Notation The author conducted an experiment in which the height of each student was measured in centimeters and those heights were matched with the same students’ scores on the first statistics test. If we find that r = 0, does that indicate that there is no association between those two variables?

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

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Change in Scale Exercise 1 stated that for the given paired data, r = 0.846. How does that value change if all of the amounts of dinners are left unchanged but all of the tips are expressed in cents instead of dollars?

Interpreting a Computer Display

In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. The display is based on Data Set 10 “Family Heights” in Appendix B. (The response y variable represents heights of sons.)

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Height of Son Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not?

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

Predictions The sample data result in a linear correlation coefficient of r = 0.846 and the regression equation y^ = -0.00777 + 0.145x. What is the best predicted amount of tip, given that the cost of dinner was \$84.62? How was the predicted value found?

Testing for a Linear Correlation

In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Powerball Jackpots and Tickets Sold Listed below are the same data from Table 10-1 in the Chapter Problem, but an additional pair of values has been added from actual Powerball results. Is there sufficient evidence to conclude that there is a linear correlation between lottery jackpots and numbers of tickets sold? Comment on the effect of the added pair of values in the last column. Compare the results to those obtained in Example 4.

Variation and Prediction Intervals

In Exercises 17–20, find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions.

Weighing Seals with a Camera The table below lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University). For the prediction interval, use a 99% confidence level with an overhead width of 9.0 cm.

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

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Fixed Percentage If a restaurant were to change its tipping policy so that a constant tip of 20% of the bill is added to the cost of the dinner, what would be the value of the linear correlation coefficient for the paired amounts of dinners/tips?