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Chapter 12: Q. 4 (page 796)

An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69of the nearly 1000players on the PGA Tour’s world money list are examined. The average number of putts per hole and the player’s total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

The correlation between total winnings and the average number of putts per hole for these players is

(a)-0.285

(b)-0.081

(c)0.007

(d)0.081

(e) 0.285

Short Answer

Expert verified

The correlation between total winnings and the average number of putts per hole for these players is option (a) -0.285.

Step by step solution

01

Given information

The given data is

02

Explanation

"R-Sq" is the square of the linear correlation coefficient rin the output:

r2=8.1%=0.081

In the output, the slope of the least-squares regression line is provided as -4139198. The linear correlation coefficient rmust be negative because the slope is negative.

The negative square root ofr2yields the linear correlation coefficient r :

localid="1650644784650" r=-r2=-0.081≈-0.285.

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Most popular questions from this chapter

In physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. A scatterplot of the data is shown below. Note that a candela (cd) is a unit of luminous intensity in the International System of Unit

Physics textbooks suggest that the relationship between light intensity y and distance x should follow an “inverse square law,” that is, a power-law model of the form y=ax-2. We transformed the distance measurements by squaring them and then taking their reciprocals. Some computer output and a residual plot from a least-squares regression analysis on the transformed data are shown below. Note that the horizontal axis on the residual plot displays predicted light intensity

(a) Did this transformation achieve linearity? Give appropriate evidence to justify your answer.

(b) What would you predict for the intensity of a 100-watt bulb at a distance of 2.1meters? Show your work.

The swinging pendulum Refer to Exercise 33. Here is Minitab output from separate regression analyses of the two sets of transformed pendulum data:

Do each of the following for both transformations.

(a) Give the equation of the least-squares regression line. Define any variables you use.

(b) Use the model from part (a) to predict the period of a pendulum with length of 80 centimeters. Show your work.

(c) Interpret the value of s in context

Insurance adjusters are always vigilant about being overcharged for accident repairs. The adjusters suspect that Repair Shop 1quotes higher estimates than Repair Shop 2. To check their suspicion,

the adjusters randomly select 12cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to fix the vehicle. The

estimates are given below in hundreds of dollars.


Assuming that the conditions for inference are reasonably met, which of the following significance tests could legitimately be used to determine whether the adjusters’ suspicion is correct?

I. A paired ttest

II. A two-sample ttest

III. A t test to see if the slope of the population regression line is 0.

(a) I only

(b) II only

(c) I and III

(d) II and III

(e) I, II, and III

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than \(200,000.

(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

We record data on the population of a particular country from 1960to 2010. A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is,

log ( population) =-13.5+0.01(years).

Based on this equation, the population of the country in the year 2020 should be about

(a)6.7

(b) 812

(c) 5,000,000

(d) 6,700,000

(e) 8,120,000.
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