Question 1. Imagine that you are head of personnel at Huge Corp. The CEO keeps getting other people's mail by mistake, so she asks you to conduct a study of mailroom productivity. You take a random sample of 27 mailroom employees and gather data on the following variables:
- productivity (PROD = letters correctly sorted per minute),
- experience (EXP = months of experience in the Huge Corp. mailroom), and
- aptitude score (SCORE = score on the test they took when they applied for a job at Huge Corp.)
You generate the following regression equation:
Predicted PROD = 2.0 + 0.5 EXP + 0.2 SCORE
a. Identify the independent variable(s) and the dependent variable(s).
b. Ernest has just been hired, and has an aptitude score of 80. What level of productivity would you expect from Ernest?
c. How much is Ernest's productivity expected to improve after he gains an additional 6 months of experience?
d. What is the best interpretation of the intercept term (2.0) in the regression equation?
e. Jack has 3 months more experience than Jill, but Jill's aptitude score is 20 points higher than Jack's. Who is expected to be more productive?
2. Literacy rate is a reflection of the educational facilities and quality of education available in a country, and mass communication plays a large part in the educational process. In an effort to relate the literacy rate of a country to various mass communication outlets, a demographer has proposed to relate literacy rate to the following variables: number of daily newspaper copies (per 1000 population), number of radios (per 1000 population), and number of TV sets (per 1000 population). Here are the data for a sample of 10 countries:
Country
|
|
newspapers radios tv sets literacyrate |
|
Czech Republic
|
/
|
|
|
Slovakia
|
|
280
|
266
|
228
|
0.98
|
|
Italy
|
|
142
|
230
|
201
|
0.93
|
|
Kenya
|
|
10
|
114
|
2
|
0.25
|
|
Norway
|
|
391
|
313
|
227
|
0.99
|
|
Panama
|
|
86
|
329
|
82
|
0.79
|
|
Philippines
|
|
17
|
42
|
11
|
0.72
|
|
Tunisia
|
|
21
|
49
|
16
|
0.32
|
|
USA
|
|
314
|
1695
|
472
|
0.99
|
|
Russia
|
|
333
|
430
|
185
|
0.99
|
|
Venezuela
|
|
91
|
182
|
89
|
0.82
|
Below is the Minitab output from a Multiple Linear Regression analysis.
| Predictor |
Coef |
SE Coef |
T |
P |
| Constant |
0.51486 |
0.09368 |
5.5 |
0.002 |
| newspaper copies |
0.0005421 |
0.0008653 |
0.63 |
0.554 |
| radios |
-0.0003535 |
0.0003285 |
-1.08 |
0.323 |
| television sets |
0.001988 |
0.00155 |
1.28 |
0.247 |
S = 0.186455 R-Sq = 69.9% R-Sq(adj) = 54.8%
|
|
Analysis of
|
Variance
|
|
|
Source DF
|
SS
|
MS
|
F
|
P
|
|
Regression 3
|
0.48397
|
0.16132
|
4.64
|
0.053
|
|
Residual Error 6
|
0.20859
|
0.03477
|
|
|
|
Total 9 0.69256
|
|
|
|
|
a. What is the response (dependent) variable? What are the predictor (independent) variables?
b. Write the least-squares regression equation for this problem.
c. For every additional daily newspaper copy per 1000 people in a population, literacy rate is predicted to be higher, keeping the number of radios and TV sets the same.
d. For countries with the same number of daily newspaper copies and same number of TV sets (per 1000 people in the population), literacy rate is predicted to be higher for every additional radio per 1000 people in the population.
e. Predict literacy rate for a country that has 200 daily newspaper copies (per 1000 in the population), 800 radios (per 1000 in the population), and 250 TV sets (per 1000 in the population).
f. Verify that the F-statistic in the output above equals MSM / MSE.
Attachment:- homework.rar