The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time: a. Calculate the value of the correlation coefficient , r. Does the value of r suggest a strong linear relationship? b. Construct a scatterplot . From the plot, does the word linear provide the most effective description of the relationship between x and y ? Explain.

Question

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Answer 1

Textbook Question

Chapter 5, Problem 68CR

The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:

Chapter 5, Problem 68CR, The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y

a. Calculate the value of the correlation coefficient, r. Does the value of r suggest a strong linear relationship?
b. Construct a scatterplot. From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

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Students have asked these similar questions

In regression analysis, the equation that describes how the response variable (y) is related to the explanatory variable (x) is:A. the correlation model.B. the regression model.C. used to predict y given a value of x.D. the coefficient of determination.

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Answer 2

Textbook Question

Chapter 5, Problem 68CR

The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:

Chapter 5, Problem 68CR, The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y

a. Calculate the value of the correlation coefficient, r. Does the value of r suggest a strong linear relationship?
b. Construct a scatterplot. From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

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Answer 3

Textbook Question

Chapter 5, Problem 68CR

The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:

Chapter 5, Problem 68CR, The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y

a. Calculate the value of the correlation coefficient, r. Does the value of r suggest a strong linear relationship?
b. Construct a scatterplot. From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 5, Problem 68CR

The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:

Chapter 5, Problem 68CR, The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y

a. Calculate the value of the correlation coefficient, r. Does the value of r suggest a strong linear relationship?
b. Construct a scatterplot. From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

Answer 8

a.

Expert Solution

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer 13

Answer to Problem 68CR

The correlation coefficient is –0.981.

Answer 14

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

Choose Stat > Basic Statistics > Correlation.
Enter the columns of x, y under Variables.
Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 1

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

Answer 15

b.

Expert Solution

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer 20

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Introduction To Statistics And Data Analysis, Chapter 5, Problem 68CR , additional homework tip 2

Answer 21

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

Choose Graph > Scatterplot > Simple > OK.
Enter the column of y under Y-variables.
Enter the column of x under X-variables.
Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.