Two Quantitative variables
Which of the following is the best description of a positive association between two variables?
A. The values will create a line when graphed on a scatterplot.
B. The values will create a line with positive slope when graphed on a scatterplot.
C. As the value of one of the variables increases, the value of the other variable tends to decrease.
D. As the value of one of the variables increases, the value of the other variable tends to increase.
E. All values of both variables are positive.
D. As the value of one of the variable increases, the value of the other variable tends to increase.
For which of the following scatterplots is the correlation between x and y closest to 1?
A.
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?
A. The total amount of rainfall recorded at their farm.
B. The type of crop planted in the plot the previous year.
C. The average daily temperature at their farm.
D. The variety of grain planted in the plot.
E. The amount of fertilizer applied to each plot of land.
E. The amount of fertilizer applied to each plot of land.
A data scientist had 5 different sets of data. For each data set the scientist fit a least-squares regression line, then graphed the residuals versus the predicted values for each. Which residual plot indicates that the least-squares regression model was the most appropriate model to fit the data?
D.
The following scatterplot displays the data collected on the mass, in grams, and the age, in days, for a sample of chameleon eggs.
Which of the following is the best description of the relationship between the mass and the age of the chameleon eggs?
A. The association is negative and linear.
B. The association is positive and linear.
C. There is no association between the variables.
D. The association is positive and nonlinear.
E. The association is negative and nonlinear.
D. The association is positive and nonlinear
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?
A. The relationship is linear because the correlation is positive.
B. The relationship is not linear because the correlation is positive.
C. The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.
D. The parties with a larger number of customers are associated with the shorter times elapsed until the party left the restaurant.
E. There is no relationship between the number of customers in a party at a table in the restaurant and the time required until the party left the restaurant.
C. The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.
A pediatrician is studying growth in boys ages 7 to 12 years old. The data shows a roughly linear relationship and the doctor creates a regression model to predict a boy's height from his age.
Should this model be used to predict the height of a 15-year-old-boy?
A. Yes, because the plot appears linear
B. Yes, because the regression model allows a prediction for any age.
C. Yes, because boys age 7 to 12 grow at a relatively constant rate.
D. No, because the pediatrician may not have any 15-year-old boys in their practice
E. No, because 15 is older than any of the boys in the study.
E. No because 15 is older than any of the boys in the study.
The following is a residual plot for a linear regression of y versus x.
What is indicated by the plot?
A. A linear model is appropriate.
B. A linear model is not appropriate.
C. Variability in y is constant for all values x
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.
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.
The relationship between group size and percent woodland appears to be negative and nonlinear. Which of the following statements explains such a relationship?
A. As the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate.
B. As the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate.
C. As the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.
D. As the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly.
E. As the percent of woodland increases, the number of deer observed in a group remains fairly constant.
C. As the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.
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?
A. 0.59 months per pound.
B. 0.59 pounds per month.
C. 0.59.
D. 0.59 months times pounds.
E. 0.59 month pounds.
C. 0.59.
Bankers at a large financial institution created the linear regression model y = 0.37 - 0.0004x to predict the proportion of customers who would default on their loans, y, based on the customer's credit score, x.
For a customer with a credit score of 700, which of the following is true?
A. The default proportion is predicted to be 0.09.
B. The default proportion will be 0.09.
C. The default proportion is predicted to be approximately 1.75 million.
D. The default proportion will be approximately 1.75 million.
E. The default proportion is predicted to be 0.28.
A. The default proportion is predicted to be 0.09.
The following is a residual plot from a regression of a variable with the independent variable x.
Based on the plot, is it reasonable to conclude that a linear model is appropriate?
A. Yes, because the plot shows no apparent pattern.
B. Yes, because the points in the plot display less variation as x increases.
C. Yes, because the sum of the residuals is close to zero.
D. No, because the plot shows no apparent pattern.
E. No, because the points in the plot display more variation as x.
A. Yes, because the plot shows no apparent pattern.
Biologists conducted a study to investigate the flying velocity of mosquitoes both before and after feeding. The following scatterplot shows the velocity after feeding, in centimeters per second, and the proportional increase in weight after feeding relative to the weight before feeding. For example, 0.5 indicates a 50 percent weight gain after feeding. One point on the graph is labeled M.
What is unusual about point M?
A. It represents a mosquito that gained the least weight after feeding.
B. It represents a mosquito that gained the most weight after feeding.
C. It represents a mosquito that flew very fast after feeding relative to all other mosquitoes.
D. It makes the linear relationship between the variables appear much stronger.
E. the point must be an error in data entry because weight cannot be less than 0.
C. It represents a mosquito that flew very fast after feeding relative to all other mosquitoes.
For which of the following scatterplots is the correlation between x and y closest to 0?
E.
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 x represents velocity and y represents the depth of the river. What is the predicted value of y, in feet, when x = 5?
0.8
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?
A. There should be a positive, linear association in the residual plot.
B. There should be a negative, linear association in the residual plot.
C. All of the points must have residuals of 0.
D. There should be no pattern in the residual plot.
E. The residuals should have a small amount of variability for low values of the predictor variable and larger amounts of variability for high values of the predictor variable.
D. There should be no pattern in the residual plot.
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?
A. A least-squares model predicts that the more baggage items that are unloaded from a flight, the greater the time required to deliver the items to the baggage claim area.
B. 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.
C. The time required to deliver an item to the baggage claim area is relatively constant, regardless of the number of baggage items unloaded from a flight.
D. The variability in the time required to deliver all items to the baggage claim area is about the same for all flights, regardless of the number of items unloaded from a flight.
E. The time required to unload baggage items from a flight is related to the time required to deliver the items to the baggage claim area.
B. 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.
A food truck owner recorded the temperature at noon, in degrees Fahrenheit, and the number of bowls of soup sold during the lunch hour for a random sample of 5 days. The data are shown in the following table.
The mean temperature of the sample is 62 degrees Fahrenheit, and the mean number sold is 14. What is the correlation between the temperature and the number sold?
r = -0.85
Identify and interpret the slope of the least-squares regression line in context.
The value of slope is 235. For each additional win, the predicted attendance per game increases by 235 people.
Students in a physics lab were studying how the length of a plastic pipe affects the frequency of the sound produced when the pipe is struck with a mallet. The class created a regression line on their data to predict the frequencies produced (measured in Hz) from the lengths of the pipes (in meters). One particular pipe had a residual of -2.24.
Interpret the value of residual.
The frequency produced by this pipe was 2.24 Hz lower than predicted by the model.