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?

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:

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.

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:

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

To determine

To test: The significance of the correlation coefficient at $\alpha =0.01$ 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 $\alpha =0.01$ and the sample size is 6.

Calculation:

The hypotheses are given below:

Null hypothesis:

$H_0:\rho =0$

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

Alternative hypothesis:

$H_1:\rho \ne 0$

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 $n-2$.

That is,

$\begin{array}{c}n-2=6-2\\ =4\end{array}$

From the “TABLE –I: Critical Values for the PPMC”, the critical value for 4 degrees of freedom and $\alpha =0.01$ 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 $\left|r\right|<\text{critical value}$.

That is, $\left|r\right|\left(=0.864\right)<\text{critical value}\left(=0.917\right)$.

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”.

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.