Question

A personnel manager for a large corporation feels that there may be a relationship between absenteeism, age and life status (single, married, divorced and other) of workers. He would like to develop a model to predict the number of days absent during a calendar year for workers using the independent variables above. A random sample of 20 workers was selected with the results presented below.

Days Absent	Age	Life Status
15	27	Single
40	61	Divorced
10	37	Married
18	23	Married
9	46	Other
20	58	Other
14	29	Other
32	67	Single
26	64	Single
8	40	Married
18	57	Other
8	28	Married
35	60	Divorced
24	39	Divorced
11	35	Single
21	45	Single
5	23	Other
9	48	Other
49	55	Divorced
3	39	Single

Use Excel to analyze the data, print out the summary output and attach it to your submission

Use the following: Y = Dependent variable; X1 = Age; X2 = Single;

X3 = Married; X4 = Divorced.

a)What is the prediction equation?

b)What is the correlation coefficient?

c)Is the overall model significant? Why?

d)What is the coefficient of determination?

e)What is the MSE?

f)List the p-value of each independent variable and say whether it is significant to the model or not. Use a 0.05 level of significance.

g)What is the predicted number of days absent for a 54 year old widower?

SHOW WORK !!

Answer 1

From the given data

a)What is the prediction equation?

The prediction equation is
Y = -4.337969341 + 0.387079755X1 + 4.46778732X2 + 2.951417182X3 + 20.53243251X4

b)What is the correlation coefficient?

correlation coefficient is sqrt(0.7643275) =0.8743

c)Is the overall model significant? Why?

P-value of regression is 0.0001319 which is < alpha = 005 so overall model significant

d)What is the coefficient of determination?

coefficient of determination is 0.76432

e)What is the MSE?

MSE = 45.9679

f)List the p-value of each independent variable and say whether it is significant to the model or not. Use a 0.05 level of significance.

p-value of x1 is 0.008201 < alpha 0.05 so it is significant
p-value of x2 is 0.2733 > alpha 0.05 so it is no significant
p-value of x3 is 0.53206 > alpha 0.05 so it is no significant
p-value of x4 is 0.000426 < alpha 0.05 so it is significant

g) The predicted number of days absent for a 54 year old widower is

The prediction equation is
Y = -4.337969341 + 0.387079755(54) = 16.5643