Question 1: A large school district is re-evaluating its teacher's salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The researcher uses years of experience to predict salary. The raw data is given in the table below. The resulting equation was: Y=19389.21+1330.12X where Y=salary and X=years of experience
|
Salary
|
Years Exp
|
|
$24,265.00
|
8
|
|
$27,140.00
|
5
|
|
$22,195.00
|
2
|
|
$37,950.00
|
15
|
|
$32,890.00
|
11
|
|
$40,250.00
|
14
|
|
$36,800.00
|
9
|
|
$30,820.00
|
6
|
|
$44,390.00
|
21
|
|
$24,955
|
2
|
|
$18,055.00
|
1
|
|
$23,690.00
|
7
|
|
$48,070.00
|
20
|
|
$42,205.00
|
16
|
a) Develop a scatter diagram.
b) What is the correlation coefficient?
c) What is the coefficient of determination?
Question 2: Bob White is conducting research on monthly expenses for medical care, including over-the-counter medicine. His dependent variable is monthly expenses for medical care while his Independent variable is number of family members. Below is his Excel output.
a) What is the prediction equation?
b) Based on his model, each additional family member increases the predicted costs by how much?
c) Based on the significance F-test, is this model a good prediction equation?
d) What percent of the variation in medical expenses is explained by the size of the family?
e) Can the null hypothesis that the slope is zero be rejected? Why or why not?
f) What is the value of the correlation coefficient?
Question 3: A large school district is reevaluating its teachers' salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The research has come up with the following prediction equation:
Y = $18012.24+1432.37X1-4.07 X2 where X1 = Yrs Exp and X2 = Yrs Exp2
(a) lf a teacher has 7 years of experience, what is the expected salary?
(b) If teachers has 10 years of experience, what is the expected salary?
Question 4: An electronics company is looking to develop a regression model to predict the number of units 'It for a special running watch. Data is provided below:
|
Sales(units)
|
Price($)
|
Advertising($)
|
Holiday
|
|
500
|
100
|
50
|
Yes
|
|
480
|
120
|
40
|
Yes
|
|
485
|
110
|
45
|
No
|
|
510
|
103
|
55
|
Yes
|
|
490
|
108
|
40
|
No
|
|
488
|
109
|
30
|
No
|
|
496
|
106
|
45
|
Yes
|
a) Define the dummy variable(s) for the regression model.
b) What is the correlation between the Holiday categorical variable and sales?
Question 5: A healthcare executive is using regression to predict total revenues. She has decided to include both patient length of stay and insurance type u her model. Insurance type can be grouped into three categories: Government-Funded, Private-Pay, and Other. Her model is
A) Y= b0
B) Y= b0+b1X1
C) Y= b0+b1X1+b2 X2
D) Y= b0+b1 X1+b2 X2+b3X3
E) Y= b0+b1X1+b2 X2+b3X3+b4X4.