Question 1:
The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
|
Car
|
Age (years)
|
Selling Price ($000)
|
Car
|
Age (years)
|
Selling Price ($000)
|
|
1
|
9
|
8.1
|
7
|
8
|
7.6
|
|
2
|
7
|
6.0
|
8
|
11
|
8.0
|
|
3
|
11
|
3.6
|
9
|
10
|
8.0
|
|
4
|
12
|
4.0
|
10
|
12
|
6.0
|
|
5
|
8
|
5.0
|
11
|
6
|
8.6
|
|
6
|
7
|
10.0
|
12
|
6
|
8.0
|
a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable?
b-1. Determine the correlation coefficient.
b-2. Determine the coefficient of determination.
c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?
Question 2:
The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and his or her blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly assigned a number of 12-ounce cans of beer to drink. Thirty minutes after they consumed their assigned number of beers, a member of the local sheriff's office measured their blood alcohol content. The sample information is reported below.
|
Student
|
Beers
|
BAC
|
Student
|
Beers
|
BAC
|
|
1
|
6
|
0.10
|
10
|
3
|
0.07
|
|
2
|
7
|
0.09
|
11
|
3
|
0.05
|
|
3
|
7
|
0.09
|
12
|
7
|
0.08
|
|
4
|
4
|
0.10
|
13
|
1
|
0.04
|
|
5
|
5
|
0.10
|
14
|
4
|
0.07
|
|
6
|
3
|
0.07
|
15
|
2
|
0.06
|
|
7
|
3
|
0.10
|
16
|
7
|
0.12
|
|
8
|
6
|
0.12
|
17
|
2
|
0.05
|
|
9
|
6
|
0.09
|
18
|
1
|
0.02
|
Use a statistical software package to answer the following questions.
a-1. Choose a scatter diagram that best fits the data.
b. Fill in the blanks below.
c. Determine the coefficient of correlation and coefficient of determination.
c-1. State the decision rule for .01 significance level: H0: ρ ≤ 0; H1: ρ > 0.
c-2. Compute the value of the test statistic.
c-3. What is the p-value?
c-4. At the .01 significance level, is it reasonable to conclude that there is a positive relationship in the population between the number of beers consumed and the BAC?
Question 3:
The following sample observations were randomly selected.
|
X:
|
5
|
3
|
6
|
3
|
4
|
4
|
6
|
8
|
|
Y:
|
13
|
15
|
7
|
12
|
13
|
11
|
9
|
5
|
a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
b. Determine the value of when X is 7. (Round your answer to 3 decimal places.)
Question 4:
The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
|
Car
|
Age (years)
|
Selling Price ($000)
|
Car
|
Age (years)
|
Selling Price ($000)
|
|
1
|
9
|
8.1
|
7
|
8
|
7.6
|
|
2
|
7
|
6.0
|
8
|
11
|
8.0
|
|
3
|
11
|
3.6
|
9
|
10
|
8.0
|
|
4
|
12
|
4.0
|
10
|
12
|
6.0
|
|
5
|
8
|
5.0
|
11
|
6
|
8.6
|
|
6
|
7
|
10.0
|
12
|
6
|
8.0
|
The regression equation is Y^ = 11.18 - 0.48X, the sample size is 12, and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?
The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
a. Determine the standard error of estimate.
b. Determine the coefficient of determination.
c. Interpret the coefficient of determination.
Question 5:
Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed:
X1 = Length of time an employee was in the industry
X2 = Mechanical aptitude test score
X3 = Prior on-the-job rating
X4 = Age
Performance on the new machine is designated y.
Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are:
|
Name
|
Performance
on New
Machine,
Y
|
Length of
Time in
Industry,
X1
|
Mechanical
Aptitude
Score,
X2
|
Prior
On-the-Job
Performance,
X3
|
Age,
X4
|
|
Mike Miraglia
|
112
|
|
12
|
|
312
|
|
121
|
|
52
|
|
|
Sue Trythall
|
113
|
|
2
|
|
380
|
|
123
|
|
27
|
|
The equation is:
Y^ = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4
a. What is this equation called?
Multiple regression equation
Multiple standard error of estimate
Coefficient of determination
b. How many dependent and independent variables are there?
c. What is the number 0.286 called?
Regression coefficient
Coefficient of determination
Homoscedasticity
Multicollinearity
d. As age increases by one year, how much does estimated performance on the new machine increase?
e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl's performance on the new machine.
Question 6:
Consider the ANOVA table that follows.
|
Analysis of Variance
|
|
Source
|
DF
|
SS
|
MS
|
F
|
|
|
Regression
|
5
|
|
3710.00
|
|
742.00
|
|
12.89
|
|
|
|
Residual Error
|
46
|
|
2647.38
|
|
57.55
|
|
|
|
|
|
Total
|
51
|
|
6357.38
|
|
|
|
|
|
|
a-1. Determine the standard error of estimate.
a-2. About 95% of the residuals will be between what two values?
b-1. Determine the coefficient of multiple determination.
b-2. Determine the percentage variation for the independent variables.
c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom.
Question 7:
Coefficient of multiple determination
The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.
|
Predictor
|
Coeff
|
SE Coeff
|
t
|
p-value
|
|
Constant
|
7.987
|
|
2.967
|
|
2.690
|
|
0.010
|
|
|
X1
|
0.122
|
|
0.031
|
|
3.920
|
|
0.000
|
|
|
X2
|
-1.120
|
|
0.053
|
|
-2.270
|
|
0.028
|
|
|
X3
|
-0.063
|
|
0.039
|
|
-1.610
|
|
0.114
|
|
|
X4
|
0.523
|
|
0.142
|
|
3.690
|
|
0.001
|
|
|
X5
|
-0.065
|
|
0.040
|
|
-1.620
|
|
0.112
|
|
|
Analysis of Variance
|
|
Source
|
DF
|
SS
|
MS
|
F
|
p-value
|
|
Regression
|
5
|
|
3710.00
|
|
742.00
|
|
12.89
|
|
0.000
|
|
|
Residual Error
|
46
|
|
2647.38
|
|
57.55
|
|
|
|
|
|
|
Total
|
51
|
|
6357.38
|
|
|
|
|
|
|
|
X1 is the number of architects employed by the company.
X2 is the number of engineers employed by the company.
X3 is the number of years involved with health care projects.
X4 is the number of states in which the firm operates.
X5 is the percent of the firm's work that is health care-related.
a. Write out the regression equation. (Round your answers to 3 decimal places. Negative answers should be indicated by a minus sign.)
b. How large is the sample? How many independent variables are there?
c-1. State the decision rule for .05 significance level: H0: β1 = β2 = β3 = β4 = β5 = 0; H1: Not all β's are 0.
c-2. Compute the value of the F statistic.
c-3. Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level.
|
For X1
|
For X2
|
For X3
|
For X4
|
For X5
|
|
H0: β1 = 0
|
H0: β2 = 0
|
H0: β3 = 0
|
H0: β4 = 0
|
H0: β5 = 0
|
|
H1: β1 ≠ 0
|
H1: β2 ≠ 0
|
H1: β3 ≠ 0
|
H1: β4 ≠ 0
|
H1: β5 ≠ 0
|
d-1. State the decision rule for .05 significance level.
d-2. Compute the value of the test statistic.
d-3. Which variable would you consider eliminating?
Attachment:- Week.rar