These are .R type files.... to be used in RStudio or I prefer Minitab the lines are 1-54 with empty spaces numbered but blank. The Data is in the next section below it is copied from excel. DO NOT post "Missing data: Reference", it's not...you don't know how this works or you're not familiar with .R files...that's all, skip it and let someone else do it.

Class Exercise .R file below:

# install packages if needed install.packages("ggplot2") # load packages if needed library(ggplot2) # read data initech <- read.csv(file.choose()) # select initech.csv # hisogram of variables hist(initech$years) hist(initech$salary) # scatterplot of variables ggplot(initech, aes(x = years, y = salary)) + geom_point() + theme_bw() + geom_smooth(method=lm, color="blue", fill="red") # Simple regression model: salary by years reg1Initech <- lm(salary ~ years, data=initech) # regression results summary(reg1Initech) # examine model fit plot(reg1Initech) # Add fit residuals and predictions to data frame initech$RegPred <- predict(reg1Initech) initech$RegResid <- residuals(reg1Initech) # residuals vs IV ggplot(initech, aes(x = years, y = RegResid)) + geom_point() + geom_abline(slope = 0, intercept = 0) + theme_bw() # examine prediction and confidence intervals temp_var <- predict(reg1Initech, interval="prediction") initech <- cbind(initech, temp_var) ggplot(initech, aes(years, salary))+ geom_point() + theme_classic() + geom_line(aes(y=lwr), color = "red", linetype = "dashed")+ geom_line(aes(y=upr), color = "red", linetype = "dashed")+ geom_smooth(method=lm, color="blue", fill="purple", se=TRUE) # make predictions use2predict <- data.frame(years=4) predict(reg1Initech, use2predict, interval="confid") # use "confid" for confidence interval, "predict" for prediction interval.

Data Set below from .csv file copied over from excel:

Years	Salary
1	41504
1	32619
1	44322
2	40038
2	46147
2	38447
2	38163
3	42104
3	25597
3	39599
3	55698
4	47220
4	65929
4	55794
4	45959
5	52460
5	60308
5	61458
5	56951
6	56174
6	59363
6	57642
6	69792
7	59321
7	66379
7	64282
7	48901
8	100711
8	59324
8	54752
8	73619
9	65382
9	58823
9	65717
9	92816
9	72550
10	71365
10	88888
10	62969
10	45298
11	111292
11	91491
11	106345
11	99009
12	73981
12	72547
12	74991
12	139249
13	119948
13	128962
13	98112
13	97159
14	125246
14	89694
14	73333
14	108710
15	97567
15	90359
15	119806
15	101343
16	147406
16	153020
16	143200
16	97327
17	184807
17	146263
17	127925
17	159785
17	174822
18	177610
18	210984
18	160044
18	137044
19	182996
19	184183
19	168666
19	121350
20	193627
20	142611
20	170131
20	134140
21	129446
21	201469
21	202104
21	220556
22	166419
22	149044
22	247017
22	247730
23	252917
23	235517
23	241276
23	197229
24	175879
24	253682
24	262578
24	207715
25	221179
25	212028
25	312549

In the script file,lines 9-18 can be used to answer the first 3 questions below:

Question 1

Do the variables seem normally distributed?

1. Yes
2. No

Question 2

Which of the below issues do you see with the data (if any)?

1. Non-linearity
2. Heteroscedasticity
3. Multicollinearity
4. Non-independence of observations

Question 3

For any identified in the two responses above, how would you correct them? (try some different transformations and see what seems to work best).

1. Squaring or cubing salary
2. Squaring or cubing years
3. -1/salary
4. -1/years
5. sqrt(salary)
6. sqrt(years)
7. log(salary)
8. log(years)

Next, run through the rest of the code to get answers to questions 4-9. You will need to make adjustments to lines 51-52 to answer questions 8 and 9.

Question 4

In Model 1, is the IV significant?

1. Yes
2. No

Question 5

In reporting the results of Model 1, how much of the variance of salary would we say was accounted for by the model (report as a percentage rounded to 1 decimal place)?

______________%

Question 6

What do you notice after looking at the scatterplot plus the regression line and confidence intervals? Does it look like the model performs equally well across all values of the IV?

__________________________________________________________________________________

Question 7

Do you notice anything amiss looking at the plot of the residuals vs the predicted values?

______________________________________________________________________________

Question 8

What does your model predict regarding the average salary of all employees with 15 years of experience at the 95% confidence level?

1. 95% confident it's between $129,207.40 and $140,495.10
2. It's exactly $134851.30
3. 95% confident it's between $80,273.37 and $189,429.20

Question 9

What does your model predict regarding the salary of a single employee with 6 years of experience at the 95% confidence level?

1. 95% confident it's between $49,461.75 and $164,781.75
2. It's exactly $57,121.75
3. 95% confident it's between $2,298.69 and $111,944.80

Now run the regression of log(salary) by years. You will need to adjust the necessary code lines to change occurrences of years to log(years) to answer questions 10-15:

Question 10

Now run the regression of log(salary) by years. Is the IV significant?

1. Yes
2. No

Question 11

In reporting the results of Model 1, how much of the variance of salary would we say was accounted for by the model (report as a percentage rounded to 1 decimal place)?

__________%

Question 12

What do you notice after looking at the scatterplot plus the regression line and confidence intervals? Does it look like the model performs equally well across all values of the IV?

___________________________________________________________________________________

Question 13

Do you notice anything amiss looking at the plot of the residuals vs the predicted values?

___________________________________________________________________________________

Question 14

What does your model predict regarding the average salary of all employees with 10 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're 95% confident it's between $75,390 and $82,024
2. It's exactly $78,637
3. We're 95% confident it's between $53,233 and $116,165

Question 15

What does your model predict regarding the salary of a single employee with 12 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're confident it's between $88,538 and $95,754
2. It's exactly $92,075
3. We're confident $62,350 and $135,973

Now run the regression of log(salary) by sqrt(years) for questions 16-21:

Question 16

Now run the regression of log(salary) by sqrt(years). Is the IV significant?

1. Yes
2. No

Question 17

In reporting the results of Model 1, how much of the variance of salary would we say was accounted for by the model (report as a percentage rounded to 1 decimal place)?

_______________%

Question 18

What do you notice after looking at the scatterplot plus the regression line and confidence intervals? Does it look like the model performs equally well across all values of the IV?

________________________________________________________________________________

Question 19

Do you notice anything amiss looking at the plot of the residuals vs the predicted values?

________________________________________________________________________________

Question 20

What does your model predict regarding the average salary of all employees with 5 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're 95% confident that it is between $51,176 and $58,035
2. It's exactly $54,498
3. We're 95% confident that it is between $35,535 and $83,580

Question 21

What does your model predict regarding the salary of a single employee with 21 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're 95% confident it's between $166,678 and $188,438
2. It's exactly $177,225
3. We're 95% confident that it's between $115,584 and $271,738

Now run the regression of salary by sqrt(years) for questions 22-28:

Question 22

Now run the regression of salary by sqrt(years). Is the IV significant?

1. Yes
2. No

Question 23

In reporting the results of Model 1, how much of the variance of salary would we say was accounted for by the model (report as a percentage rounded to 1 decimal place)?

_____________%

Question 24

What do you notice after looking at the scatterplot plus the regression line and confidence intervals? Does it look like the model performs equally well across all values of the IV?

_____________________________________________________________________________________

Question 25

Do you notice anything amiss looking at the plot of the residuals vs the predicted values?

_____________________________________________________________________________________

Question 26

What does your model predict regarding the average salary of all employees with 19 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're 95% confident that it's between $157,927 and $175,108
2. It's exactly $166,518
3. We're 95% confident that it's between $100,357 and $232,678

Question 27

What does your model predict regarding the average salary of all employees with 4 years of experience at the 95% confidence level? (note: order of operations and rounding could lead to slight variations in your answers. Pick the answer below that most closely matches your finding).

1. We're 95% confident that it's between $30,503 and $52,198
2. It's exactly $41,351
3. We're 95% confident that it's between $0 (prediction is -$25,140) and $107842

Question 28

Which of the 4 models that you ran would you say performs the best and why?

__________________________________________________________________________________