Question

The recommended air pressure in a basketball is between7and9pounds per square inch (psi). When dropped from a height of6feet, a properly inflated basketball should bounce upward between52and56inches (http://www.bestsoccerbuys.com/balls-basketball.html). The basketball coach at a local high school purchased10new basketballs for the upcoming season, inflated the balls to pressures between7and9psi, and performed the bounce test mentioned above. The data obtained are given in the following table.

Pressure (psi)	8.1	8.0	8.4	7.2	8.7	7.5	8.7	7.5	8.1	8.5
Bounce height (inches)	54.1	54.3	55.2	53.3	55.4	52.2	55.7	54.6	54.8	55.3

a. With the pressure as an independent variable and bounce height as a dependent variable, computeSSx⁢x,SSx⁢y, andSSy⁢y.

Enter the exact answers.

SSx⁢x⁢=Enter you answer; SS_xx
SSx⁢y=Enter you answer; SS_xy
SSy⁢y=Enter you answer; SS_yy

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b. Find the least squares regression line.

Round your answers to three decimal places.

y^=Enter you answer to the field 1 in accordance to the question statement+Enter you answer to the field 2 in accordance to the question statementx

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c. Interpret the meaning of the values ofaandbcalculated in part b.

ais the Choose your answer; a is the                                                                      psi air pressure increase needed to increase the bounce height one inch.inches the bounce height increases per every one psi increase in air pressure.bounce height of a basketball with zero psi air pressure.psi air pressure that leads to zero inch bounce height.
bis the Choose your answer; b is the                                                                      bounce height of a basketball with zero psi air pressure.inches the bounce height increases per every one psi increase in air pressure.psi air pressure that leads to zero inch bounce height.psi air pressure increase needed to increase the bounce height one inch.

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d. Calculaterandr2and explain what they mean.

Round your answers to three decimal places.

r=Enter you answer; r

This represents Choose your answer; r represents                                                                      the y-intercept of the linear regression line.the proportion of the variation explained by the use of the regression model.the strength of the linear relationship between the two variables.the slope of the linear regression line.the x-intercept of the linear regression line.


r2=Enter you answer; r^2

This represents Choose your answer; r^2 represents                                                                      the slope of the linear regression line.the strength of the linear relationship between the two variables.the y-intercept of the linear regression line.the proportion of the variation explained by the use of the regression model.the x-intercept of the linear regression line.

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e. Compute the standard deviation of errors.

Round your answer to three decimal places.

se=Enter your answer in accordance to the question statementEnter your answer in accordance to the question statement

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f. Predict the bounce height of a basketball forx=8.0.

Round your answer to three decimal places.

Enter your answer in accordance to the question statementEnter your answer in accordance to the question statement inches

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g. Construct a98%confidence interval forB.

Round your answers to three decimal places.

Enter your answer; confidence interval, lower bound to Enter your answer; confidence interval, upper bound

Answer 1