QTN 561: Week 5 Weekly Learning Assessments
princess_92073
week_5_assessments.docxChapter 13 Exercise 6
|
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 |
|
|
Click here for the Excel Data File
|
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? |
|
|
|
|
|
(Click to select)CarSelling priceAge is the independent variable and (Click to select)selling priceagecar is the dependent variable. |
|
b-1. |
Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) |
|
X |
Y |
|
|
( |
( |
( |
|
9.0 |
8.1 |
|
1.192 |
0.007 |
1.420 |
0.099 |
|
7.0 |
6.0 |
|
-0.908 |
3.674 |
0.825 |
1.741 |
|
11.0 |
3.6 |
2.083 |
|
4.340 |
10.945 |
-6.892 |
|
12.0 |
4.0 |
3.083 |
|
9.507 |
8.458 |
-8.967 |
|
8.0 |
5.0 |
-0.917 |
-1.908 |
|
3.642 |
1.749 |
|
7.0 |
10.0 |
-1.917 |
3.092 |
|
9.558 |
-5.926 |
|
8.0 |
7.6 |
-0.917 |
0.692 |
0.840 |
|
-0.634 |
|
11.0 |
8.0 |
2.083 |
1.092 |
4.340 |
|
2.274 |
|
10.0 |
8.0 |
1.083 |
1.092 |
1.174 |
1.192 |
|
|
12.0 |
6.0 |
3.083 |
-0.908 |
9.507 |
0.825 |
|
|
6.0 |
8.6 |
-2.917 |
1.692 |
8.507 |
2.862 |
-4.934 |
|
6.0 |
8.0 |
-2.917 |
1.092 |
8.507 |
1.192 |
-3.184 |
|
107.000 |
82.900 |
|
|
|
|
|
|
|
|
|
= |
|
|
= |
|
sx |
= |
|
sy |
= |
|
|
r |
= |
|
|
b-2. |
Determine the coefficient of determination. (Round your answer to 3 decimal places.) |
|
|
|
|
|
|
|
c. |
Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.) |
|
|
|
|
|
(Click to select)ModerateNoStrong correlation between age of car and selling price. So, % of the variation in the selling price is explained by the variation in the age of the car. |
Chapter 13 Exercise 12
|
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. (Round your answers to 3 decimal places.) |
|
|
|
|
|
|
|
|
|
|
sx |
|
|
sy |
|
|
|
|
c. |
Determine the coefficient of correlation and coefficient of determination. (Round your answers to 3 decimal places.) |
|
|
|
|
Coefficient of correlation |
|
|
Coefficient of determination |
|
|
|
|
|
c-1. |
State the decision rule for .01 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.) |
|
Reject H0 if t > |
|
|
c-2. |
Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
|
Value of the test statistic |
|
|
c-3. |
What is the p-value? (Hint: use your analysis software) (Round p-value to 4 decimal places.) |
|
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? |
|
(Click to select)Fail to rejectReject H0 . There is (Click to select)a positive correlationno correlationnegative correlation between beers consumed and BAC. |
Chapter 13 Exercise 14
|
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.) |
|
X |
Y |
|
|
( |
( |
( |
||||
|
5 |
13 |
|
2.375 |
|
5.641 |
|
||||
|
3 |
15 |
−1.875 |
|
3.516 |
|
−8.203 |
||||
|
6 |
7 |
|
|
|
13.141 |
−4.078 |
||||
|
3 |
12 |
−1.875 |
1.375 |
|
|
|
||||
|
4 |
13 |
−0.875 |
|
0.766 |
|
−2.078 |
||||
|
4 |
11 |
|
0.375 |
|
0.141 |
|
||||
|
6 |
9 |
1.125 |
−1.625 |
|
|
|
||||
|
8 |
5 |
|
|
|
31.641 |
−17.578 |
||||
|
|
|
|
|
|
|
|
||||
|
|
= |
|
|
|
= |
|
|
sx |
= |
|
|
sy |
= |
|
|
r |
= |
|
|
b |
= |
|
|
a |
= |
|
|
Y' = + X |
|
b. |
Determine the value of |
|
|
|
|
|
Chapter 13 Exercise 26
|
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) |
|||
|
1 |
|
9 |
|
8.1 |
|
|
2 |
|
7 |
|
6.0 |
|
|
3 |
|
11 |
|
3.6 |
|
|
4 |
|
12 |
|
4.0 |
|
|
5 |
|
8 |
|
5.0 |
|
|
6 |
|
7 |
|
10.0 |
|
|
7 |
|
8 |
|
7.6 |
|
|
8 |
|
11 |
|
8.0 |
|
|
9 |
|
10 |
|
8.0 |
|
|
10 |
|
12 |
|
6.0 |
|
|
11 |
|
6 |
|
8.6 |
|
|
12 |
|
6 |
|
8.0 |
|
|
|
Click here for the Excel Data File
|
a. |
Determine the standard error of estimate. (Round your answer to 3 decimal places.) |
|
|
|
|
Standard error of estimate |
|
|
b. |
Determine the coefficient of determination. (Round your answer to 3 decimal places.) |
|
|
|
|
|
|
|
c. |
Interpret the coefficient of determination. (Round your answer to the nearest whole number.) |
|
|
|
|
percent of the variation in the selling price is explained by the variation in the age of the car. |
Chapter 14 Exercise 2
|
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: |
|
|
|
a. |
What is this equation called? (MULTIPLE CHOICE) |
|
b. |
How many dependent and independent variables are there? (MULTIPLE CHOICE) |
|
c. |
What is the number 0.286 called? (MULTIPLE CHOICE) |
|
d. |
As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.) |
|
|
|
|
|
|
|
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. (Round your answer to 3 decimal places.) |
|
|
|
|
|
|
Chapter 14 exercise 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. (Round your answer to 2 decimal places.) |
|
|
|
|
Standard error of estimate |
|
|
a-2. |
About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.) |
|
|
|
|
95% of the residuals will be between and . |
|
b-1. |
Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.) |
|
|
|
|
Coefficient of multiple determination value is . |
|
b-2. |
Determine the percentage variation for the independent variables. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) |
|
|
|
|
The independent variables explain % of the variation. |
|
c. |
Determine the coefficient of multiple determination, adjusted for the degrees of freedom. (Round your answer to 3 decimal places.) |
|
|
|
|
Coefficient of multiple determination |
|
Chapter 14 Exercise 8
|
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.) |
|
|
|
|
Ŷ = + X1 + X2 + X3 + X4 + X5. |
|
b. |
How large is the sample? How many independent variables are there? |
|
|
|
|
|
|
|
Sample n |
|
|
Independent variables k |
|
|
|
|
|
c-1. |
State the decision rule for .05 significance level: H0: β1 = β2 = β3 =β4 =β5 =0; H1: Not all β's are 0. (Round your answer to 2 decimal places.) |
|
|
|
|
Reject H0 if F > |
|
|
c-2. |
Compute the value of the F statistic. (Round your answer to 2 decimal places.) |
|
|
|
|
Computed value of F is |
|
|
c-3. |
Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level. |
|
|
|
|
(Click to select)Do not RejectReject H0. (Click to select)Not allAll of the regression coefficients are zero. |
|
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. (Round your answers to 3 decimal places.) |
|
|
|
|
Reject H0 if t < or t > . |
|
d-2. |
Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative answers should be indicated by a minus sign.) |
|
|
|
|
|
t − value |
|
X1 |
|
|
X2 |
|
|
X3 |
|
|
X4 |
|
|
X5 |
|
|
|
|
d-3. |
Which variable would you consider eliminating? |
|
|
|
|
Consider eliminating variables (Click to select)X3 and X5X3 and X4X1 and X2X1 and X5X2 and X3. |
Chapter 13 Exercise 16
|
Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled. |
|
Number of Contacts, X |
Sales ($ thousands), Y |
Number of Contacts, X |
Sales ($ thousands), Y |
||||
|
14 |
|
24 |
|
23 |
|
30 |
|
|
12 |
|
14 |
|
48 |
|
90 |
|
|
20 |
|
28 |
|
50 |
|
85 |
|
|
16 |
|
30 |
|
55 |
|
120 |
|
|
46 |
|
80 |
|
50 |
|
110 |
|
|
|
|
a. |
Determine the regression equation. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round final answers to 2 decimal places.) |
|
X |
Y |
|
|
( |
( |
( |
||||
|
14 |
|
|
|
376.36 |
1376.41 |
719.74 |
||||
|
12 |
14 |
−21.4 |
−47.1 |
|
|
|
||||
|
20 |
|
−13.4 |
|
179.56 |
|
443.54 |
||||
|
16 |
30 |
|
−31.1 |
|
967.21 |
|
||||
|
46 |
|
12.6 |
|
|
357.21 |
|
||||
|
23 |
|
−10.4 |
|
|
967.21 |
|
||||
|
48 |
90 |
|
28.9 |
213.16 |
|
421.94 |
||||
|
50 |
85 |
|
23.9 |
275.56 |
|
396.74 |
||||
|
55 |
|
|
|
466.56 |
3469.21 |
1,272.24 |
||||
|
50 |
110.0 |
16.6 |
48.9 |
|
|
|
||||
|
|
|
|
|
|
|
|
||||
|
|
= |
|
|
|
= |
|
|
sx |
= |
|
|
sy |
= |
|
|
r |
= |
|
|
b = |
|
a = |
Y' = + X |
|
b. |
Determine the estimated sales if 40 contacts are made.(Do not round intermediate calculations. Round final answers to 2 decimal places.) |
Chapter 13 Exercise 18
|
We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance. The question is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are shown below. |
|
|
Assets |
Return |
|
Assets |
Return |
|
Fund |
($ millions) |
(%) |
Fund |
($ millions) |
(%) |
|
AARP High Quality Bond |
$622.2 |
10.8 |
MFS Bond A |
$494.5 |
11.6 |
|
Babson Bond L |
160.4 |
11.3 |
Nichols Income |
158.3 |
9.5 |
|
Compass Capital Fixed Income |
275.7 |
11.4 |
T. Rowe Price Short-term |
681.0 |
8.2 |
|
Galaxy Bond Retail |
433.2 |
9.1 |
Thompson Income B |
241.3 |
6.8 |
|
Keystone Custodian B-1 |
437.9 |
9.2 |
|
|
|
|
|
Click here for the Excel Data File
|
b-1. |
Compute the coefficient of correlation. (Round your answer to 3 decimal places. Negative amount should be indicated by a minus sign.) |
|
|
|
|
|
r = |
|
b-2. |
Compute the coefficient of determination. (Round your answer to 3 decimal places.) |
|
|
|
|
|
r2 = |
|
c. |
Give a description of the degree of association between the variables. |
|
|
|
|
|
There is (Click to select)a very stronga strongvery little association between the variables. |
|
d. |
Determine the regression equation. Use assets as the independent variable. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) |
|
|
|
|
|
b = |
|
|
|
|
|
a = |
|
e. |
For a fund with $400.0 million in sales, determine the five-year rate of return (in percent). (Round your answer to 4 decimal places.) |
|
|
|
|
On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 80%. The standard error of estimate was 10. There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam. |
|
Source |
DF |
SS |
MS |
|
Regression |
|
|
|
|
Error |
|
|
|
|
Total |
|
|
|
|
|
