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Chapter 3: Q 77. (page 210)

Suppose that a tall child with an arm span of 120 cm and a height of 118 cm was added to the sample used in this study. What effect will this addition have on the correlation and the slope of the least-squares regression line?

a. Correlation will increase, and the slope will increase.

b. Correlation will increase, and the slope will stay the same.

c. Correlation will increase, and the slope will decrease.

d. Correlation will stay the same, and the slope will stay the same.

e. Correlation will stay the same, and the slope will increase.

Short Answer

Expert verified

The correct option is (b).

Step by step solution

01

Given information and Explanation

It is given that xbe as Arm span and ybe the height.

And also,

y铃�=6.4+0.93xx=120y=118

Now, let us find the predicted value as:

y铃�=6.4+0.93x=6.4+0.93(120)=118

As a result, the predicted and actual values are the same, indicating that the point will fall along the regression line. As a result, the data becomes more linear. As a result, the correlation will grow. And because this point has no effect on the regression line, the slope will remain unchanged.

Thus, option (b) is the correct option.

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Most popular questions from this chapter

Late bloomers? Japanese cherry trees tend to blossom early when spring weather is warm and later when spring weather is cool. Here are some data on the average March temperature (in degrees Celsius) and the day in April when the first cherry blossom appeared over a 24-year period:

a. Make a well-labeled scatterplot that鈥檚 suitable for predicting when the cherry trees will blossom from the temperature. Which variable did you choose as the explanatory variable? Explain your reasoning.

b. Use technology to calculate the correlation and the equation of the least-squares regression line. Interpret the slope and y-intercept of the line in this setting.

c. Suppose that the average March temperature this year was 8.2掳C. Would you be willing to use the equation in part (b) to predict the date of the first blossom? Explain your reasoning.

d. Calculate and interpret the residual for the year when the average March temperature was 4.5掳C.

e. Use technology to help construct a residual plot. Describe what you see.

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鈥檚 change. Calculation from data for an 18-year period gives x炉=1.75% sx=5.36% y炉=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.

b. Suppose that the percent change in a particular January was 2 standard deviations above average. Predict the percent change for the entire year without using the least-squares line.

Joan is concerned about the amount of energy she uses to heat her home.

The scatterplot shows the relationship between x = mean temperature in a particular month

and y = mean amount of natural gas used per day (in cubic feet) in that month, along with the regression line y^=1425鈭�19.87x

a. Predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30掳F.

b. Predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 65掳F.

c. How confident are you in each of these predictions? Explain your reasoning.

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.

Each year, students in an elementary school take a standardized math test at the end of the school year. For a class of fourth-graders, the average score was 55.1 with a standard deviation of 12.3. In the third grade, these same students had an average score of 61.7 with a standard deviation of 14.0. The correlation between the two sets of scores is r = 0.95. Calculate the equation of the least-squares regression line for predicting a fourth-grade score from a third-grade score.

a. y^=3.58+0.835x

b. y^=15.69+0.835x

c. y^=2.19+1.08x

d. y^=鈭�11.54+1.08x
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