Question 1

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 2

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 3

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.
-$r = - 0.466 , n = 15$

Accepted Answer

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

Question 4

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 $\alpha$
-$\mathrm { n } = 6 , \alpha = 0.05$

Accepted Answer

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

Question 5

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 6

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

Accepted Answer

A)  $\pm 0.648$ 
B)  $- 0.648$ 
C)  $0.648$ 
D)  $\pm 0.564$ 
A)  $\pm 0.648$ 
B)  $- 0.648$ 
C)  $0.648$ 
D)  $\pm 0.564$

Question 7

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

@#LAT-DLM&. Critical values: @#LAT-DLM&.
Fail to r

Question 8

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

Accepted Answer

The predictor variable is x, representin

Question 9

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): $$\begin{array} { c | r r r r r r r r } 
\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$$

Accepted Answer

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

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.
-$\mathrm { r } = - 0.285 , \mathrm { n } = 90$

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $\hat { y } = 150.7 - 6.8 x$ 
B)  $\hat { y } = - 150.7 + 6.8 x$ 
C)  $\hat { y } = - 140.4 + 6.2 x$ 
D)  $\hat { y } = 140.4 - 6.2 x$ 
A)  $\hat { y } = 150.7 - 6.8 x$ 
B)  $\hat { y } = - 150.7 + 6.8 x$ 
C)  $\hat { y } = - 140.4 + 6.2 x$ 
D)  $\hat { y } = 140.4 - 6.2 x$

Question 12

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...

Question 13

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

Accepted Answer

A)  $- 0.635$ 
B)  $\pm 0.635$ 
C)  $\pm 0.503$ 
D)  $0.635$ 
A)  $- 0.635$ 
B)  $\pm 0.635$ 
C)  $\pm 0.503$ 
D)  $0.635$

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

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 16

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 17

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 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

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.
-$\mathrm { r } = 0.71 , \mathrm { n } = 25$

Accepted Answer

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

Question 20

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

Accepted Answer

A) 
  
B) 
  
C) 
  
A) 
  
B) 
  
C)

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

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.

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. - $r = - 0.466 , n = 15$

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 $\alpha$ - $\mathrm { n } = 6 , \alpha = 0.05$

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.

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

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

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 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

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. - $\mathrm { r } = - 0.285 , \mathrm { n } = 90$

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 1 3 5 7 9 143 116 100 98 90

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

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?

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).

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? 2 4 6 9 10 12 28 33 39 45 47 52

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. - $\mathrm { r } = 0.71 , \mathrm { n } = 25$

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

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimates and Sample Size

Hypothesis Testing

Inferences From Two Samples

Chi-Square and Analysis of Variance

Filters

Exam 10: Correlation and Regression

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

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

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.

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

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

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 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 1 3 5 7 9 143 116 100 98 90

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

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?

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).

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? 2 4 6 9 10 12 28 33 39 45 47 52

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

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimates and Sample Size

Hypothesis Testing

Inferences From Two Samples

Chi-Square and Analysis of Variance

Filters

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.

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. - $r = - 0.466 , n = 15$

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

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