Question 1

Ten trucks were ranked according to their comfort levels and their prices.
 $$\begin{array} { c c c } 
\hline \text { Make } & \text { Comfort } & \text { Price } \
\hline \text { A } & \text { 1 } & 6 \
\text { B } & 6 & 2 \
\text { C } & 2 & 3 \
\text { D } & 8 & 1 \
\text { E } & 4 & 4 \
\text { F } & 7 & 8 \
\text { G } & 9 & 16 \
\text { H } & 1 Q & 9 \
\text { J } & \mathbf { 3 } & 5 \
\hline
\end{array}$$ 
Find the rank correlation coefficient and test the claim of correlation between comfort and price. Use a significance level of 0.05.

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Question 2

Suppose there is significant correlation between two variables. Describe two cases under which it might be inappropriate to use the linear regression equation for prediction. Give examples to support these cases.

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Question 3

Use the rank correlation coefficient to test for a correlation between the two variables.
-Use the sample data below to find the rank correlation coefficient and test the claim of correlation between math and verbal scores. Use a significance level of 0.05. 
$$\begin{array} { l l l l l l l l l l } 
\text { Mathematics } & 347 & 440 & 327 & 456 & 427 & 349 & 377 & 398 & 425 \
\hline \text { Verbal } & 285 & 378 & 243 & 371 & 340 & 271 & 294 & 322 & 385
\end{array}$$

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Question 4

Describe what scatterplots are and discuss the importance of creating scatterplots.

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Question 5

Use the rank correlation coefficient to test for a correlation between the two variables.
-Given that the rank correlation coefficient, rs, for 73 pairs of data is -0.663, test the claim of correlation between the two variables. Use a significance level of 0.05.

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Question 6

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

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Question 7

Use the rank correlation coefficient to test for a correlation between the two variables.
-The scores of twelve students on the midterm exam and the final exam were as follows. $$\begin{array} { l c c } 
\hline \text { Student } & \text { Midterm } & \text { Final } \
\hline \text { Navarro } & 93 & 91 \
\text { Reaves } & 89 & 85 \
\text { Hurlburt } & 71 & 73 \
\text { Knuth } & 65 & 77 \
\text { Lengyel } & 62 & 67 \
\text { Mcmeekan } & 74 & 79 \
\text { Bolker } & 77 & 65 \
\text { Ammatto } & 87 & 83 \
\text { Pothakos } & 82 & 89 \
\text { Sul1 ivan } & 81 & 71 \
\text { Hahl } & 91 & 81 \
\text { Zurfiuh } & 83 & 94 \
\hline
\end{array}$$
 Find the rank correlation coefficient and test the claim of correlation between midterm score and final exam score. Use a significance level of 0.05.

Accepted Answer

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Question 8

The variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average, than shorter people. Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient and explain why. Then give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero.

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Question 9

Use the rank correlation coefficient to test for a correlation between the two variables.
-A college administrator collected information on first-semester night-school students. A random sample taken of 12 students yielded the following data on age and GPA during the first semester. 
$\begin{array}{llcc}
  \text {  Age} &  \text {  GPA} \
 \underline{\text {x  }} & \underline{\text {y}}\
18&1.2\
26&3.8\
27&2.0\
37&3.3\
33&2.5\
47&1.6\
20&1.4\
48&3.6\
50&3.7\
38&3.4\
34&2.7\
22&2.8
\end{array}$
Do the data provide sufficient evidence to conclude that the variables age, $x$, and GPA, $y$, are correlated? Apply a rank-correlation test. Use $\alpha = 0.05$.

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Question 10

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a data point that is potentially an influential point. How could she confirm that this data point is indeed an influential point?

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Question 11

Suppose paired data are collected consisting of, for each person, their weight in pounds and the number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph.
How would the value of the correlation coefficient, r, change if all of the weights were converted to kilograms?

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Question 12

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

The answer of Use the rank correlation coefficient to test...

Question 13

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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Question 14

Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a) a strong positive correlation, b) a weak positive correlation, and c) no correlation?

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Question 15

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.

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Question 16

Use the rank correlation coefficient to test for a correlation between the two variables.
-Given that the rank correlation coefficient, r $\mathrm { r } _ { \mathrm { S } },$ , for 33 pairs of data is 0.338, test the claim of
correlation between the two variables. Use a significance level of 0.01.

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Question 17

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?

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Question 18

What is the relationship between the linear correlation coefficient and the usefulness of the regression equation for making predictions?

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Question 19

Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient and the value of the predictor variable.

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Question 20

Applicants for a particular job, which involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish (x) and their score on the test (y). 
$$\begin{array}{l}
\begin{array} { l c c c c c c c c c c } 
\hline \mathrm { x } & 3 & 4 & 4 & 2 & 5 & 3 & 4 & 5 & 3 & 2 \
\hline \mathrm { y } & 57 & 78 & 72 & 58 & 89 & 63 & 73 & 84 & 75 & 48 \
\hline
\end{array}\
\text { The regression equation } \hat { y } = 31.55 + 10.90 x \text { was obtained. Construct a residual plot for the }
\end{array}$$

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Quiz 10: Correlation and Regression

Suppose there is significant correlation between two variables. Describe two cases under which it might be inappropriate to use the linear regression equation for prediction. Give examples to support these cases.

Describe what scatterplots are and discuss the importance of creating scatterplots.

Use the rank correlation coefficient to test for a correlation between the two variables. -Given that the rank correlation coefficient, rs, for 73 pairs of data is -0.663, test the claim of correlation between the two variables. Use a significance level of 0.05.

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

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a data point that is potentially an influential point. How could she confirm that this data point is indeed an influential point?

Suppose paired data are collected consisting of, for each person, their weight in pounds and the number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph. How would the value of the correlation coefficient, r, change if all of the weights were converted to kilograms?

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.

Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a) a strong positive correlation, b) a weak positive correlation, and c) no correlation?

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.

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?

What is the relationship between the linear correlation coefficient and the usefulness of the regression equation for making predictions?

Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient and the value of the predictor variable.

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.