# STATS week 5 Quiz 2015

August 30, 2017

Question
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?

is the independent variable and 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 ( )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 =

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.)

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 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.

1.
value:
10.00 points
Required information

a-1. Choose a scatter diagram that best fits the data.

References
eBook & Resources
Multiple ChoiceDifficulty: 2 IntermediateLearning Objective: 13-02 Calculate a correlation coefficient to test and interpret the relationship between two variables.
Check my work

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
WorksheetDifficulty: 2 IntermediateLearning Objective: 13-02 Calculate a correlation coefficient to test and interpret the relationship between two variables.
Check my work

3.
value:
10.00 points
Required information

c-1. State the decision rule for .01 significance level: H0: ? ? 0; H1: ? > 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 Megastat) (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?

H0 . There is between beers consumed and BAC.

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 ( )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 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 , 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 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
________________________________________

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.

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:

= 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?

dependent, independent

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? (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.)

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 .

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
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.)

? = + 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: ?1 = ?2 = ?3 =?4 =?5 =0; H1: Not all ?’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.

H0. of the regression coefficients are zero.

For X1 For X2 For X3 For X4 For X5
H0: ?1 = 0 H0: ?2 = 0 H0: ?3 = 0 H0: ?4 = 0 H0: ?5 = 0
H1: ?1 ? 0 H1: ?2 ? 0 H1: ?3 ? 0 H1: ?4 ? 0 H1: ?5 ? 0
________________________________________

d-1. State the decision rule for .05 significance level. (Round your answers to 3 decimal places.)

Reject H0 if 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 .

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