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Chapter 3: Q T3.8. (page 216)

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

Short Answer

Expert verified

The correct option is (b)16.5掳F

Step by step solution

01

Given information

The regression equation for least-squares

y铃�=25.2+3.3x

02

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

03

Explanation

replacingxbyx+5y铃�=25.2+3.3(x+5)=(25.2+3.3x)+16.5

It is observed that if x is increased by 5 then the expected value y increases by 16.5F

Hence, the correct option is (b)

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Most popular questions from this chapter

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

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.

Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon, left by the skeletons of single-celled creatures called diatoms, is a measure of the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look further into the past. Here is a scatterplot of data from 2300 to 12,000 years ago:

a. Identify the unusual point in the scatterplot and estimate its x and y coordinates.

b. Describe the effect this point has on

i. the correlation.

ii. the slope and y-intercept of the least-squares line.

iii. the standard deviation of the residuals.

Long jumps Here are the 40-yard-dash times (in seconds) and long-jump distances (in inches) for a small class of 12 students:

a. Sketch a scatterplot of the data using dash time as the explanatory variable.

b. Use technology to calculate the equation of the least-squares regression line for predicting the long-jump distance based on the dash time. Add the line to the scatterplot from part (a).

c. Explain why the line calculated in part (b) is called the 鈥渓east-squares鈥� regression line.

Crickets keep chirping In Exercise 44, we summarized the relationship between x = temperature in degrees Fahrenheit and y = chirps per minute for the striped ground cricket, with the regression line y^=鈥�0.31+0.212x. For this model, technology gives s = 0.97 and r2 = 0.697.

a. Interpret the value of s.

b. Interpret the value of r2.
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