/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q AP1.17. In retail stores, there is a lot... [FREE SOLUTION] | 91影视

91影视

In retail stores, there is a lot of competition for shelf space. Not only are there national brands for most products, but many stores have their own in-house

brands. Since shelf space is not infinite, the question is how many linear feet to allocate to each product and which shelf (top, bottom, or somewhere in the middle) to put it on. The middle shelf is the most popular and lucrative,

since many shoppers, if undecided, will simply pick the product that is at eye level. A local store that sells many upscale goods is trying to determine how much shelf space to allocate to its own brand of men鈥檚 personal grooming products. The middle shelf space is randomly varied between three and six linear feet over the next 12 weeks and weekly sales revenue (in dollars) from the store鈥檚 brand of personal-grooming products for men is recorded. Below is some computer output from the study, along with a scatterplot.

(a) Does it appear that the weekly sales revenue is related to the shelf length allocated to the house brand? Justify your answer.

(b) Write the equation of the least-squares regression line. Be sure to define any variables you use.

(c) If the store manager were to decide to allocate five linear feet of shelf space to the store鈥檚 brand of men鈥檚 grooming products, what is the best estimate of the weekly sales revenue?

(d) Interpret the value of s.

(e) Identify and interpret the coefficient of determination.

(f) The store manager questions the intercept of the regression line: 鈥淎m I supposed to believe that this analysis tells me that I can sell these products with no shelf space?鈥 How do you answer her?

Short Answer

Expert verified

Part (a) No.

Part (b) The equation isy=317.94+152.680x

Part (c) The best estimate is $1081.34

Part (d) An average the predicted sale of the week is likely to be deviated by $22.9212 from the actual or true sale.

Part (e) 98.2% of the variation on the response variable is explained by the least square line

Part (f) The length of the shelf is 0

Step by step solution

01

Part (a) Step 1: Given information

The figure is :

02

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Part (a) Step 3: Explanation

Output is

The pattern in the scatter plot is linear and positive, according to the provided scatter plot. In addition, there are no outliers in the plot and the points do not deviate from the main trend. As a result, the weekly sales revenue may be considered to be proportional to the length of the house given to the brand of house.

04

Part (b) Step 1: Calculation

The general equation of the regression line is,

y=a+bx

The dependent variable (X) is shelf length, and the dependent variable (Y) is sales, according to the query. The constant value is 317.94, and the coefficient of the variable "Shelf length" is 317.94, according to the provided output.

Thus, a=318.16and152.680

Putting the values of a and b in the regression line. Thus:

y=a+bx=317.94+152.680x

Thus, the regression line isy=317.94+152.680x

05

Part (c) Step 1: Calculation

The most accurate prediction of weekly sales income is:

y=317.94+152.680x=317.94+152.68(5)=1081.34

Thus, the best estimate is$1081.34

06

Part (d) Step 1: Explanation

s is 22.9212 in the output. It demonstrates that the expected sale of the week is likely to be $22.9212 off from the actual or genuine sale on average.

07

Part (e) Step 1: Explanation

The coefficient of determination reveals how much variance in the response variable is explained by the predictor variable. The coefficient of determination in this case is 98.2% As a result, the least square line may account for 98.2 percent of the variation in the response variable.

08

Part (f) Step 1: Explanation

The data range is between 3 and 6 feet, as can be observed. As a result, stating that the shelf's length is 0 would be incorrect. As a result, he should provide the right response.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Chocolate gets my heart pumping Cardiologists at Athens Medical School in Greece wanted to test whether chocolate affected blood flow in the blood vessels. The researchers recruited 17healthy young volunteers, who were each given a 3.5-ounce bar of dark chocolate, either bittersweet or fake chocolate.

On another day, the volunteers were switched. The subjects had no chocolate outside the study, and investigators didn鈥檛 know whether a subject had eaten the real or the fake chocolate. An ultrasound was taken of each volunteer鈥檚 upper arm to see the functioning of the cells in the walls of the main artery. The investigators found that blood vessel function was improved when the subjects ate bittersweet chocolate, and that there were no such changes when they ate the placebo (fake chocolate).

(a) What type of design did the investigators use in their study?

(b) Explain why the investigators chose this design instead of a completely randomized design.

(c) Why is it important to randomly assign the order of the treatments for the subjects?

Call the shots A newspaper advertisement for an upcoming TV show said: 鈥淪hould handgun control be tougher? You call the shots in a special call-in

poll tonight. If yes, call 1-900-720-6181If not, call 1-900-720-6182A charge is 50 cents for the first minute.鈥 Explain why this opinion poll is almost certainly biased.

Customer satisfaction A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 45,000

people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify the

population and the sample.

Ring-no-answer A common form of nonresponse in telephone surveys is 鈥渞ing-no-answer.鈥 That is, a call is made to an active number but no one answers. The Italian National Statistical Institute looked at nonresponse to a government survey of households in Italy during the periods January 1 to Easter and July 1 to August 31 All calls were made between7 and 10 p.m., but 21.4% gave 鈥渞ing-no-answer鈥 in one period versus 41.5% 鈥渞ing-no-answer鈥 in the other period15 Which period do you think had the higher rate of no answers? Why? Explain why a high rate of nonresponse makes sample results less reliable.

Look, Ma, no hands! Does talking on a hands-free cell phone distract drivers? Researchers recruit 40student subjects for an experiment to investigate this question. They have a driving simulator equipped with a hands-free phone for use in the study.

(a) Researchers are considering the design shown in the figure below. What type of design is this?

(b) Explain how blocking could be used to improve the design in (a).

(c) Why is it important to randomly assign the treatments within each block?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.