Homework due April 8

A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is:

y = 16.6 + 0.65t

where y is the predicted weight and t is the age of the child. A 20-month old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds, for this child?

A) -7.85

B) -4.60

C) 4.60

D) 5.00

E) 7.85

• A

• B

• C

• D

• E

Each of 100 laboratory rats has available both plain water and a mixture water and caffeine in their cages. After 24 hours, two measures were recorded for each rat: the amount of caffeine the rat consumed, X, and the rat’s blood pressure, Y. The correlation between X and Y was found to be 0.428. Which of the following conclusions is justified on the basis of this study?

A) The correlation between X and Y in the population of rats is also 0.428.

B) If the rats stop drinking the water/caffeine mixture, this would cause a reduction in their

blood pressure.

C) About 18% of the variation in blood pressure can be explained by a linear relationship

between blood pressure and caffeine consumed.

D) Rats with lower blood pressure do not like the water/caffeine mixture as much as do rats

with higher blood pressure.

E) Since the correlation is not very high, the relationship between the amount of caffeine

consumed and blood pressure is not linear.

• A

• B

• C

• D

• E

Consider n pairs of numbers. The mean and standard deviation of the x-values are 5 and 4, respectively. The mean and standard deviation of the y-values 10 and 10, respectively. Of the following, which could be the least squares regression line?

• y = -5.0 + 3x

• y = 3x

• y= 8.5 + 0.3x

  Pick this one, the others are wrong

.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 ( for x between 9 and 25)

Where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

A) 3.3

B) 16.5

C) 25.2

D) 28.5

E) 41.7

• A

• B

• C

• D

• E

We record data on the population of narfles on Planet Zerg from 1960 to 2010. A scatter plot reveals a clear curved relationship between population and year. However, a different scatter plot suggests a strong linear relationship between the natural logarithm of the population and the year. The least-squares regression line for the transformed data is modeled by the equation (where year represents the actual year number):

ln(population) = -13.5 + 0.01(year)

What would this equation predict the population on Planet Zerg to be in 2008?

A) 1.88

B) 6.58

C) 20.08

D) 65.80

E) 720.54

• A

• B

• C

• D

• E

As shown, a least-squares regression line has been fitted to the winning percentages for a local sports team in each of the years 1983 through 1995. The percentage for the 1996 season was then plotted (as circled). Which of the following statements correctly describes how the value for the 1996 season will change the appearance of the least-squares regression line and the correlation coefficient if a new least-squares regression line (LSRL) is fitted to the 1983 through 1996 data?

A) The 1996 point will not have any effect on the LSRL since it follows the same downward trend.

B) The 1996 point will make the LSRL closer to horizontal and the correlation coefficient stronger.

C) The 1996 point will make the LSRL closer to horizontal and the correlation coefficient weaker.

D) The 1996 point will make the LSRL steeper and the correlation coefficient stronger.

E) The 1996 point will make the LSRL steeper and the correlation coefficient weaker.

• A

• B

• C

• D

• E

The computer output below shows the result of a linear regression analysis predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river:

Which of the following statements is a correct interpretation of the value 19.0 in the output?

A) On average, there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in the concentration of zinc found in the fish.

B) On average, there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in the concentration of lead found in the fish.

C) The concentration of zinc (in ppm) is about 19 times the concentration of lead (in ppm).

D) The concentration of lead (in ppm) is about 19 times the concentration of zinc (in ppm).

• A

• B

• C

• D

Which of the following inequalities correctly describes the values of the correlation coefficient, r, for each of the three data sets? Assume the scales are the same for each of these graphs.

A) r_a < r_b < r_c

B) r_c < r_a < r_b

C) r_b < r_c < r_a

D) r_b < r_a < r_c

E) r_a < r_c < r_b

• A

• B

• C

• D

• E

Two measures x and y were taken on 18 subjects. The first of two regressions, Regression I, yielded y = 24.5 + 16.1x . The second regression, Regression II, yielded log(y) = 1.6 + 0.51(log x). The residual plots are shown.

• A

• B

A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds’ total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

• Underestimate, because the residual is positive.

• Underestimate, because the residual is negative.

• Overestimate, because the residual is positive.

• Overestimate, because the residual is negative.

• Neither, because the residual is 0.

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CCSS.HSF.LE.B.5