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Chapter 3: Q 78. (page 210)

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.

Short Answer

Expert verified

The correct option is (e)r2will stay the same, swill decrease.

Step by step solution

01

Given information

The regression equation is:y铃�=6.4+0.93x

02

Explanation

The coefficient of determination reveals how much variance in the response variable is explained by the predictor variable. The relationship between the variables is unaffected by the change in unit. Because there is no change in the relationship. As a result, the coefficient of determination will remain unchanged. The sample size has a negative relationship with the standard deviation. The s would be reduced by dividing by 100 As a result, the residual's standard deviation would decrease. Hence, the correct option is (e).

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Most popular questions from this chapter

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.

An AP庐 Statistics student designs an experiment to see whether today鈥檚 high school students are becoming too calculator-dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes鈥攐ne with a calculator and one without鈥攊n random order. To analyze the data, the student constructs a scatterplot that displays a linear association between the number of correct answers with and without a calculator for the 30 students. A least-squares

regression yields the equation. calculator^ = 鈭�1.2 + 0.865 (pencil) r = 0.79

Which of the following statements is/are true?

I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.

II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same.

III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was smaller than the standard deviation on the calculator quizzes.

a. I only

b. II only

c. III only

d. I and III only

e. I, II, and III

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model y^=25.2+3.3x , where x is the number of chirps per minute and y^ is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of = chirps per minute?

a. 3.3掳F

b. 16.5掳F

c. 25.2掳F

d. 28.5掳F

e. 41.7掳F

Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled 鈥淔itted value,鈥� which means the same thing as 鈥減redicted value.鈥�

Which of the following gives a correct interpretation of s in this setting?

a. For every 1掳C increase in temperature, fish activity is predicted to increase by 4.785 units.

b. The typical distance of the temperature readings from their mean is about 4.785掳C.

c. The typical distance of the activity level ratings from the least-squares line is about 4.785 units.

d. The typical distance of the activity level readings from their mean is about 4.785 units.

e. At a temperature of 0掳C, this model predicts an activity level of 4.785 units.
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