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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

Will you expect a positive, zero, or negative linear correlation between the two variables for each of the following examples? a. SAT scores and GPAs of students b. Stress level and blood pressure of individuals c. Amount of fertilizer used and yield of corn per acre d. Ages and prices of houses e. Heights of husbands and incomes of their wives

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars. $$ \begin{array}{l|rrrrrrrr} \hline \text { Age } & 8 & 3 & 6 & 9 & 2 & 5 & 6 & 3 \\ \hline \text { Price } & 45 & 210 & 100 & 33 & 267 & 134 & 109 & 235 \\ \hline \end{array} $$ a. Do you expect the ages and prices of cars to be positively or negatively related? Explain. b. Calculate the linear correlation coefficient. c. Test at a \(2.5 \%\) significance level whether \(\rho\) is negative.

The following table gives information on GPAs and starting salaries (rounded to the nearest thousand dollars) of seven recent college graduates. $$ \begin{array}{l|rrrrrrr} \hline \text { GPA } & 2.90 & 3.81 & 3.20 & 2.42 & 3.94 & 2.05 & 2.25 \\ \hline \text { Starting salary } & 48 & 53 & 50 & 37 & 65 & 32 & 37 \\ \hline \end{array} $$ a. With GPA as an independent variable and starting salary as a dependent variable, compute \(\mathrm{SS}_{x x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x y}\) b. Find the least squares regression line. c. Interpret the meaning of the values of \(a\) and \(b\) calculated in part b. d. Calculate \(r\) and \(r^{2}\) and briefly explain what they mean. e. Compute the standard deviation of errors. fonstruct a \(95 \%\) confidence interval for \(B\). g. Test at a \(1 \%\) significance level whether \(B\) is different from zero. h. Test at a \(1 \%\) significance level whether \(\rho\) is positive.

The following data give the experience (in years) and monthly salaries (in hundreds of dollars) of nine randomly selected secretaries. $$ \begin{array}{l|rrrrrrrrr} \hline \text { Experience } & 14 & 3 & 5 & 6 & 4 & 9 & 18 & 5 & 16 \\ \hline \begin{array}{l} \text { Monthly } \\ \text { salary } \end{array} & 62 & 29 & 37 & 43 & 35 & 60 & 67 & 32 & 60 \\ \hline \end{array} $$ Construct a \(90 \%\) confidence interval for the mean monthly salary of all secretaries with 10 years of experience. Construct a \(90 \%\) prediction interval for the monthly salary of a randomly selected secretary with 10 years of experience.

The following data give information on the ages (in years) and the number of breakdowns during the last month for a sample of seven machines at a large company. $$ \begin{array}{l|rrrrrrr} \hline \text { Age (years) } & 12 & 7 & 2 & 8 & 13 & 9 & 4 \\ \hline \begin{array}{l} \text { Number of } \\ \text { breakdowns } \end{array} & 10 & 5 & 1 & 4 & 12 & 7 & 2 \\ \hline \end{array} $$ a. Taking age as an independent variable and number of breakdowns as a dependent variable, what is your hypothesis about the sign of \(B\) in the regression line? (In other words, do you expect \(B\) to be positive or negative?) b. Find the least squares regression line. Is the sign of \(b\) the same as you hypothesized for \(B\) in part a? c. Give a brief interpretation of the values of \(a\) and \(b\) calculated in part b. d. Compute \(r\) and \(r^{2}\) and explain what they mean. e. Compute the standard deviation of errors. f. Construct a \(99 \%\) confidence interval for \(B\). g. Test at a \(2.5 \%\) significance level whether \(B\) is positive. h. At a \(2.5 \%\) significance level, can you conclude that \(\rho\) is positive? Is your conclusion the same as in part g?