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Chapter 13: Problem 66

Will you expect a positive, zero, or negative linear correlation between the two variables for each of the following examples? a. Grade of a student and hours spent studying b. Incomes and entertainment expenditures of households c. Ages of women and makeup expenses per month d. Price of a computer and consumption of Coca-Cola e. Price and consumption of wine

Short Answer

Expert verified
The expected correlation for each example is: Grade and hours spent studying - positive; Incomes and entertainment expenditures - positive; Women's age and makeup expenses - could vary (positive, negative, or zero); Price of a computer and consumption of Coca-Cola - zero; Price and consumption of wine - negative.

Step by step solution

01

Analyze the relationship between grades and hours spent studying

When a student studies more, usually his or her grades improve. So, there is a positive correlation between grades of a student and hours spent studying.
02

Analyze the relationship income and entertainment expenditure

Generally, the more income a household has, the more they spend on entertainment. Thus, there is a positive correlation between incomes and entertainment expenditures of households.
03

Analyze the relationship between women's ages and makeup expenses

Women's ages and makeup expenses per month might not increase or decrease in the same trend. It could vary greatly depending on personal preferences or circumstances. Hence, the correlation could be positive, negative, or zero.
04

Analyze the relationship between price of a computer and consumption of Coca-Cola

The price of a computer and the consumption of Coca-Cola seem unrelated. People who buy expensive computers don't necessarily drink more Coca-Cola or vice versa. Hence, we would expect a zero correlation here.
05

Analyze the relationship between price and consumption of wine

Usually, as the price of a product increases, fewer people will buy it, and hence, the consumption decreases. So, there is a negative correlation between price and consumption of wine.

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Most popular questions from this chapter

Explain the following. a. Population regression line b. Sample regression line c. True values of \(A\) and \(\underline{B}\) d. Estimated values of \(A\) and \(B\) that are denoted by \(a\) and \(b\), respectively

The following table gives the total 2008 payroll (on the opening day of the season, rounded to the nearest million dollars) and the number of runs scored during the 2008 season by each of the American League baseball teams. $$ \begin{array}{lrr} \hline \text { Team } & \begin{array}{c} \text { Total Payroll } \\ \text { (millions of dollars) } \end{array} & \text { Runs Scored } \\ \hline \text { Baltimore Orioles } & 67 & 782 \\ \text { Boston Red Sox } & 123 & 845 \\ \text { Chicago White Sox } & 96 & 811 \\ \text { Cleveland Indians } & 82 & 805 \\ \text { Detroit Tigers } & 115 & 821 \\ \text { Kansas City Royals } & 71 & 691 \\ \text { Los Angeles Angels } & 114 & 765 \\ \text { Minnesota Twins } & 65 & 829 \\ \text { New York Yankees } & 201 & 789 \\ \text { Oakland Athletics } & 62 & 646 \\ \text { Seattle Mariners } & 99 & 671 \\ \text { Tampa Bay Rays } & 63 & 774 \\ \text { Texas Rangers } & 69 & 901 \\ \text { Toronto Blue Jays } & 81 & 714 \\ \hline \end{array} $$ a. Find the least squares regression line with total payroll as the independent variable and runs scored as the dependent variable. b. Is the equation of the regression line obtained in part a the population regression line? Why or why not? Do the values of the \(y\) -intercept and the slope of the regression line give \(A\) and \(B\) on \(a\) and \(b\) ? c. Give a brief interpretation of the values of the \(y\) -intercept and the slope obtained in part a. d. Predict the number of runs scored by a team with a total payroll of \(\$ 84\) million.

A researcher took a sample of 25 electronics companies and found the following relationship between \(x\) and \(y\), where \(x\) is the amount of money (in millions of dollars) spent on advertising by a company in 2009 and \(y\) represents the total gross sales (in millions of dollars) of that company for 2009 . $$ \hat{y}=3.6+11.75 x $$ a. An electronics company spent \(\$ 2\) million on advertising in \(2009 .\) What are its expected gross sales for \(2009 ?\) b. Suppose four electronics companies spent \(\$ 2\) million each on advertising in \(2009 .\) Do you expect these four companies to have the same actual gross sales for 2009 ? Explain. c. Is the relationship between \(x\) and \(y\) exact or nonexact?

Can the values of \(B\) and \(\rho\) calculated for the same population data have different signs? Explain.

Explain each of the following concepts. You may use graphs to illustrate each concept. A. Perfect positive linear correlation b. Perfect negative linear correlation c. Strong positive linear correlation d. Strong negative linear correlation e. Weak positive linear correlation f. Weak negative linear correlation g. No linear correlation
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