The manager of a DVD rental store analyzed the number of DVD rentals (y) to the number of weeks the DVD had been available (x) and found a strong negative correlation. What does this mean? As the number of weeks the DVD has been available increases, the number of rentals of that DVD increases. As the number of weeks the DVD has been available increases, the number of rentals of that DVD decreases. No customers rent old DVDs. When a DVD is new, it causes people to rent it.

The manager of a DVD rental store analyzed the number of DVD rentals (y) to the number of weeks the DVD had been available (x) and found a strong negative correlation. What does this mean? As the number of weeks the DVD has been available increases, the number of rentals of that DVD increases. As the number of weeks the DVD has been available increases, the number of rentals of that DVD decreases. No customers rent old DVDs. When a DVD is new, it causes people to rent it.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The correlation was found to be r=0.675. The percentage (to two decimal places) of variation in grocery bills explained by the family's weekly income regression line is:
A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.
The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). X1 = money spent on television advertising (in 1000's of dollars) X2 money spent on promotion (i.e., free samples) X3 = money spent on newspaper advertising (in 1000's of dollars) X4 average discounts offered to retail outlets (in %) Using data from the previous 18 months, the company decides to collect data on 6 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R´ for this model is 0.93, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places.
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if the slope is negative then is the correlation coefficient also negative?
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Summarize the definitions for linear correlation, quadratic correlations and exponential correlations. Provide an example graph of each of the types of correlation along with your summarized definitions.
A random sample of college students was surveyed about how they spend their time each week. The scatterplot below displays the relationship between the number of hours each student typically works per week at a part- or full-time job and the number of hours of television each student typically watches per week. The correlation between these variables is r = –0.63, and the equation we would use to predict hours spent watching TV based on hours spent working is as follows: Predicted hours spent watching TV = 17.21 – 0.23(hours spent working) Since we are using hours spent working to help us predict hours spent watching TV, we’d call hours spent working a(n) __________________ variable and hours spent watching TV a(n) __________________ variable. The correlation coefficient, along with what we see in the scatterplot, tells us that the relationship between the variables has a direction that is _________________ and a strength that is ______________________. According to the…
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		As the number of weeks the DVD has been available increases, the number of rentals of that DVD increases.
		As the number of weeks the DVD has been available increases, the number of rentals of that DVD decreases.
		No customers rent old DVDs.
		When a DVD is new, it causes people to rent it.