AP Stat Unit 2 Progress Check: MCQ Part B

Bankers at a large financial institution created the linear regression model dˆ=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?

The default proportion is predicted to be 0.09.

The following scatterplot shows two variables along with a least-squares regression line. Which of the following points is an outlier for the data?

(5,24)

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. 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?

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?

Explanatory: number of times the advertisement is played; response: number of new customers

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?

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 nˆ=150−3p, where nˆ represents the predicted number of turkey sandwiches sold in one day for a price of p dollars per sandwich. Which of the following is the best description of the slope of the model?

For each increase of $1 in the price of the sandwich, the number sold is predicted to decrease, on average, by 3.

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?

The sign of the slope coefficient

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(priceˆ)=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?

$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 yˆ=−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?

$40,000

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?

(5.1,105)

The least-squares regression model yˆ=−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?

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 residual plot

In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Which of the following statements is the best interpretation of the value 6.8 shown in the output?

ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP.

A researcher studying koi fish collected data on three variables, A, B, and C. The following residual plots show the residual for a model for predicting each variable from the age of the fish.

The plot for variable AA only

A botanist created a linear model to predict plant height from soil acidity (pH level) for a certain type of plant. The slope of the model was 2.5 centimeters per pH level, the standard deviation of the sample of plant heights was 4 centimeters, and the standard deviation of the soil acidities was 1 pH level. What is the value of the correlation coefficient?

0.625

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 ?

No, because $100,000 is much greater than the values used in the experiment.

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?

Yes, because the plot shows no apparent pattern.

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. Which of the following statements is the best interpretation of the residual plots?

The residual plot for model II indicates that it is the most appropriate among the three models.