Concept explainers
For Exercises 1 through 7, do a complete regression analysis by performing the following steps.
a. Draw the
b. Compute the value of the
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?
a.
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:
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.
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:
From the MINITAB output, the value of the correlation is 0.864.
c.
To test: The significance of the correlation coefficient at
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
Calculation:
The hypotheses are given below:
Null hypothesis:
That is, there is no linear relation betweenthe rating and the amount spent.
Alternative hypothesis:
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
That is,
From the “TABLE –I: Critical Values for the PPMC”, the critical value for 4 degrees of freedom and
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
That is,
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.
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
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