hline 13 & 22.40492 \\ \hline 14 & 23.55711 \\ \hline 15 & 25.12731 \\ \hline 16 & 30.9133 \\ \hline 17 & 30.25502 \\ \hline 18 & 31.35148 \\ \hline 19 & 31.24208 \\ \hline 20 & 34.62525 \\ \hline \end{tabular} 3 Let's dig more deeply into whether the relationship between earnings and schooling is approximately linear. (a) Start by making a scatter plot. Then plot the predicted values from your regression along with the raw data points, as we did in chapter 2. Does the regression line look like it's fitting the data well? (b) Now run a fourth-order polynomial regression (i.e., include schooling, schooling 2, schooling 3, and schooling 4. Do those predictions meaningfully differ from the predictions coming from the linear regression? (c) Now run different regressions for some different ranges of schooling. Do those lines look meaningfully different from the predictions you get from a single regression including all the data? (d) Does all this make you think the simple linear approach was reasonable or unreasonable? \begin{tabular}{|c|c|} \hline schooling & earnings \\ \hline 0 & 12.5572 \\ \hline 1 & 12.37059 \\ \hline 2 & 12.28345 \\ \hline 3 & 12.53942 \\ \hline 4 & 13.60204 \\ \hline 5 & 13.69685 \\ \hline 6 & 14.46392 \\ \hline 7 & 15.48792 \\ \hline 8 & 16.58223 \\ \hline 9 & 17.75331 \\ \hline 10 & 18.31583 \\ \hline 11 & 18.93581 \\ \hline 12 & 20.69255 \\ \hline 13 & 22.40492 \\ \hline 14 & 23.55711 \\ \hline 15 & 25.12731 \\ \hline 16 & 30.9133 \\ \hline 17 & 30.25502 \\ \hline 18 & 31.35148 \\ \hline 19 & 31.24208 \\ \hline 20 & 34.62525 \\ \hline \end{tabular} 3 Let's dig more deeply into whether the relationship between earnings and schooling is approximately linear