Question

1. 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

Solution :

Regression Statistics
Multiple R	0.631134
R Square	0.39833
Adjusted R Square	0.323121
Standard Error	1.127399
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.731776	6.731776	5.296324	0.050363
Residual	8	10.16822	1.271028
Total	9	16.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	12.66355	0.644792	19.63974	4.7E-08	11.17666	14.15044	11.17666	14.15044
X Variable 1	0.457944	0.198987	2.301374	0.050363	-0.00092	0.916809	-0.00092	0.916809

a) and c)

b)

d)

y = 12.664 + 0.458 * x

when x = 4

y = 12.664 + 0.458 * 4

yhat = 14.496

e)

Coefficient of determination r^2 = 0.6311 * 0.6311

Coefficient of determination r^2 = 0.3983

Coefficient of non determination = 1- r^2 = 1 - 0.3983

Coefficient of non determination = 0.6017

39.83% is explained and 60.17% is unexplained from the linear relationship.

f)

the typical starting wage per hour = 12.664

the typical increase in wage for each additional year on the job = 0.458