Unit 2

The following is a residual plot for linear regression of Y versus X What is indicated by the plot? (A) A linear model is appropriate. B. linear model is not appropriate. (C) Variability in y is constant for all values I. (D) At least one point is influential with respect to the regression. (E) At least one point is an outlier with respect to the regression.

B. A linear model is not appropriate

The least-squares regression line y = 1.8 - 0.2x summarizes the relationship between velocity, in feet per second, and depth, in feet, in measurements taken for a certain river, where [ represents velocity and y represents the depth of the river. What is the predicted value of y, in feel, when x = 5 (A) -16 (B) -1 (C)-0.2 D .0.8 (E) 1.8

D. 0.8

For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate? A. 0.71 b. 0.00 c. -0.14 d.-0.87 e. -1.00

A. 0.71

Which of the following scatter plots could represent a data set with a correlation coefficient of r= -1

A. Downward sloping image

A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Observational data were collected from 20 lion cubs. The researcher recorded how long they spent playing and the age when they began hunting. Because male and female lions have different hunting behaviors, the researcher recorded the data for males and females separately. The two scatterplots show the data for the 10 female lions and the 10 male lions. a. For female cubs only b. For kale cubs only c. For both make cubs and female cubs, with equal evidence d. For both make cubs abs female cubs. With more evidence for female cubs than male cubs e. For neither male cubs nor female cubs.

A. For female cubs only

. Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 years after partial-cut harvesting, and the percent of trees that were harvested in each of I1 forests. Which of the following is the best description of the relationship displayed in the scatterplot? A. Negative, linear, and strong (B) Positive, linear, and weak (C) Negative, nonlinear, and strong (D) Positive, nonlinear, and weak (E) Positive, nonlinear, and strong

A. Negative, linear and strong

The computer output below shows the result of a linear regression analysis for predicting the concentration of zin 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 I ppm in concentration of zinc found in the fish. b. On average there is a predicted increase of 19.0 ppm in concentration of zine for every increase of I ppm in concentration of lead found in the fish. C. The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead. (D) The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc. E. Approximately 19% of the variability in zine concentration is predicted by its linear relationship with lead concentration.

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

6. 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? A.Underestimate, because the residual is positive. (B)Underestimate, because the residual is negative. (C) Overestimate, because the residual is positive. (D)Overestimate, because the residual is negative. (E) Neither, because the residual is 0.

A. Underestimate because the residual is positive

3. As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medical records of 1,436 people. The table below summarizes tanning booth use for people in the study who did and did not have skin cancer. of the people who had skin cancer what fraction used a tanning booth? (A) 190/265 (B)190/896 (C) 190/1,436 (D) 265/1, 436 (E) 896/1, 436

B. 190/896

A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient? A) 0.64 B. 0.60 (C) 0.40 (D)0.36 (E)0.13

B. 0.60

13. In a study to detenmine whether miles driven is a good predictor of trade-in value, Il cars of the same age, make; model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars, Five of the points are labeled A, B, C, D, and E, respectively. which of the five labeled points is the most influential with respect to a regression of trade in value versus miles driven? a. A B. b c. C d. D e. E

B. b

For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches, The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long? (A) Yes, because 3 inches falls above the maximum value of lengths in the sample. (B) Yes, because the regression equation is based on a random sample. (C)Yes, because the association between length and weight is positive. D. No, because 3 inches falls above the maximum value of lengths in the sample (E)No, because there may not be any 3-inch fish of this species in the pond

D. No because 3 inches far above the maximum value of lengths in the sample

A study was conducted on three types of home siding and the type of damage done to the siding by woodpeckers. Each hole made by a woodpecker was classified as either drumming (territorial signaling), foresting (looking for food), or nesting. The following bar chart shows the relative frequency of the holes for each type of siding Which of the following statements is supported by the bar chart? (A) The proportion of holes created for drumming is the same for all three siding types. (B) The proportion of holes created for drumming is greatest for grooved plywood. c . The proportion of holes created for drumming is least for grooved plywood. D. The number of holes created for drumming is least for grooved plywood. E. The number of holes created for drumming is greatest for nonwood.

c . The proportion of holes created for drumming is least for grooved plywood.