Question

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the table below.

Sales	Price
3	$12
4	$11
6	$10
10	$9
8	$8
10	$7

Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The 95% confidence interval that estimates the average weekly sales for a price of $9 is ________.

A. (1.96, 13.16)

B.(7.26, 7.86)

C.(5.93, 9.19)

D.(1.26, 13.86)

E.(1.69, 12.66)

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Question 6 0.25 pts

An office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees.

Employee	Presentations	New Clients
1	7	2
2	9	3
3	9	4
4	10	3
5	11	5
6	12	3

The manager would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The 90% prediction interval that estimates the number of new clients per month for an employee who makes nine presentations per month is ________.

A.(2.90, 3.97)

B.(1.83, 5.04)

C.(0.82, 5.44)

D.(0.00, 6.86)

E.

(0.34, 4.66)

Answer 1

Q 5) Let y=weekly sales

x= price of the novel

The regression line that we want to estimate is

where is the intercept, is the slope and is a random error

We calculate the following

n=6 is the number of observations

The sample means are

The sum of squares are

The estimated value of the slope is

The estimated value of the intercept is

the estimated regression line is

The 95% confidence interval that estimates the average weekly sales for a price of $9

The expected weekly sales for a price if $9 (x=9) is

The sum of square errors is

the mean square error is

The standard error of regression is

The standard error of is

The significance level for 95% confidence interval is

The right tail critical value is

The degrees of freedom is n-2=6-2=4

Using the t tables for df=4 and area under the right tail=0.025, we get

The 95% confidence interval is

ans: The 95% confidence interval that estimates the average weekly sales for a price of $9 is C.(5.93, 9.19)

Question 6) Let x= number of Presentations made per month

y= number of New Clients per month

The regression equation that we want to estimate is

The regression line that we want to estimate is

where is the intercept, is the slope and is a random error

We calculate the following

n=6 is the number of observations

The sample means are

The sum of squares are

The estimated value of the slope is

The estimated value of the intercept is

the estimated regression line is

The 90% prediction interval that estimates the number of new clients per month for an employee who makes nine presentations per month

The expected number of new clients for x=9 number of presentations is

The sum of square errors is

the mean square error is

The standard error of regression is

The standard error of prediction is

The significance level for 90% confidence interval is

The right tail critical value is

The degrees of freedom is n-2=6-2=4

Using the t tables for df=4 and area under the right tail=0.05, we get

The 90% confidence interval is

ans: The 90% prediction interval that estimates the number of new clients per month for an employee who makes nine presentations per month is  C.(0.82, 5.44)