Question 1

A regression equation is obtained for the following set of data. For what range of x-values
would it be reasonable to use the regression equation to predict the y-value? Why? $$\begin{array} { r | r r r r r r } 
\mathrm { x } & 2 & 4 & 6 & 9 & 10 & 12 \
\hline \mathrm { y } & 28 & 33 & 39 & 45 & 47 & 52
\end{array}$$

Accepted Answer

Explanations will vary. An example follo...

Question 2

The following table gives the US domestic oil production rates (excluding Alaska) over the past few years. A regression equation was fit to the data and the residual plot is shown below. $\begin{array} { l  } \begin{array}{c|c}
\text { Year } & \text { Millions of barrels per day } \
\hline 1987 & 6.39 \
1988 & 6.12 \
1989 & 5.74 \
1990 & 5.58 \
1991 & 5.62 \
1992 & 5.46 \
1993 & 5.26 \
1994 & 5.10
\end{array}&\begin{array}{c|c}
\text { Year } & \text { Millions of barrels per day } \
\hline 1995 & 5.08 \
1996 & 5.07 \
1997 & 5.16 \
1998 & 5.08 \
1999 & 4.83 \
2000 & 4.85 \
2001 & 4.84 \
2002 & 4.83
\end{array}\end{array}$

Does the residual plot suggest that the regression equation is a bad model? Why or why
not?

Accepted Answer

Yes, the residual plot suggests that the...

Question 3

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data.
- n=16,α=0.01\mathrm { n } = 16 , \alpha = 0.01n=16,α=0.01

Accepted Answer

A)    −0.635- 0.635−0.635 
B)    ±0.635\pm 0.635±0.635 
C)    ±0.503\pm 0.503±0.503 
D)    0.6350.6350.635

Question 4

Use the rank correlation coefficient to test for a correlation between the two variables.
-Ten luxury cars were ranked according to their comfort levels and their prices. $$\begin{array} { c c c } 
\hline \text { Make } & \text { Comfort } & \text { Price } \
\hline \text { A } & \mathbf { 5 } & 1 \
\text { B } & 8 & 7 \
\text { C } & 9 & 3 \
\text { D } & 10 & 5 \
\text { E } & 4 & 4 \
\text { F } & 3 & 2 \
\text { G } & 2 & 10 \
\text { H } & 1 & 9 \
\text { I } & 7 & 6 \
\mathbf { J } & 6 & 8 \
\hline
\end{array}$$
 Find the rank correlation coefficient and test the claim of correlation between comfort and price. Use a significance level of 0.05.

Accepted Answer

. Critical values:

.
Fail to r...

Question 5

Define the terms predictor variable and response variable. Give examples for each.

Accepted Answer

The predictor variable is x, representin...

Question 6

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
- x13579y1431161009890\begin{array}{r|rrrrr}\mathrm{x} & 1 & 3 & 5 & 7 & 9 \\hline \mathrm{y} & 143 & 116 & 100 & 98 & 90\end{array}xy​1143​3116​5100​798​990​​

Accepted Answer

A)    y^=150.7−6.8x\hat { y } = 150.7 - 6.8 xy^​=150.7−6.8x 
B)    y^=−150.7+6.8x\hat { y } = - 150.7 + 6.8 xy^​=−150.7+6.8x 
C)    y^=−140.4+6.2x\hat { y } = - 140.4 + 6.2 xy^​=−140.4+6.2x 
D)    y^=140.4−6.2x\hat { y } = 140.4 - 6.2 xy^​=140.4−6.2x

Question 7

Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero.

Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.

Accepted Answer

Because the linear correlation coefficie...

Question 8

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.
- r=−0.285,n=90\mathrm { r } = - 0.285 , \mathrm { n } = 90r=−0.285,n=90

Accepted Answer

A)   Critical values:  r=±0.217r = \pm 0.217r=±0.217 , no significant linear correlation
B)   Critical values:  r=±0.207r = \pm 0.207r=±0.207 , no significant linear correlation
C)   Critical values:  r=±0.207\mathrm { r } = \pm 0.207r=±0.207 , significant linear correlation
D)   Critical values:  r=0.217\mathrm { r } = 0.217r=0.217 , significant linear correlation

Question 9

Define rank. Explain how to find the rank for data which repeats (for example, the data set:
4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

Accepted Answer

A rank is a number assigned to an indivi...

Question 10

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.
- r=0.71,n=25\mathrm { r } = 0.71 , \mathrm { n } = 25r=0.71,n=25

Accepted Answer

A)   Critical values:  r=±0.396r = \pm 0.396r=±0.396 , significant linear correlation
B)   Critical values:  r=±0.487\mathrm { r } = \pm 0.487r=±0.487 , no significant linear correlation
C)   Critical values:  r=±0.487\mathrm { r } = \pm 0.487r=±0.487 , significant linear correlation
D)   Critical values:  r=±0.396r = \pm 0.396r=±0.396 , no significant linear correlation

Question 11

Given that the rank correlation coefficien $\mathrm { r } _ { \mathrm { S } },$ for 15 pairs of data is -0.636, test the claim of correlation between the two variables. Use a significance level of 0.01.

Accepted Answer

$\mathrm { r } _ { \mathrm { S } } = - 0.636$. Critical values: $\mathrm { r } _ { \mathrm { S } } = \pm 0.654$.
Fail to reject the null hypothesis $\varrho _ { \mathrm { S } } = 0$. There does not appear to be a correlation between the two variables.

Question 12

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance
level  α\alphaα 
- n=6,α=0.05\mathrm { n } = 6 , \alpha = 0.05n=6,α=0.05

Accepted Answer

A)    r=±0.811r = \pm 0.811r=±0.811 
B)    r=±0.917\mathrm { r } = \pm 0.917r=±0.917 
C)    r=0.811r = 0.811r=0.811 
D)    r=0.878r = 0.878r=0.878

Question 13

Determine which scatterplot shows the strongest linear correlation.
-Which shows the strongest linear correlation?

Accepted Answer

A)  
B)  
C)

Question 14

The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

Accepted Answer

Yes, the residual plot suggests that the...

Question 15

Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Accepted Answer

Two variables may have a high correlation without being causally related. They may be strongly correlated because they are both associated with other variables, called lurking variables, that cause changes in both variables under consideration.
For example, a study found a positive linear correlation between teachers' salaries and the dollar amount of liquor sales. This does not imply causation (it does not imply that increasing teachers' salaries would cause an increase in liquor sales). A possible explanation is that both variables are tied to other variables, such as the rate of inflation, that pull them along together. Examples will vary.

Question 16

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.
- r=−0.466,n=15r = - 0.466 , n = 15r=−0.466,n=15

Accepted Answer

A)   Critical values:  r=±0.514\mathrm { r } = \pm 0.514r=±0.514 , no significant linear correlation
B)   Critical values:  r=±0.532r = \pm 0.532r=±0.532 , no significant linear correlation
C)   Critical values:  r=±0.514r = \pm 0.514r=±0.514 , significant linear correlation
D)   Critical values:  r=0.514\mathrm { r } = 0.514r=0.514 , no significant linear correlation  A

Question 17

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data.
- n=10,α=0.05\mathrm { n } = 10 , \alpha = 0.05n=10,α=0.05

Accepted Answer

A)    ±0.648\pm 0.648±0.648 
B)    −0.648- 0.648−0.648 
C)    0.6480.6480.648 
D)    ±0.564\pm 0.564±0.564

Question 18

For each of 200 randomly selected cities, Pete recorded the number of churches in the city (x) and the number of homicides in the past decade (y). He calculated the linear correlation coefficient and was surprised to find a strong positive linear correlation for the two variables. Does this suggest that building new churches causes an increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was
obtained? Explain your answer with reference to the term lurking variable.

Accepted Answer

The positive linear correlation coeffici...

Question 19

Find the value of the linear correlation coefficient r.
-The paired data below consist of the costs of advertising (in thousands of dollars)  and the number of products sold (in thousands) :   Cost 923425910 Number 8552556867868373\begin{array} { c | r r r r r r r r } 	ext { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\hline 	ext { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73\end{array} Cost  Number ​985​252​355​468​267​586​983​1073​​

Accepted Answer

A)   0.235
B)   0.708
C)   - 0.071
D)   0.246

Question 20

The sample data below are the typing speeds (in words per minute) and reading speeds (in words per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes reading speed. 
$$\begin{array} { l l l l l l l l l l } 
\hline \mathrm { x } & 60 & 56 & 52 & 63 & 70 & 58 & 44 & 79 & 62 \
\hline \mathrm { y } & 370 & 551 & 528 & 348 & 645 & 454 & 503 & 618 & 500 \
\hline
\end{array}$$ 
The regression equation $\hat { y } = 290.2 + 3.502 \mathrm { x }$ was obtained. Construct a residual plot for the data.

Accepted Answer

The answer of The sample data below are the typing...

Exam 10: Correlation and Regression

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Explanations will vary. An example follo...
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Yes, the residual plot suggests that the...
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Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - $\mathrm { n } = 16 , \alpha = 0.01$

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. Critical values: .
Fail to r...
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Define the terms predictor variable and response variable. Give examples for each.

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The predictor variable is x, representin...
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Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - $\begin{array}{r|rrrrr}\mathrm{x} & 1 & 3 & 5 & 7 & 9 \\\hline \mathrm{y} & 143 & 116 & 100 & 98 & 90\end{array}$

Correct Answer
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Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero. Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.

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Because the linear correlation coefficie...
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Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $\mathrm { r } = - 0.285 , \mathrm { n } = 90$

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Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

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A rank is a number assigned to an indivi...
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Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $\mathrm { r } = 0.71 , \mathrm { n } = 25$

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Given that the rank correlation coefficien $\mathrm { r } _ { \mathrm { S } },$ for 15 pairs of data is -0.636, test the claim of correlation between the two variables. Use a significance level of 0.01.

Correct Answer
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\(\mathrm { r } _ { \mathrm { S } } = - 0.636\). Critical values: \(\mathrm { r } _ { \mathrm { S } } = \pm 0.654\). Fail to reject the null hypothesis \(\varrho _ { \mathrm { S } } = 0\). There does not appear to be a correlation between the two variables.

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level $\alpha$ - $\mathrm { n } = 6 , \alpha = 0.05$

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Determine which scatterplot shows the strongest linear correlation. -Which shows the strongest linear correlation?

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The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

Correct Answer
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Yes, the residual plot suggests that the...
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Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $r = - 0.466 , n = 15$

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A

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - $\mathrm { n } = 10 , \alpha = 0.05$

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The positive linear correlation coeffici...
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Exam 10: Correlation and Regression

Correct AnswerverifiedExplanations will vary. An example follo...View AnswerShow Answer

Correct AnswerverifiedYes, the residual plot suggests that the...View AnswerShow Answer

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - n=16,α=0.01\mathrm { n } = 16 , \alpha = 0.01n=16,α=0.01

Correct AnswerverifiedShow Answer

Correct Answerverified. Critical values: .Fail to r...View AnswerShow Answer

Define the terms predictor variable and response variable. Give examples for each.

Correct AnswerverifiedThe predictor variable is x, representin...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero. Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.

Correct AnswerverifiedBecause the linear correlation coefficie...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

Correct AnswerverifiedA rank is a number assigned to an indivi...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Given that the rank correlation coefficien rS,\mathrm { r } _ { \mathrm { S } },rS​, for 15 pairs of data is -0.636, test the claim of correlation between the two variables. Use a significance level of 0.01.

Correct Answerverified\(\mathrm { r } _ { \mathrm { S } } = - 0.636\). Critical values: \(\mathrm { r } _ { \mathrm { S } } = \pm 0.654\). Fail to reject the null hypothesis \(\varrho _ { \mathrm { S } } = 0\). There does not appear to be a correlation between the two variables.

Correct AnswerverifiedShow Answer

Determine which scatterplot shows the strongest linear correlation. -Which shows the strongest linear correlation?

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The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

Correct AnswerverifiedYes, the residual plot suggests that the...View AnswerShow Answer

Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - r=−0.466,n=15r = - 0.466 , n = 15r=−0.466,n=15

Correct AnswerverifiedA

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - n=10,α=0.05\mathrm { n } = 10 , \alpha = 0.05n=10,α=0.05

Correct AnswerverifiedShow Answer

Correct AnswerverifiedThe positive linear correlation coeffici...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
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Explanations will vary. An example follo...
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Correct Answer
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Yes, the residual plot suggests that the...
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Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - $\mathrm { n } = 16 , \alpha = 0.01$

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Correct Answer
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. Critical values: .
Fail to r...
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The predictor variable is x, representin...
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Correct Answer
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Because the linear correlation coefficie...
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A rank is a number assigned to an indivi...
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Correct Answer
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Given that the rank correlation coefficien $\mathrm { r } _ { \mathrm { S } },$ for 15 pairs of data is -0.636, test the claim of correlation between the two variables. Use a significance level of 0.01.

Correct Answer
verified
\(\mathrm { r } _ { \mathrm { S } } = - 0.636\). Critical values: \(\mathrm { r } _ { \mathrm { S } } = \pm 0.654\). Fail to reject the null hypothesis \(\varrho _ { \mathrm { S } } = 0\). There does not appear to be a correlation between the two variables.

Correct Answer
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Correct Answer
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Correct Answer
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Yes, the residual plot suggests that the...
View Answer

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $r = - 0.466 , n = 15$

Correct Answer
verified
A

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. - $\mathrm { n } = 10 , \alpha = 0.05$

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Correct Answer
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The positive linear correlation coeffici...
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