Question

The reasons given by workers for quitting their jobs generally fall into one of two categories:

(1) Worker quits to seek or take a different job, or (2) worker quits to withdraw from the labor force. Economic theory suggests that wages and quit rates are related. The table below lists quit rates (quits per 100 employees) and the average hourly wage in a sample of 15 manufacturing industries.

Industry	Quit Rate, y	Average Wage, x ($)
1	1.4	8.20
2	.7	10.35
3	2.6	6.18
4	3.4	5.37
5	1.7	9.94
6	1.7	9.11
7	1.0	10.59
8	0.5	13.29
9	2.0	7.99
10	3.8	5.54
11	2.3	7.50
12	1.9	6.43
13	1.4	8.83
14	1.8	10.93
15	2.0	8.80

Use Excel to find the regression equation and the coefficient of determination:

1. Do the data present sufficient evidence to conclude that the average hourly wage contributes useful information for the prediction of quit rates? What does your model suggest about the relationship between quit rates and wages?
2. Predict the Quit rate for an average wage of $7.50.
3. Make a scatterplot to represent the data. Comment on the relationship between Quit Rate, y and Average Wage, x.
4. Using excel, find the correlation coefficient r, and coefficient of determination R2 and interpret each.
5. Construct a 95% confidence interval for the population mean quit rate for the industries. Interpret your result.
6. Write a paragraph stating what the results can be used in the industry.

Answer 1

Using Excel<data<data analysis<Regression

Here is the output:

Regression Analysis
	r²	0.729
	r	-0.854
	Std. Error	0.486
	n	15
	k	1
	Dep. Var.	Quit Rate, y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	8.2507	1	8.2507	34.90	.0001
Residual	3.0733	13	0.2364
Total	11.3240	14
Regression output				confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	4.8615	0.52	9.35	0.00	3.74	5.99
Average Wage, x ($)	-0.3466	0.0587	-5.908	.0001	-0.4733	-0.2198
		95% Confidence Interval	95% Prediction Interval
	Predicted	lower	upper	lower	upper	Leverage
	2.2624	1.9572	2.5675	1.1685	3.3562	0.084

The regression Equation is y= 4.8615-0.3466x

Coefficient of determination,r^2=0.729

Do the data present sufficient evidence to conclude that the average hourly wage contributes useful information for the prediction of quit rates? What does your model suggest about the relationship between quit rates and wages

Answer:

Since P value (=0.0001)<alpha(0.05). There is significant evidence to conclude that he average hourly wage contributes useful information for the prediction of quit rates.

R=-0.854 which implies that there is negative association between the variables quit rate and Average wage that is if the quit rate increases then average wage decreases and if quit rate increases then average wage decreases.

Predict the Quit rate for an average wage of $7.50.

The regression Equation is y= 4.8615-0.3466x

Put x=7.50

y= 4.8615-0.3466*7.50= 2.2624

Make a scatterplot to represent the data. Comment on the relationship between Quit Rate, y and Average Wage, x.

4 3.5 3 2.5 Quit Rate, y 2 1.5 1 0.5 0 4 6 12 14 8 10 Average Wage, x(S)

There is negative association between the variables quit rate and Average wage that is if the quit rate increases then average wage decreases and if quit rate increases then average wage decreases.

Using excel, find the correlation coefficient r, and coefficient of determination R2 and interpret each.

r=-0.854

Interpretation: There is strong negative relationship exists between variables x and y.

r^2=0.729

Interpretation: The 72.9% variation caused in Y by the variable X.

Construct a 95% confidence interval for the population mean quit rate for the industries. Interpret your result.

The 95% confidence interval is (-0.4733,-0.2198)

We are 95% confident that the he population mean quit rate for the industries lies between -0.4733 and -0.2198.

Write a paragraph stating what the results can be used in the industry.

The correlation coefficient and the regression equation will be used in the industries. As both will help in making predictions and helps in understanding the process.