(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 school- ing, schooling, schooling, and schooling. 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?

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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5.3

 

Let's dig more deeply into whether the relationship between earnings and schooling is approximately linear.

schooling
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
earnings
12.5572
12.37059
12.28345
12.53942
13.60204
13.69685
14.46392
15.48792
16.58223
17.75331
18.31583
18.93581
20.69255
22.40492
23.55711
25.12731
30.9133
30.25502
31.35148
31.24208
34.62525
Transcribed Image Text:schooling 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 earnings 12.5572 12.37059 12.28345 12.53942 13.60204 13.69685 14.46392 15.48792 16.58223 17.75331 18.31583 18.93581 20.69255 22.40492 23.55711 25.12731 30.9133 30.25502 31.35148 31.24208 34.62525
your
(a) Start by making a scatter plot. Then plot the predicted values from y
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?
300 (b) Now run a fourth-order polynomial regression (i.e., include school-
ing, schooling², schooling, and schooling. 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?
Transcribed Image Text:your (a) Start by making a scatter plot. Then plot the predicted values from y 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? 300 (b) Now run a fourth-order polynomial regression (i.e., include school- ing, schooling², schooling, and schooling. 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?
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