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The owner of Maumee FordMercuryVolvo 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? 
is the independent variable and is the dependent variable. 
b1.  Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) 
X  Y  ( )2  ( )2  ( )( )  
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  = 
b2.  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.) 
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. 
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 12ounce 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. 
Click here for the Excel Data File 
1.
value: 10.00 points
Required information
a1.  Choose a scatter diagram that best fits the data. 
2.
value: 10.00 points
Required information
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  
References
eBook & Resources
Worksheet Difficulty: 2 Intermediate Learning Objective: 1302 Calculate a correlation coefficient to test and interpret the relationship between two variables.
3.
value: 10.00 points
Required information
c1.  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 > 
c2.  Compute the value of the test statistic. (Round your answer to 2 decimal places.) 
Value of the test statistic 
c3.  What is the pvalue? (Hint: use Megastat) (Round pvalue to 4 decimal places.) 
pvalue 
c4.  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? 
H0 . There is between beers consumed and BAC. 
1.
value: 10.00 points
The following sample observations were randomly selected. 
Click here for the Excel Data File 
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  ( )2  ( )2  ( )( )  
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 when X is 7. (Round your answer to 3 decimal places.) 
The owner of Maumee FordMercuryVolvo 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 
The regression equation is , 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? 
H0 and conclude the slope is zero. 
The owner of Maumee FordMercuryVolvo 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. 
1.
value: 10.00 points
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 onthejob 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 OntheJob Performance, X3  Age, X4  
Mike Miraglia  112  12  312  121  52  
Sue Trythall  113  2  380  123  27  
The equation is: 
= 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4 
a.  What is this equation called?  

b.  How many dependent and independent variables are there? 
dependent, independent 
c.  What is the number 0.286 called?  

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 onthejob 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.) 
1.
value: 10.00 points
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  
a1.  Determine the standard error of estimate. (Round your answer to 2 decimal places.) 
Standard error of estimate 
a2.  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 . 
b1.  Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.) 
Coefficient of multiple determination value is . 
b2.  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 
1.
value: 10.00 points
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  pvalue  
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  pvalue  
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  

c1.  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 > 
c2.  Compute the value of the F statistic. (Round your answer to 2 decimal places.) 
Computed value of F is 
c3.  Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level. 
H0. 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 
d1.  State the decision rule for .05 significance level. (Round your answers to 3 decimal places.) 
Reject H0 if t < or t > . 
d2.  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  

d3.  Which variable would you consider eliminating? 
Consider eliminating variables . 
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 fiveyear performance. The question is: Can the fiveyear 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 Shortterm  681.0  8.2 
Galaxy Bond Retail  433.2  9.1  Thompson Income B  241.3  6.8 
Keystone Custodian B1  437.9  9.2  
Click here for the Excel Data File
b1.  Compute the coefficient of correlation. (Round your answer to 3 decimal places. Negative amount should be indicated by a minus sign.) 
r = 
b2.  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 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 $400.0 million in sales, determine the fiveyear rate of return (in percent). (Round your answer to 4 decimal places.) 
= The equation should be used with caution. Assets do not account for much of the variation in the rate of return. 
Mr. James McWhinney, president of DanielJames Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ 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  
Click here for the Excel Data File 
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  ( ) 2  ( )2  ( )( )  
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.) 
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 
0
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