Emhof

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?

−0.87

The table shows several values of xx and their corresponding values of yy. Which of the following is closest to the correlation between xx and yy?

0.98

The following is a residual plot for a linear regression of yy versus xx.

A linear model is not appropriate.

A set of bivariate data was used to create a least-squares regression line. Which of the following is minimized by the line?

The sum of the squared residuals

An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses—0.0, 0.5, 1.0, 1.5, 2.0—in milligrams (mg) of medication. The results are shown in the scatterplot below.

The variation in the hours of pain relief is not the same across the doses.

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 ŷ = 25.2 + 3.3x 9 < x < 25, where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

B 16.5 ° F

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

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

Consider n pairs of numbers (x1,y1), (x2,y2), ..., and (xn, yn). The mean and standard deviation of the x-values are x̄ =5 and sx = 4, respectively. The mean and standard deviation of the y-values are ȳ = 10 and sy = 10 respectively. Of the following, which could be the least squares regression line?

ŷ = 8.5 + 0.3x

A researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age.

No, because the graph displays a UU-shaped pattern.

The least-squares regression line yˆ=1.8−0.2xy^⁢=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 xx represents velocity and yy represents the depth of the river. What is the predicted value of yy, in feet, when x=5x=5?

D 0.8

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?

0.60

A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output.

30

Researchers observed the grouping behavior of deer in different regions. The following scatterplot shows data collected on the size of the group and the percent of the region that was woodland.

As the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.

A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.

Machine A usually, but not always, produced fewer defective parts than machine B.

At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association?

The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.80.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

The proportion of the variation in height that is explained by a regression on age is 0.640.64.

An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot?

There should be no pattern in the residual plot.

Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?

1

Which of the following is the best description of a positive association between two variables?

As the value of one of the variables increases, the value of the other variable tends to increase.

A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height?

B There is no linear relationship between time and height.

Data were collected on the fiber diameter and the fleece weight of wool taken from a sample of 2020 sheep. The data are shown in the following graphs. Graph 11 is a scatterplot of fleece weight versus fiber diameter with the respective least-squares regression line shown. Graph 22 is the associated plot of the residuals versus the predicted values.

C

A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?

C 0.59

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males.

For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day.

In a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was "horrible" and 9 was "excellent". For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot below was constructed.The horizontal axis represents the student rating, and the vertical axis represents the parent rating.Thus, an individual data point would represent the rating of a single movie.

The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give higher scores.

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-squares regression line produced from a random sample is Milkˆ=40.8−1.1(Age)Milk^=40.8−1.1(Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?

A cow of 5 years is predicted to produce 5.5 more gallons per week.

A researcher collected data on the latitude, in degrees north of the equator, and the average low temperature, in degrees Fahrenheit, for a random sample of cities in Europe. The data were used to create the following equation for the least-squares regression line.predicted average low temperature=65.5−0.70(latitude)predicted average low temperature=65.5−0.70(latitude) Which of the following is the best interpretation of the slope of the line?

B For each one degree north of the equator increase, the predicted average low temperature decreases on average by 0.700.70 degree Fahrenheit.

The least-squares regression line Sˆ=0.5+1.1LS^=0.5+1.1L models the relationship between the listing price and the actual sales price of 12 houses, with both amounts given in hundred-thousands of dollars. Let LL represent the listing price and SS represent the sales price.

For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $110,000.

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.

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 11 forests.

Negative, linear, and strong

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?

No, because 3 inches falls above the maximum value of lengths in the sample.

A family would like to build a linear regression equation to predict the amount of grain harvested per acre of land on their farm. They subdivide their land into several smaller plots of land for testing and would like to select an explanatory variable they can control. Which of the following is an appropriate explanatory variable that the family could use to create a linear regression equation?

The amount of fertilizer applied to each plot of land

The height hh and collar size cc, both in centimeters, measured from a sample of boys were used to create the regression line cˆ=−94+0.9hc^=−94+0.9h. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?

The cc-intercept of the regression line

An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree.

The height increases, on average, by 0.48 meter each year.

A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?

The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.

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.

Underestimate, because the residual is positive.