Univariate linear regression Note: Solutions to this problem must follow the method described in class and the linear regression
handout. There is some flexibility in how your solution is coded, but you may not use special functions that automatically perform linear regression for you. Load in the BodyBrain Weight.csv dataset. Perform linear regression using two different models: M1: brain_weight = w0 + w1 x body_weight M2: brain_weight = w0 + w1 x body_weight + w2 x body_weight2
a. For each model, follow the steps shown in class to solve for w. Report the model, including w values and variable names for both models.
b. Use subplots to display two graphs, one for each model. In each graph, include: • Labeled x and y axes • Title • Scatterplot of the dataset • A smooth line representing the model
c. For each model, calculate the sum squared error (SSE). Show your 2 SSE values together in a bar plot.
d. Which model do you think is better? Why? Is there a different model that you think would better represent the data?
Body weight (kg) Brain weight (g)
0.023 0.4
0.048 0.33
0.075 1.2
0.12 1
0.122 3
0.2 5
0.28 1.9
0.55 2.4
0.75 12.3
0.785 3.5
0.93 3.5
1.04 5.5
1.35 8.1
1.41 17.5
2.5 12.1
3 25
3.3 25.6
3.6 21
4.288 39.2
5.3 41.6
6.8 179
10 115
10.55 179.5
27.66 115
35 56
36.33 119.5
52.16 440
55.5 175
60 81
62 1320
85 325
93 225
100 157
110 288
110 442
187.1 419
192 180
207 406
250 334
465 423
480 712
521 655
529 680
1400 590
2547 4603
6654 5712
a. For each model, follow the steps shown in class to solve for w. Report the model, including w values and variable names for both models.
b. Use subplots to display two graphs, one for each model. In each graph, include: • Labeled x and y axes • Title • Scatterplot of the dataset • A smooth line representing the model
c. For each model, calculate the sum squared error (SSE). Show your 2 SSE values together in a bar plot.
d. Which model do you think is better? Why? Is there a different model that you think would better represent the data?
Body weight (kg) Brain weight (g)
0.023 0.4
0.048 0.33
0.075 1.2
0.12 1
0.122 3
0.2 5
0.28 1.9
0.55 2.4
0.75 12.3
0.785 3.5
0.93 3.5
1.04 5.5
1.35 8.1
1.41 17.5
2.5 12.1
3 25
3.3 25.6
3.6 21
4.288 39.2
5.3 41.6
6.8 179
10 115
10.55 179.5
27.66 115
35 56
36.33 119.5
52.16 440
55.5 175
60 81
62 1320
85 325
93 225
100 157
110 288
110 442
187.1 419
192 180
207 406
250 334
465 423
480 712
521 655
529 680
1400 590
2547 4603
6654 5712
1 answer:
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