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Chapter 3: Q T3.4. (page 215)

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�

What was the actual activity level rating for the fish at a temperature of 20掳C?

a. 87

b. 84

c. 81

d. 66

e. 3

Short Answer

Expert verified

The correct option is (a)87

Step by step solution

01

Given information

x=Temperature

y=Activity level rating

02

Explanation

Least-squares regression line:

y铃�=a+bx

Calculating the value of aand busing Minitab

a=148.62b=鈭�3.2167

General least-squares regression line:

y铃�=148.62鈭�3.2167x

Finding the expected activity level at 20degrees Celsius by replacing xin the least-squares regression line equation with 20and calculating:

y=Resudal+y铃�=84.286+3=87.286鈮�87

The estimated level of activity is 84.286

The real value would be added to the equation with y

y=Resudal+y铃�=84.286+3=87.286鈮�87

The real level rating for the fish at a temperature of 20degrees Celsius has been found to be around 87

Hence, the correct option is (a)

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Most popular questions from this chapter

Using data from the LPGA tour, a regression analysis was performed using x = average driving distance and y = scoring average. Using the output from the regression analysis shown below, determine the equation of the least-squares regression line.

a. y^=87.974+2.391x

b. y^=87.974+1.01216x

c. y^=87.974鈭�0.060934x

d. y^=鈭�0.060934+1.01216x

e. y^=鈭�0.060934+87.947x

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.

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

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.
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