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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
a. Positive. b. Positive. c. Highly dependent on individual preferences, but could be negative assuming younger individuals spend more. d. Zero. e. Negative.

Step by step solution

01

Correlation Assessment for Scenario A

For the variable pair 'Grade of a student and hours spent studying', one can predict a positive correlation. As the number of hours spent studying tends to increase, so does a student's grade.
02

Correlation Assessment for Scenario B

Looking at 'Incomes and entertainment expenditures of households', one would expect a positive correlation as well. That is because, typically, households with higher incomes spend more on entertainment.
03

Correlation Assessment for Scenario C

In the case of 'Ages of women and makeup expenses per month', without any further information, it's hard to predict a clear correlation. This can vary considerably based on personal preferences. However, assuming that younger individuals might spend more on makeup products, one might assume a negative correlation.
04

Correlation Assessment for Scenario D

For 'Price of a computer and consumption of Coca-Cola', there is likely zero correlation because these two variables seem unlikely to impact each other.
05

Correlation Assessment for Scenario E

Concerning 'Price and consumption of wine', conventional wisdom would predict a negative correlation. As the price of wine increases, the quantity consumed is likely to decrease.

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Most popular questions from this chapter

The owner of a small factory that produces working gloves is concerned about the high cost of air conditioning in the summer but is afraid that keeping the temperature in the factory too high will lower productivity. During the summer, he experiments with temperature settings from \(68^{\circ} \mathrm{F}\) to \(81^{\circ} \mathrm{F}\) and measures each day's productivity. The following table gives the temperature and the number of pairs of gloves (in hundreds) produced on each of the 8 randomly selected days. $$ \begin{array}{l|cccccccc} \hline \text { Temperature }\left({ }^{\circ} \mathrm{F}\right) & 72 & 71 & 78 & 75 & 81 & 77 & 68 & 76 \\ \hline \text { Pairs of gloves } & 37 & 37 & 32 & 36 & 33 & 35 & 39 & 34 \\ \hline \end{array} $$ a. Do the pairs of gloves produced depend on temperature, or does temperature depend on pairs of gloves produced? Do you expect a positive or a negative relationship between these two variables? b. Taking temperature as an independent variable and pairs of gloves produced as a dependent variable, compute \(\mathrm{SS}_{x x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x x}\) c. Find the least squares regression line. d. Interpret the meaning of the values of \(a\) and \(b\) calculated in part \(\mathrm{c}\). e, Plot the scatter diagram and the regression line. f. Calculate \(r\) and \(r^{2}\), and explain what they mean. g. Compute the standard deviation of errors. h. Predict the number of pairs of gloves produced when \(x=74\). i. Construct a \(99 \%\) confidence interval for \(B\). i. Test at a \(5 \%\) significance level whether \(B\) is negative. k. Using \(\alpha=.01\) can you conclude that \(\rho\) is negative?

The following table, reproduced from Exercise \(13.53\), gives the experience (in years) and monthly salaries (in hundreds of dollars) of nine randomly selected secretaries. $$ \begin{array}{l|rrrrrrrrr} \hline \text { Experience } & 14 & 3 & 5 & 6 & 4 & 9 & 18 & 5 & 16 \\ \hline \text { Monthly salary } & 62 & 29 & 37 & 43 & 35 & 60 & 67 & 32 & 60 \\\ \hline \end{array} $$ a. Do you expect the experience and monthly salaries to be positively or negatively related? Explain. b. Compute the linear correlation coefficient. c. Test at a \(5 \%\) significance level whether \(\rho\) is positive.

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

A population data set produced the following information. $$ N=460, \quad \Sigma x=3920, \quad \Sigma y=2650, \quad \Sigma x y=26,570, \quad \sum x^{2}=48,530 $$ Find the population regression line.

Two variables \(x\) and \(y\) have a negative linear relationship. Explain what happens to the value of \(y\) when \(x\) increases. Give one example of a negative relationship between two variables.
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