AP STATS 2ND TEST
The following scatterplot shows a company's monthly sales, in thousands of dollars, versus monthly advertising dollars spent, in thousands of dollars. Which of the following points is most likely a high-leverage point with respect to a regression of monthly sales versus advertising dollars? A (5.1,105) B (5.8,110) C (6.0,125) D (6.7,108) E
A (5.1,105)
Bankers at a large financial institution created the linear regression model d^=0.37−0.0004s to predict the proportion of customers who would default on their loans, d, based on the customer's credit score, s. 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.
A researcher studying koi fish collected data on three variables, �, �, and �. The following residual plots show the residual for a model for predicting each variable from the age of the fish. A conclusion that a linear model between the variable and age is appropriate is supported by which plot or plots? A The plot for variable A only B The plot for variable B only C The plot for variable C only D The plots for variables A and C E The plots for variables B and C
A The plot for variable A only
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 increases.
A Yes, because the plot shows no apparent pattern.
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? A −0.85 B −0.68 C 0.68 D 0.73 E 0.85
A −0.85
A real estate agent wants to predict the selling price of single-family homes from the size of each house. A scatterplot created from a sample of houses shows an exponential relationship between price, in thousands of dollars, and size, in 100 square feet. To create a linear model, the natural logarithm of price was taken and the least-squares regression line was given as ln(price^)=2.08+0.11(size). Based on the model, which of the following is closest to the predicted selling price for a house with a size of 3,200 square feet? A $54,500 B $270,000 C $354,000 D $398,000 E $560,000si
B $270,000
A grocery store wants to examine the relationship between the sales amounts each day at two different locations, store A and store B. The sales amount each day, in dollars, was recorded for 10 days at each store. The least-squares regression line is y^=−3,000+1.2x, where x represents the sales amounts each day at store A and y represents the sales amounts each day at store B. If the mean of the 10 sales amounts for store B is $45,000, what is the mean of the 10 sales amounts for store A? A $35,000 B $40,000 C $42,000 D $45,000 E $51,000
B $40,000
Workers at a warehouse of consumer goods gather items from the warehouse to fill customer orders. The number of items in a sample of orders and the time, in minutes, it took the workers to gather the items were recorded. A scatterplot of the recorded data showed a curved pattern, and the square root of the number of items was taken to create a linear pattern. The following table shows computer output from the least-squares regression analysis created to predict the time it takes to gather items from the number of items in an order. Predictor����Constant3.0979Square root of items2.7633R-Sq=96.7% Based on the regression output, which of the following is the predicted time, in minutes, that it took to gather the items if the order has 22 items? A 7.99 B 16.06 C 17.29 D 27.49 E 63.89
B 16.06
A small business owner has created a linear regression model to predict the number of new customers who will visit a shop based on the number of times the owner has an advertisement played on the radio. What is the explanatory variable and what is the response variable? A Explanatory: number of new customers; response: number of times the advertisement is played B Explanatory: number of times the advertisement is played; response: number of new customers C Explanatory: number of times the advertisement is played; response: number of purchases made by customers D Explanatory: number of purchases made by customers; response: number of times the advertisement is played E Explanatory: number of previous customers; response: number of new customers
B Explanatory: number of times the advertisement is played; response: number of new customers
A certain cell phone plan charges a fee of $1 for each international call made plus $0.02 for each second of talk time for the international call. A business owner tracked the time and cost for each of the calls made by the employees when they traveled internationally for business. What is the appropriate value of the correlation between time and cost for the international calls? A The appropriate value is 1.02 because each call takes at least one second. B The appropriate value is 1 because there is a perfect linear relationship between the time of the call and how much it costs. C The appropriate value is 0.97 because there is a strong positive relationship between the time and cost of a call. D The appropriate value is −0.50 because the phone company should discount the price for business owners who make many international calls. E The appropriate value is 0 because there is no variability in the cost of the calls.
B The appropriate value is 1 because there is a perfect linear relationship between the time of the call and how much it costs.
The following scatterplot shows the ages, in years, of 12 of the wealthiest people in the world along with their net worth, in billions of dollars. The data point at age 83 is labeled Q. Suppose point Q is removed from the data set. Which of the following is likely not affected by the removal? A The correlation coefficient B The sign of the slope coefficient C The value of the slope coefficient D The sum of the squared residuals E The net worth intercept
B The sign of the slope coefficient
A teacher collected information from a class of 25 students about the time, in hours, they spent studying the previous week and the time, in hours, they spent on the Internet the previous week. The value of the correlation coefficient between hours spent studying and hours spent on the Internet was −0.72. If the teacher changes the units of each variable from hours to minutes, what will be the value of the correlation coefficient between minutes studying and minutes spent on the Internet? A −43.2 B −0.72 C −0.012 D 0.72 E
B −0.72
The least-squares regression model y^=−3.4+5.2x and correlation coefficient r=0.66 were calculated for a set of bivariate data with variables x and y Which of the following is closest to the proportion of the variation in y that cannot be explained by the explanatory variable? A 81% B 66% C 56% D 44% E 34%
C 56%
A marketing consultant created a linear regression model to predict the number of units sold by a client based on the amount of money spent on marketing by the client. Which of the following is the best graphic to use to evaluate the appropriateness of the model? A A dotplot B A histogram C A residual plot D A boxplot E A bar chart
C A residual plot
Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least-squares regression line. Computer output is shown in the following table. Which of the following statements is an interpretation of the value 0.75 shown in the table? A Monthly growth is expected to increase by 0.75 cm when rainfall increases by 1 cm. B Rainfall is expected to increase by 0.75 cm when monthly growth increases by 1 cm. C For a month with 0 cm of rainfall, the monthly growth is expected to be approximately 0.75 cm. D For a plant with 0 cm of monthly growth, the month had an expected rainfall of approximately 0.75 cm. E Approximately 75% of the variability in monthly growth is due to its linear relationship with rainfall.
C For a month with 0 cm of rainfall, the monthly growth is expected to be approximately 0.75 cm.
Jordan is working on a business model for a sandwich shop. Based on past data, he developed the model y^=150−3x, where y^ represents the predicted number of turkey sandwiches sold in one day for a price of x dollars per sandwich. Which of the following is the best description of the slope of the model? A For each increase of $3 in the price of the sandwich, the number sold is predicted to decrease, on average, by 150. B For each increase of $3 in the price of the sandwich, the number sold is predicted to increase, on average, by 150. C For each increase of $1 in the price of the sandwich, the number sold is predicted to decrease, on average, by 3. D For each increase of $1 in the price of the sandwich, the number sold is predicted to increase, on average, by 3. E For each increase of $1 in the price of the sandwich, the number sold is predicted to decrease, on average, by 150.
C For each increase of $1 in the price of the sandwich, the number sold is predicted to decrease, on average, by 3.
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.
A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960. Model I predicts y from x. Model II predicts ln(y), the natural logarithm of y, from x. Model III predicts ln(y) from ln(x). The following graphs show the residual plot for each model. Residual Plot for Model I Residual Plot for Model II Residual Plot for Model III Which of the following statements is the best interpretation of the residual plots? A The residual plot for model I indicates that a quadratic model is the most appropriate among the three models. B The residual plots for models I and III indicate that either model is appropriate and better than model II. C The residual plot for model II indicates that it is the most appropriate among the three models. D All the residual plots indicate that any of the three models are appropriate for the prediction. E All the residual plots indicate that none of the three models is appropriate for the prediction
C The residual plot for model II indicates that it is the most appropriate among the three models.
For which of the following scatterplots is the correlation between � and � closest to −1 ?
CHOOSE THE STRONG NEGATIVE LINEAR LINE
The following scatterplot shows two variables along with a least-squares regression line. Which of the following points is an outlier for the data? A (1,22) B (2,17) C (4,13) D (5,24) E
D (5,24)
Jacques, an artisan cheese maker, collects data on every step of the cheese-making process for each batch he makes. Jacques noticed that the daily high temperature in his shop on the day he made a batch of cheese was related to the pH of the cheese the next morning. He computed the correlation between the daily high temperature and the pH of the cheese to be −0.64. What information does the correlation provide about the relationship between the daily high temperature and the pH of the cheese? A The relationship is linear because the correlation is negative. B The relationship is not linear because the correlation is negative. C The morning pH of the cheese tends to be higher when the daily high temperature in the shop is warmer, compared to when the daily high temperature is cooler. D The morning pH of the cheese tends to be higher when the daily high temperature in the shop is cooler, compared to when the daily high temperature is warmer. E There is no relationship between the daily high temperature and the pH of the cheese
D The morning pH of the cheese tends to be higher when the daily high temperature in the shop is cooler, compared to when the daily high temperature is warmer.
A certain middle school opens at 7 A.M., and classes begin at 8 A.M. A sociologist gathered data on the number of minutes after 7 A.M. that a student arrives at school and the number of friends the student has on social media. The correlation between the two variables indicated a strong negative relationship. Which of the following is an appropriate interpretation of the correlation? A Students who arrive early to school have more friends on social media. B Students who arrive late to school have more friends on social media. C Having a lot of friends on social media causes a student to arrive late for school. D As the number of minutes of arriving after 7 A.M. increases, the number of friends on social media tends to increase. E As the number of minutes of arriving after 7 A.M. increases, the number of friends on social media tends to decrease.
E As the number of minutes of arriving after 7 A.M. increases, the number of friends on social media tends to decrease.
A marketing consultant, Sofia, has been studying the effect of increasing advertising spending on product sales. Sofia conducts several experiments, each time spending less than $1,000 in advertising. When she analyzed the relationship between x = advertising spending and y= product sales, the relationship was linear with r=0.90. Her boss is thrilled and asks her to estimate product sales for $100,000 in advertising spending. Is it appropriate for her to calculate a predicted amount of product sales with advertising spending of $100,000 ? A Yes, because the association is linear. B Yes, because the association is positive. C Yes, because the association is strong. D No, because the value of the correlation is not equal to 1. E No, because $100,000 is much greater than the values used in the experiment.
E No, because $100,000 is much greater than the values used in the experiment.
The scatterplot below displays the relationship between the percent change in the population of wolves and the moose density, in number of moose per square kilometer, over a 19-year period in a certain region. Notice that the association is negative, and that the points seem to be more spread out at higher moose densities. Suppose the variables on the scatterplot were reversed, so that moose density was the response variable on the vertical axis, and percent change in wolf population was the explanatory variable on the horizontal axis. Which of the following would be true? A The association would still be negative, but the strength of the association would increase. B The association would be positive, and the strength of the association would increase. C The association would still be negative, but the strength of the association would decrease. D The association would be positive, but the strength of the association would not change. E The direction and strength of the association would not change.
E The direction and strength of the association would not change.
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.
The association is positive and nonlinear