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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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.
A pediatrician wants to determine the relation that exists between a child's height (x) and head circumference (y). She randomly selects 11 children from her practice and measures their height and head circumference in inches. She finds that the correlation is 0.477 and the regression equation is y = 0.149x + 8.15 What proportion of the variation in head circumference can be explained by the variation in the values of height? % Report answer as a percentage accurate to one decimal place.
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.
A linear model was fit to predict weekly Sales of frozen pizza (in pounds) from the average Price ($/unit) charged by a sample of stores in a city in 39 weeks over a three -year period. The average Sales were 63, 200 pounds (SD = 10, 670 pounds), and the correlation between Price and Sales was -0.529. If the Price in a particular week was two SD higher than the mean Price, how much pizza would you predict was sold that week?
A pediatrician wants to determine the relation that exists between a child's height (x) and head circumference (y). She randomly selects 11 children from her practice and measures their height and head circumference in inches. She finds that the correlation is 0.694, and the regression equation is y = 0.294x + 2.02. What proportion of the variation in head circumference can be explained by the variation in the values of height? Round your answer to three decimal places. %
A researcher is studying the intensity of hurricanes that entered the Gulf of Mexico between 1975-2015 and the average water temperature of the Gulf of Mexico at the hurricane's peak strength. What is the independent and dependent variable in this study?
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). X 1 = 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) = average discounts offered to retail outlets (in %) Using data from the previous 16 months, the company decides to collect data on 2 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R for this model is 0.81, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places.
A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable. T or F
A researcher studied the relationship between the amount of carbohydrates (x) and the amount of salt (y) in different food products. sample of 36 food products yielded these calculations: r = -0.1245, ŷ=0.5545– 0.1636x According to the correlation, if a food contains more carbohydrates, is it likely to contain more salt or less salt? Why or why not?
For 39 nations, a correlation of 0.887 was found between y = Internet use (%) and x = gross domestic product (GDP, in thousands of dollars per capita). The regression equation is y = -3.68 + 1.73x. Complete parts (a) through (c). a. Based on the correlation value, the slope had to be positive. Why? A. The slope and correlation are positive because gross domestic product could not be negative. B. The correlation and the slope are positive because the y-intercept is negative. C. That is a very unusual fact, because the slope and correlation usually have different signs. D. Although slope and correlation usually have different values, they always have the same sign.

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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.