Your Code

You have been asked to create regression models in the Module Two Problem Set. Review the Problem Set Report template to see the questions you will be answering about your models.

Use the empty blocks below to write the R code for your models and get outputs. Then use the outputs to answer the questions in your problem set report.

Note: Use the + (plus) button to add new code blocks or the scissor icon to remove empty code blocks, if needed.

In[12]:

Edit Metadata

# Step 1: Loading the Data Set# Loading mtcars data set from a mtcars.csv filemtcars # Converting appropriate variables to factors mtcars2 # Print the first six rowsprint("head")head(mtcars2, 6)?# Step 2: Subsetting Data and Correlation Matrixmyvars # Print the first six rowsprint("head")head(mtcars_subset, 6)?# Print the correlation matrixprint("cor")corr_matrix # Step 3: Multiple Regression With Interaction Term# Create the multiple regression model and print summary statistics. Note that this model includes the interaction term.model1 # Step 4: Adding in a Qualitative Predictor# Subsetting data to only include the variables that are neededmyvars # Create the modelmodel2 # Step 5: Fitted Values# Predicted valuesprint("fitted")fitted_values # Step 6: Residuals# Residualsprint("residuals")residuals # Step 7: Diagnostic Plots ? Residuals against Fitted Valuesplot(fitted_values, residuals, main = "Residuals against Fitted Values", xlab = "Fitted Values", ylab = "Residuals", col="red", pch = 19, frame = FALSE)?# Step 8: Diagnostic Plots ? Q-Q Plotqqnorm(residuals, pch = 19, col="red", frame = FALSE)qqline(residuals, col = "blue", lwd = 2)?# Step 9: Confidence Interval for Parameter Estimates# Confidence intervals for model parametersprint("confint")conf_90_int # Step 10: Predictions, Prediction Interval, and Confidence Intervalnewdata

[1] "head"

car	mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
Mazda RX4	21.0	6	160	110	3.90	2.620	16.46	0	1	4	4
Mazda RX4 Wag	21.0	6	160	110	3.90	2.875	17.02	0	1	4	4
Datsun 710	22.8	4	108	93	3.85	2.320	18.61	1	1	4	1
Hornet 4 Drive	21.4	6	258	110	3.08	3.215	19.44	1	0	3	1
Hornet Sportabout	18.7	8	360	175	3.15	3.440	17.02	0	0	3	2
Valiant	18.1	6	225	105	2.76	3.460	20.22	1	0	3	1

[1] "head"

mpg	wt	drat
21.0	2.620	3.90
21.0	2.875	3.90
22.8	2.320	3.85
21.4	3.215	3.08
18.7	3.440	3.15
18.1	3.460	2.76

[1] "cor"

	mpg	wt	drat
mpg	1.0000	-0.8677	0.6812
wt	-0.8677	1.0000	-0.7124
drat	0.6812	-0.7124	1.0000

Call: lm(formula = mpg ~ wt + drat + wt:drat, data = mtcars_subset) Residuals: Min 1Q Median 3Q Max -3.8913 -1.8634 -0.3398 1.3247 6.4730 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.550 12.631 0.439 0.6637 wt 3.884 3.798 1.023 0.3153 drat 8.494 3.321 2.557 0.0162 * wt:drat -2.543 1.093 -2.327 0.0274 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.839 on 28 degrees of freedom Multiple R-squared: 0.7996, Adjusted R-squared: 0.7782 F-statistic: 37.25 on 3 and 28 DF, p-value: 6.567e-10

Call: lm(formula = mpg ~ wt + drat + wt:drat + am, data = mtcars_subset) Residuals: Min 1Q Median 3Q Max -3.6907 -1.4711 -0.2512 0.9344 6.7453 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.247 12.914 0.251 0.8034 wt 4.168 3.822 1.091 0.2851 drat 9.562 3.529 2.710 0.0116 * am1 -1.464 1.597 -0.917 0.3674 wt:drat -2.708 1.111 -2.438 0.0216 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.847 on 27 degrees of freedom Multiple R-squared: 0.8057, Adjusted R-squared: 0.7769 F-statistic: 27.99 on 4 and 27 DF, p-value: 2.948e-09

[1] "fitted"

1

22.3202071012681

2

20.6895074959298

3

24.0747502539664

4

19.2785936167189

5

18.3566004049746

6

18.1948543136102

7

17.7829147976458

8

19.9455031142101

9

20.4155783618075

10

18.5453485011573

11

18.5453485011573

12

15.7244271929934

13

17.1343818387994

14

16.9270355673574

15

11.4830468223862

16

10.468474335848

17

9.65079623894033

18

25.654703888853

19

34.0906848946004

20

28.8096807794287

21

24.1983096753214

22

17.9964150947557

23

18.378418393557

24

16.124985574862

25

16.6489676538974

26

27.4785433498266

27

27.3857668975878

28

28.6890131121626

29

19.1154587119623

30

20.7842398534528

31

16.2835591339497

32

21.7238845270116

[1] "residuals"

1

-1.32020710126808

2

0.310492504070191

3

-1.2747502539664

4

2.12140638328108

5

0.343399595025413

6

-0.0948543136101894

7

-3.48291479764585

8

4.45449688578988

9

2.38442163819248

10

0.654651498842696

11

-0.745348501157303

12

0.675572807006601

13

0.16561816120057

14

-1.72703556735736

15

-1.08304682238617

16

-0.068474335848017

17

5.04920376105967

18

6.74529611114699

19

-3.69068489460044

20

5.09031922057126

21

-2.69830967532141

22

-2.49641509475568

23

-3.17841839355699

24

-2.82498557486204

25

2.55103234610262

26

-0.178543349826627

27

-1.38576689758782

28

1.71098688783741

29

-3.31545871196233

30

-1.08423985345285

31

-1.28355913394969

32

-0.323884527011619

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