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Chapter 3: Q 8. (page 171)

More putting success Refer to your graph from Exercise 4 Describe the relationship between distance from hole and percent of putts made for the sample of professional golfers.

Short Answer

Expert verified

Negative, strong, curved association with no outliers.

Step by step solution

01

Given information

For scatterplot:

Horizontal axis: Distance (ft .)

Vertical axis: Percent made.

02

Explanation

Strength: The dots on the scatterplot are fairly close together in the pattern, and there are no significant deviations from this overall pattern. As a result, strength will be abundant.

Form: There looks to be a bit of curvature in the scatterplot. As a result, the shape will be slightly bent.

Direction: No points in the other scatterplot points significantly vary from the general pattern in the scatterplot. As a result, there are no outliers.

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Most popular questions from this chapter

Suppose that the measurements of arm span and height were converted from centimeters to meters by dividing each measurement by 100. How will this conversion affect the values of r2 and s?

a. r2 will increase, s will increase.

b. r2 will increase, s will stay the same.

c. r2 will increase, s will decrease.

d. r2 will stay the same, s will stay the same.

e. r2 will stay the same, s will decrease.

The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year’s change. Calculation from data for an 18-year period gives x = X=1.75%sx=5.36%y=9.07%sy=15.35%r=0.596

(a) Find the equation of the least-squares line for predicting full-year change from January change. Show your work.

(b) The mean change in January is x=1.75%. Use your regression line to predict the change in the index in a year in which the index rises1.75% in January. Why could you have given this result (up to roundoff error) without doing the calculation?

In addition to the regression line, the report on the Mumbai measurements says that r2 =0.95. This suggests that

a. although arm span and height are correlated, arm span does not predict height very accurately.

b. height increases by 0.95=0.97 cm for each additional centimeter of arm

span.

c. 95% of the relationship between height and arm span is accounted for by the regression line.

d. 95% of the variation in height is accounted for by the regression line with x = arm span. e. 95% of the height measurements are accounted for by the regression line with x = arm span.

Managing diabetes People with diabetes measure their fasting plasma glucose (FPG, measured in milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months. The table gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.

a. Make a scatterplot with HbA as the explanatory variable. Describe what you see.

b. Subject 18 is an outlier in the x-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.

c. Subject 15 is an outlier in the y-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.

It’s still early We expect that a baseball player who has a high batting average in the first month of the season will also have a high batting average for the rest of the season. Using 66 Major League Baseball players from a recent season,33 a least-squares regression line was calculated to predict rest-of-season batting average y from first-month batting average x. Note: A player’s batting average is the proportion of times at-bat that he gets a hit. A batting average over 0.300 is considered very good in Major League Baseball.

a. State the equation of the least-squares regression line if each player had the same batting average the rest of the season as he did in the first month of the season.

b. The actual equation of the least-squares regression line is y^=0.245+0.109x

Predict the rest-of-season batting average for a player who had a 0.200 batting average the first month of the season and for a player who had a 0.400 batting average the first month of the season.

c. Explain how your answers to part (b) illustrate regression to the mean.
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