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Chapter 3: Q T3.7. (page 216)

When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least squares regression line. Suppose the slope of the least-squares regression line is 20.44. We may conclude that

a. the intercept will also be 鈭�0.44.

b. the intercept will be 1.0.

c. the correlation will be 1/鈭�0.44.

d. the correlation will be 1.0.

e. the correlation will also be 鈭�0.44.

Short Answer

Expert verified

The correct option is (e) the correlation will also be 鈭�0.44

Step by step solution

01

Given information

x=y=0sx=sy=1b=鈭�0.44

02

Concept

b=rsysx

03

Explanation

b=rsysxr=bsxsy=鈭�0.4411=鈭�0.44

Hence, the correct option is (e).

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Most popular questions from this chapter

It鈥檚 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鈥檚 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.

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child鈥檚 residual is

a. 鈭�3.2 cm.

b. 鈭�2.2 cm.

c. 鈭�1.3 cm.

d. 3.2 cm.

e. 62.2 cm.

More wins? Refer to Exercise 37

a. Interpret the slope of the regression line.

b. Does the value of the y-intercept have meaning in this context? If so, interpret the y-intercept. If not, explain why.

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.

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 xto be the percent change in a stock market index in January and the response variable yto be the change in the index for the entire year. We expect a positive correlation between xand y because the change during January contributes to the full year鈥檚 change. Calculation from data for an 18-year period gives

x炉=1.75%sz=5.36%y炉=9.07%sy=15.35%r=0.596

(a) What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January?

(b) For these data, s=8.3Explain what this value means
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