Question

A personnel specialist with a large accounting firm is interesting in determining the effect of seniority (the number of years with the company) on hourly wages for secretaries. She selects a random sample of 10 secretaries and collects the following data on their years with the company (X) and hourly wages (Y):

                 X                  Y    

                 0                  12

                 2                  13

                 3                  14

                 6                  16

                 5                  15

                 3                  14

                 4                  13

                 1                  12

                 1                  15

                 2                  15   

1. Draw a scatter plot of the data.
2. Calculate the regression slope and Y-intercept.
3. Draw the regression line on the scatter plot.
4. Predict the hourly wage of a randomly selected secretary who has been with the company for 4 years.
5. Find the coefficients of determination and non-determination and interpret what they mean.
6. Based on these results, what is the typical starting wage per hour, and what is the typical increase in wage for each additional year on the job?

Answer 1

Given that,

X=0,2,3,6,5,3,4,1,1,2
y=12,13,14,16,15,14,13,12,15,15

a) Scatter plot between X & Y isb) regression slope and Y-intercept is,

Y= 0.4579*x + 12.6636

c) the regression line on the scatter plot is,

d) Prediction of the hourly wage of a randomly selected secretary who has been with the company for 4 years is

0.4579* 4 + 12.6636 = 14.49533

e) Coefficients of determination is

R^2= SSR/RSS=sum((y^2-mean(y^))^2) / sum((y-mean(y))^2) = 6.731776/ 16.9 =0.3983~0.40 means our model based upon given data can explained only 40% variation in Y by X.

f) Typical increase in wage for each additional year on the job is 0.4579

Note: I have done this problem in R. So, I am attaching my R-code for your refrence as below:

x=c(0,2,3,6,5,3,4,1,1,2)
y=c(12,13,14,16,15,14,13,12,15,15)
plot(x,y)
model<-lm(y~x)
abline(lm(y~x))
predict_4=predict(model,data.frame(x=4))
y1=predict(model,data.frame(x))
SSR=sum((y1-mean(y1))^2)
RSS=sum((y-mean(y))^2)
coefficient_determination=SSR/RSS