Elementary Statistics: A Step By Step Approach
Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.1.1RE

For Exercises 1 through 7, do a complete regression analysis by performing the following steps.

a. Draw the scatter plot.

b. Compute the value of the correlation coefficient.

c. Test the significance of the correlation coefficient at α = 0.01, using Table I.

d. Determine the regression line equation if r is significant.

e. Plot the regression line on the scatter plot, if appropriate.

f. Predict y′ for a specific value of x, if appropriate.

Sections 10–1 and 10–2

1. Customer Satisfaction and Purchases At a large department store customers were asked to rate the service and the materials purchased on a scale from 1 to 10, with 10 being the highest rating. Then the amount that they spent was recorded. Is there evidence of a relationship between the rating and the amount that they spent?

Chapter 10, Problem 10.1.1RE, For Exercises 1 through 7, do a complete regression analysis by performing the following steps. a.

a.

Expert Solution
Check Mark
To determine

To construct: The scatterplot for the variablesthe rating and the amount spent.

Answer to Problem 10.1.1RE

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 10, Problem 10.1.1RE , additional homework tip  1

Explanation of Solution

Given info:

The data shows the rating the rating and the amount spent (y) values.

Calculation:

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

  • Choose Graph > Scatterplot.
  • Choose Simple and then click OK.
  • Under Y variables, enter a column ofRating.
  • Under X variables, enter a column ofAmount spent.
  • Click OK.

b.

Expert Solution
Check Mark
To determine

To compute: The value of the correlation coefficient.

Answer to Problem 10.1.1RE

The value of the correlation coefficientis 0.864.

Explanation of Solution

Calculation:

Correlation coefficient r:

Software Procedure:

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

  • Select Stat >Basic Statistics > Correlation.
  • In Variables, select x and y from the box on the left.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 10, Problem 10.1.1RE , additional homework tip  2

From the MINITAB output, the value of the correlation is 0.864.

c.

Expert Solution
Check Mark
To determine

To test: The significance of the correlation coefficient at α=0.01 using Table I.

Answer to Problem 10.1.1RE

The conclusion is that,there is no linear relation between the rating and the amount spent.

Explanation of Solution

Given info:

The level of significance is α=0.01 and the sample size is 6.

Calculation:

The hypotheses are given below:

Null hypothesis:

H0:ρ=0

That is, there is no linear relation betweenthe rating and the amount spent.

Alternative hypothesis:

H1:ρ0

That is, there is a linear relation between the rating and the amount spent.

The sample size is 6.

The formula to find the degrees of the freedom is n2 .

That is,

n2=62=4

From the “TABLE –I: Critical Values for the PPMC”, the critical value for 4 degrees of freedom and α=0.01 level of significance is 0.917.

Rejection Rule:

If the absolute value of r is greater than the critical value then reject the null hypothesis.

Conclusion:

From part (b), the value of r is0.864 that is the absolute value of r is 0.864.

Here, the absolute value of r is less than the critical value |r|<critical value .

That is, |r|(=0.864)<critical value(=0.917) .

By the rejection rule,accept the null hypothesis.

There is no sufficient evidence to support the claim that “there is alinear relation betweenthe rating and the amount spent”.

d.

Expert Solution
Check Mark
To determine

To find: The regression equation for the given data.

Answer to Problem 10.1.1RE

The regression equation for the given is not valid.

Explanation of Solution

it is observed that the r is not significant.

Thus, the regression is not valid.

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Chapter 10 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 10.1 - When two variables are correlated, can the...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 23ECh. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECCh. 10.1 - Prob. 29ECCh. 10.1 - Prob. 30ECCh. 10.2 - Applying the Concepts 102 Stopping Distances...Ch. 10.2 - What two things should be done before one performs...Ch. 10.2 - What are the assumptions for regression analysis?Ch. 10.2 - Prob. 3ECh. 10.2 - What is the symbol for the slope? 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