BASIC PRAC OF STATISTICS+LAUNCHPAD+REE
BASIC PRAC OF STATISTICS+LAUNCHPAD+REE
8th Edition
ISBN: 9781319123680
Author: Moore
Publisher: MAC HIGHER
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Chapter 5, Problem 5.42E

(a)

To determine

To find: The correlation for all four data sets.

To find: The least-squares regression line for all four data sets.

To find: The predicted value for x=10 using least-squares regression line for all four data sets.

(a)

Expert Solution
Check Mark

Answer to Problem 5.42E

The correlation for the data set A is 0.816.

The correlation for the data set B is 0.816.

The correlation for the data set C is 0.816.

The correlation for the data set D is 0.8176.

The least-squares regression line for the data set A is y^=3.00+0.500x.

The least-squares regression line for the data set B is y^=3.00+0.500x.

The least-squares regression line for the data set C is y^=3.00+0.500x.

The least-squares regression line for the data set D is y^=3.00+0.500x.

The predicted value for x=10 using least-squares regression line for the data set A is 8.001.

The predicted value for x=10 using least-squares regression line for the data set B is 8.001.

The predicted value for x=10 using least-squares regression line for the data set C is 8.000.

The predicted value for x=10 using least-squares regression line for the data set D is 8.001.

Explanation of Solution

Given info:

The four data sets are used to exploring the correlation and regression.

Calculation:

Correlation for Data set A:

Software procedure:

Step-by-step procedure to find the correlation between the x and y for data set A by using the MINITAB software:

  • Select Stat >Basic Statistics > Correlation.
  • In Variables, select x and y.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  1

From the MINITAB output, the correlation between the x and y for data set A is 0.816.

Correlation for Data set B:

Software procedure:

Step-by-step procedure to find the correlation between the x and y for data set B by using the MINITAB software:

  • Select Stat >Basic Statistics > Correlation.
  • In Variables, select x and y.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  2

From the MINITAB output, the correlation between the x and y for data set B is 0.816.

Correlation for Data set C:

Software procedure:

Step-by-step procedure to find the correlation between the x and y for data set C by using the MINITAB software:

  • Select Stat >Basic Statistics > Correlation.
  • In Variables, select x and y.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  3

From the MINITAB output, the correlation between the x and y for data set C is 0.816.

Correlation for Data set D:

Software procedure:

Step-by-step procedure to find the correlation between the x and y for data set D by using the MINITAB software:

  • Select Stat >Basic Statistics > Correlation.
  • In Variables, select x and y.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  4

From the MINITAB output, the correlation between the x and y for data set D is 0.817.

Equation of the least-squares line for Data set A:

Software procedure:

Step-by-step procedure to find the equation of the least-squares line by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  5

From the MINITAB output, the least-squares line for predicting y from x for data set A is y^=3.00+0.500x.

Equation of the least-squares line for Data set B:

Software procedure:

Step-by-step procedure to find the equation of the least-squares line by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  6

From the MINITAB output, the least-squares line for predicting y from x for data set B is y^=3.00+0.500x.

Equation of the least-squares line for Data set C:

Software procedure:

Step-by-step procedure to find the equation of the least-squares line by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  7

From the MINITAB output, the least-squares line for predicting y from x for data set C is y^=3.00+0.500x.

Equation of the least-squares line for Data set D:

Software procedure:

Step-by-step procedure to find the equation of the least-squares line by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  8

From the MINITAB output, the least-squares line for predicting y from x for data set D is y^=3.00+0.500x.

Predicted value for x=10 for Data set A:

Software procedure:

Step-by-step procedure to find the predicted value for x=10 using least-squares regression line for the data set A by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • In option, enter 10 under prediction.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  9

From the MINITAB output, the predicted value for x=10 using least-squares regression line for the data set A is 8.001.

Predicted value for x=10 for Data set B:

Software procedure:

Step-by-step procedure to find the predicted value for x=10 using least-squares regression line for the data set B by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • In option, enter 10 under prediction.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  10

From the MINITAB output, the predicted value for x=10 using least-squares regression line for the data set B is 8.001.

Predicted value for x=10 for Data set C:

Software procedure:

Step-by-step procedure to find the predicted value for x=10 using least-squares regression line for the data set C by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • In option, enter 10 under prediction.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  11

From the MINITAB output, the predicted value for x=10 using least-squares regression line for the data set C is 8.000.

Predicted value for x=10 for Data set D:

Software procedure:

Step-by-step procedure to find the predicted value for x=10 using least-squares regression line for the data set D by using the MINITAB software:

  • Choose Stat > Regression > Regression.
  • In Responses, enter the column of y.
  • In Predictors, enter the column of x.
  • In option, enter 10 under prediction.
  • Click OK.

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  12

From the MINITAB output, the predicted value for x=10 using least-squares regression line for the data set D is 8.001.

From the results, it can be observed that the correlation for all four data sets, the least-squares regression line and the predicted value for x=10 all four data sets are similar.

(b)

To determine

To construct: The scatterplot for each of the data sets with regression line.

(b)

Expert Solution
Check Mark

Answer to Problem 5.42E

Scatterplot for Data set A:

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  13

Scatterplot for Data set B:

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  14

Scatterplot for Data set C:

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  15

Scatterplot for Data set D:

Output using the MINITAB software is given below:

BASIC PRAC OF STATISTICS+LAUNCHPAD+REE, Chapter 5, Problem 5.42E , additional homework tip  16

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step-by-step procedure to construct scatterplot for x and y for all four data sets by using the MINITAB software:

  • Choose Graph > Scatter plot.
  • Choose With Regression, and then click OK.
  • Under Y variables, enter a column of y.
  • Under X variables, enter a column of x.
  • Click OK.

Observation:

The scatterplot shows that the predicted values are passed through the regression line of the model. Moreover, there is outlier that appears in the x and y directions for the data set A, B, and C. Also, the scatterplot for the data set D shows that the most of the points are plotted around 8.

(c)

To determine

To identify: Which of the four cases would you be willing to use the regression line to describe the dependence of y on x.

(c)

Expert Solution
Check Mark

Answer to Problem 5.42E

The data set A would use the regression line to describe the dependence of y on x.

Explanation of Solution

From the scatterplots for all data sets, it can be observed that the points for data set A are scattered around the straight line when compared to the other data sets. Hence, the data set A would use the regression line to describe the dependence of y on x.

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