91Ó°ÊÓ

Explain the meaning and concept of SSE. You may use a graph for illustration purposes.

Two variables \(x\) and \(y\) have a positive linear relationship. Explain what happens to the value of \(y\) when \(x\) increases.

A car rental company charges \(\$ 50\) a day and 20 cents per mile for renting a car. Let \(y\) be the total rental charges (in dollars) for a car for one day and \(x\) be the miles driven. The equation for the relationship between \(x\) and \(y\) is $$ y=50+.20 x $$ a. How much will a person pay who rents a car for one day and drives it 100 miles? b. Suppose each of 20 persons rents a car from this agency for one day and drives it 100 miles. Will each of them pay the same amount for renting a car for a day or do you expect each person to pay a different amount? Explain. c. Is the relationship between \(x\) and \(y\) exact or nonexact?

A diabetic is interested in determining how the amount of aerobic exercise impacts his blood sugar. When his blood sugar reaches \(170 \mathrm{mg} / \mathrm{dL}\), he goes out for a run at a pace of 10 minutes per mile. On different days, he runs different distances and measures his blood sugar after completing his run. Note: The preferred blood sugar level is in the range of 80 to \(120 \mathrm{mg} / \mathrm{dL}\). Levels that are too low or too high are extremely dangerous. The data generated are given in the following table. $$ \begin{array}{l|rrrrrrrrrrrr} \hline \text { Distance (miles) } & 2 & 2 & 2.5 & 2.5 & 3 & 3 & 3.5 & 3.5 & 4 & 4 & 4.5 & 4.5 \\ \hline \text { Blood sugar (mg/dL) } & 136 & 146 & 131 & 125 & 120 & 116 & 104 & 95 & 85 & 94 & 83 & 75 \\ \hline \end{array} $$ a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between distance run and blood sugar level? b. Find the predictive regression equation of blood sugar level on the distance run. c. Give a brief interpretation of the values of \(a\) and \(b\) calculated in part \(\underline{b}\). d. Plot the predictive regression line on the scatter diagram of part a and show the errors by drawing vertical lines between scatter points and the predictive regression line e. Calculate the predicted blood sugar level count after a run of \(3.1\) miles \((5\) kilometers) f. Estimate the blood sugar level after a 10 -mile run. Comment on this finding.

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

The recommended air pressure in a basketball is between 7 and 9 pounds per square inch (psi). When dropped from a height of 6 feet, a properly inflated basketball should bounce upward between 52 and 56 inches. The basketball coach at a local high school purchased 10 new basketballs for the upcoming season, inflated the balls to pressures between 7 and 9 psi, and performed the bounce test mentioned above. The data obtained are given in the following table. $$ \begin{array}{l|rrrrrrrrrr} \hline \text { Pressure (psi) } & 7.8 & 8.1 & 8.3 & 7.4 & 8.9 & 7.2 & 8.6 & 7.5 & 8.1 & 8.5 \\ \hline \text { Bounce height (inches) } & 54.1 & 54.3 & 55.2 & 53.3 & 55.4 & 52.2 & 55.7 & 54.6 & 54.8 & 55.3 \\ \hline \end{array} $$ a. With the pressure as an independent variable and bounce height 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 explain what they mean. e. Compute the standard deviation of errors. f. Predict the bounce height of a basketball for \(x=8.0\). g. Construct a \(98 \%\) confidence interval for \(B\). h. Test at the \(5 \%\) significance level whether \(B\) is different from zero. i. Using \(\alpha=.05\), can you conclude that \(\rho\) is different from zero?

Construct a \(95 \%\) confidence interval for the mean value of \(y\) and a \(95 \%\) prediction interval for the predicted value of \(y\) for the following. a. \(\hat{y}=13.40+2.58 x\) for \(x=8\) given \(s_{e}=1.29, \bar{x}=11.30, \mathrm{SS}_{x x}=210.45\), and \(n=12\) b. \(\hat{y}=-8.6+3.72 x\) for \(x=24\) given \(s_{e}=1.89, \bar{x}=19.70, \mathrm{SS}_{x x}=315.40\), and \(n=10\)