Statistics Honors - Topics 3: Simple Linear Regression Quizzes/Review/Test

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. Which of the following is an appropriate summary of the scatterplot?

Colleges with higher tuition tend to have higher graduation rates.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data list the number of absences and GPAs for 15 randomly selected students. Using technology, what is the value of r2?

0. 32

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following is the coefficient of determination?

0.63

Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?

26.50 mpg

An economist studies the relationship between the unemployment rate of adult males and male life expectancy for 12 European countries. The relationship is shown in the scatterplot. The value of r for the scatterplot is -0.423. Which statement best explains the relationship between the variables in the scatterplot?

Higher unemployment rates may have an association with unhealthy lifestyles, which is also associated with lower life expectancy.

A certain standardized test measures students' knowledge in math and English. The scatterplot displays the scores for 10 randomly selected students. The equation ŷ = 54.16 + 0.87x is called the least-squares regression line because it

makes the sum of the squared residuals as small as possible.

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class. The results are displayed in the scatterplot. The equation ŷ = -7.61 + 0.19x is called the least-squares regression line because it

minimizes the sum of the squared residuals.

Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances and fares, in dollars, for an adult living in a city over a month period. The value of r for the scatterplot is 0.950. Which of the labeled points weakens the overall association between distance and fare?

point A

The scatterplot illustrates the relationship between two quantitative variables: the amount of an active ingredient in a medicine and the level of pain relief (on a scale of 1 to 10). The relationship in the scatterplot is

positive and nonlinear.

Given the least-squares regression line, , what is the predicted amount of an unstable element that is left after 6 years?

5.468 grams

Many new cars provide detailed information about engine performance on the dashboard. One such feature allows drivers to observe current fuel efficiency, recorded in miles per gallon, as they drive. A consumer takes a long trip driving at different speeds, while a passenger records both driving speed in miles per hour and fuel efficiency for a number of selected points along the trip. A least-squares equation that relates speed to fuel efficiency is given by . Based on the residual plot shown, is a linear model appropriate for comparing driving speed and fuel efficiency?

A linear model is not appropriate because the residual plot shows a clear pattern.

A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a game and how well that game is rated among board game players. Information was collected on several board games, and was used to obtain the regression equation ŷ = 27.273x + 18.182, where x represents time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). What is the predicted rating of a game that takes 90 minutes to play?

59.0915 points

The length, x (in inches), and weight, y (in ounces), for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the value for r2 was determined to be 96%. Which of the following is the best interpretation of this value?

96% of the variation in the bass's weight is determined by the variation in the bass's length.

The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different mileage and determines each car's price using a used car website. The analysis is given in the computer output. Which of the following represents the value of the average residual for a car's price?

3860.7

Given the least-squares regression line, , what is the predicted amount of an unstable element, in grams, that is left after 8 years?

4.468 grams

One method used to measure the speed of supercomputers is the number of floating-point mathematical operations the computer can perform in one second. This is often referred to by the acronym FLOPS. For many years since 1992, the number of FLOPS performed by the largest supercomputer available that year was recorded, and the natural log of each value of the response variable taken. Based on the scatterplot and computer output, a reasonable estimate for the number of computations performed per second by the largest supercomputer in 2007 is:

580,473 billion FLOPS

A statistics student is studying if there is a relationship between the price of a used car and the number of miles it had been driven. She collects data for 20 cars of the same model with different mileage and determines each car's price using a used car website. The analysis is given in the computer output. Using the computer output, what is the predicted price for a car with 10,000 miles on the odometer?

$22,347.20

Data were recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 5 minutes?

59.44 oC

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?

71.02

An anthropologist is interested in the relationship between fathers' and sons' heights. She collects a simple random sample of 25 fathers and 25 sons and determines that the least-squares regression line is ŷ = -2.8 + 1.1x, where ŷ is the predicted height of each son and x is the height of his father (both measured in inches). One father is 70 inches tall and the residual for his son's height is 2.5. What is the son's actual height?

76.7 inches

A statistics student is studying if there is a relationship between the price of a used car and the number of miles it had been driven. She collects data for 20 cars of the same model with different mileage and determines each car's price using a used car website. The analysis is given in the computer output. Using the computer output, what is the correlation?

??? NOT 0.82

A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is . Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship?

A linear model is appropriate because the residual plot shows no pattern.

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, what is the correlation?

-0.56

Fuel efficiency, measured in miles per gallon, is a feature often considered by shoppers looking for a new car. The scatterplot shows the vehicle weight of 15 car models in pounds, plotted against their highway fuel efficiency. Which of the following is a reasonable value for r, given the relationship shown in the scatterplot?

-0.898

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. Using the computer output, what is the correlation coefficient?

0.722

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table. Using technology, what is the value of r2?

0.83

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the results are given in the computer output. Which of the following represents the average distance between the actual weight and the predicted weight of the bass?

1.80

The lengths, in inches, and corresponding weights, in ounces, for 15 different-sized bluegill fish were measured and recorded. Given the regression equation, , what is the expected weight for a bluegill fish that is 11 inches long?

19.47 ounces

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following represents the standard deviation of the residuals?

1.61

As an object travels away from a light source, the intensity of the light on the object diminishes. To measure the influence of distance on light intensity, a student uses a light meter to record intensity, in lumens, from a source at various distances. The results, which compare distance in centimeters to the recorded light intensity, are shown in the scatterplot. To develop a linear model, the student next took the log of each distance and the log of each intensity and used computer software to find a least-square equation, shown in the computer output. Using the computer output, the best estimate of the light intensity at 19 centimeters is:

0.0876

A nutritionist is curious about how the concentration of a vitamin supplement changes as a function of time (in hours) since a pill has been swallowed. The nutritionist measures the concentration for six hours after the pill was swallowed. He calculates the equation of the least-squares regression line as ŷ = 0.0093 - 0.00121x where ŷ is the concentration and x is the number of hours since the pill was swallowed. The graph shown is the residual plot for this model where the residuals are measured in parts per thousand. Based on the residual plot, is the linear model appropriate?

No, there is a clear pattern in the residual plot, indicating that the linear model is not appropriate.

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. Using the computer output, the slope of the least-squares regression line means for each additional centimeter in

arm span, foot length is predicted to increase by about 0.186 cm.

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. The equation of the line ŷ = -14.7 + 1.59x is called the least-squares regression line because it

minimizes the sum of the squared vertical distances from the points to the line

When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is . What is the predicted area, in cm2, of the circle 8 seconds after the stone was dropped?

201.03 cm2

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. What is the predicted distance of a ball that is hit with a club speed of 168 ft/sec?

230 yards

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, the y-intercept is

3.79, which means a student with no absences is predicted to have a GPA of 3.79.

A homeowner notices that the electric bill for the house is often much higher in the summer months. Collecting data from the last 18 monthly electric bills, the amount of each bill is plotted against the mean temperature for each month. The logs of both the mean monthly temperature and the electric bill are taken in order to develop a linear model. Based on the scatterplot and computer output, a reasonable estimate for the home's electric bill when the mean monthly temperature is 76 degrees is:

$141.85

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. Using the computer output, what is the predicted number of pretzels a person with a handspan of 21 cm could grab?

18.58 pretzels

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance, in miles. One of the flights was 500 miles and its residual was 115.00. What was the fare for this flight?

542.50

Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by . Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?

A linear model is not suitable because the residual plot shows a curved pattern.

An entertainment reporter examines the average ticket prices of Broadway shows, comparing them to the number of total performances the shows have had. A resulting scatterplot shows a strong, positive relationship. The value of r for the scatterplot is 0.763. Which statement best explains the relationship between the variables?

More popular shows have higher ticket prices and offer more performances.

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for s was found to be 3.05. Which of the following is the best interpretation of s?

The average residual is about 3.05 pretzels.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the correlation?

The correlation will be weakened because the point falls outside the pattern of the data.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. He collects data for 15 randomly selected students and determines the value for s was 0.67. Which of the following gives the best interpretation of this value?

The typical distance between the observed and predicted GPAs was about 0.67 points.

The scatterplot illustrates the relationship between distance and success rate of field-goal attempts for a sample of football kickers. The relationship in the scatterplot is

strong and negative.

An anthropologist is interested in the relationship between fathers' and sons' heights. She collects a simple random sample of 25 fathers and 25 sons, and determines that the least-squares regression line is ŷ = -2.8 + 1.1x, where ŷ is the predicted height of each son and x is the height of his father (both measured in inches). One father is 72 inches tall, and his son is 75 inches tall. What is the residual for the son's height?

-1.4

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. An analysis is performed on the data for 15 randomly selected students and is displayed in the computer output. Which of the following represents the value of the average residual for a student's GPA?

0.691

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The computer output displays the regression analysis. Which of the following represents the typical distance between the actual and predicted numbers of pretzels?

3.05

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. He collects data for 15 randomly selected students and determines the value for r2 was 31%. Which of the following gives the best interpretation of this value?

31% of the variation in the GPA is accounted for by the linear relationship with number of absences.

Online entertainment streaming services have gained in popularity in recent years as an alternative to traditional television. One such company has seen steady growth in each period of 3 months, called a quarter, over the past 4 years. The scatterplot shows the relationship between the number of quarters since January 2014 and the log of the number of members to the streaming service. A least-squares equation that summarizes this relationship is . Based on the scatterplot and residual plot, what type of model is appropriate for comparing time and subscribers?

An exponential model is appropriate because the relationship between period and the log of subscribers is roughly linear and the residual plot shows no distinct pattern.

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. How would the correlation change if the graduation rate was plotted on the x-axis and tuition plotted on the y-axis?

The correlation would stay the same.

Car rideshare services are a popular option for people needing to move about in large cities. The scatterplot shows the distances of trips and fares, in dollars, for an adult living in a city over a period of a month. The value of r for the scatterplot is 0.950. How would the value of the correlation coefficient change if the fares were plotted on the x-axis and distances on the y-axis?

The value of the correlation coefficient would not change.

One statistic used to measure a country's wealth is the gross domestic product (GDP). A higher GDP indicates higher wealth. A researcher compared the GDP per person for 12 countries with the life expectancy of that country. The data for the 12 countries are shown in the scatterplot. The value of r for the scatterplot is 0.608. How does the country of Jordan, labeled in the graph, influence the correlation?

This data point weakens the correlation.

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the y-intercept of the regression line?

When the number of procrastination days is 0, the predicted grade is 96.5 points.

A statistics student is interested in the relationship between the number of aunts and uncles a person has and the number of cousins. She surveys a simple random sample of 12 people and asks them how many of each they have. She calculates the least-squares regression line and finds the equation is ŷ = 2.6 + 1.64x, where ŷ is the number of cousins and x is the number of aunts and uncles. The residual plot is shown. Based on the residual plot, is the linear model appropriate?

Yes, there is no clear pattern in the residual plot.

An engineer is interested in the relationship between the weight of a car (measured in pounds) and the fuel economy (measured in miles per gallon of gas). To investigate the relationship, she collects a simple random sample of 10 cars and records their weight and fuel efficiency. She finds the equation of the least-squares regression line to be ŷ = 69 - 0.0114x, where ŷ is the fuel efficiency (mpg) and x is the weight (in pounds). The residual plot is shown. Based on the residual plot, is the linear model appropriate?

Yes, there is no clear pattern in the residual plot.

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table. Using technology, the slope of the least-squares regression line is

0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $5 million budget?

0.861 points

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. The measurements are given in the table. Using technology, what is the value of r2?

0.96

Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Scatterplot A displays the relationship between the car's speed and fuel efficiency. Two transformations of the data are shown in scatterplots B and C. Scatterplot B displays the relationship between the car's speed and the natural log of the fuel efficiency. Scatterplot C displays the relationship between the natural log of the car's speed and the natural log of the fuel efficiency. Which scatterplot best represents the relationship between a car's speed and its fuel efficiency?

A power model would best represent the relationship because scatterplot C is fairly linear.

Football coaches running their summer practices noticed that the players who weighed more typically had slower times for their 40-yard dash. What are the explanatory variable and response variable for this relationship?

Explanatory variable: player weight Response variable: player 40-yard-dash time

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, the slope of the least-squares regression line is

-0.10, which means for each additional absence, the GPA is predicted to decrease by 0.10 points.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect will this point have on the value of r2 if it is not included in the data?

?? NOT: The value of r2 would decrease substantially because this point does not follow the pattern of the data.

Machine engineers are designing a new ice machine for use in restaurants. They notice that designs that use cubes containing higher volumes of water take longer to freeze. What are the explanatory variable and response variable for this relationship?

Explanatory variable: volume of water Response variable: time to freeze

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. Using the computer output, the slope of the least-squares regression line means for each additional

centimeter in handspan, the number of pretzels is predicted to increase by about 1.585.

Medical researchers studying a medication in male and female patients 20 to 29 years old noticed that, up to a certain amount, a larger concentration of an active ingredient lead to greater levels of symptom relief. What is the explanatory variable?

concentration of active ingredient

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay). Which hospital represented in the scatterplot would be considered a high leverage point?

the hospital with 310 beds

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed, and the computer output is shown. Using the computer output, what is the equation of the least-squares regression line?

ŷ = -7.611 + 0.186x

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, what is the equation for the least-squares regression line?

ŷ = 3.79 - 0.10x

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of the set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. What is the predicted price of a set that has 500 pieces?

$41.20

A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $250,000 budget?

0.17225 points

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. What is the predicted grade of a student who procrastinated for 2 days?

89.22

The lengths and weights for 15 different-sized bluegill fish were measured and recorded. Scatterplot A displays the relationship between the length, in inches, and the weight, in ounces, for each fish. Two transformations of the data are shown in the scatterplots B and C. Scatterplot B displays the relationship between the length and the natural log of the weight. Scatterplot C displays the relationship between the natural log of the length and the natural log of the weight. Which model best represents the relationship between the bluegills' lengths and weights?

A power model would best represent the relationship because scatterplot C is fairly linear.

The daily print publication of newspapers has declined in many large cities over the past 25 years. The Philadelphia Inquirer weekday print circulation was at its highest in 2001, with an average daily circulation of 226,000 copies, and has decreased every year since then. To develop a linear model for estimating yearly circulation, the log of the daily circulation in thousands was taken. Based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year?

An exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern.

Real estate agents in a county with a large, urban residential area noticed that families with larger incomes tend to live in homes that sell for higher prices. What are the explanatory variable and response variable for this relationship?

Explanatory variable: family income Response variable: price of the home

An official for a national dog show studies the characteristics of one breed of dog, the Dandie Dinmont Terrier. Two common measurements are the height and weight of the dog, and the official would like to develop a model that would be helpful in predicting weight based on a given height. The official first makes a scatterplot that relates height and weight, then another that compares the logs of each measurement. Based on the graphs, which type of model is likely appropriate for predicting weight from height?

A power model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.

A homeowner notices that the electric bill for the house is often much higher in the summer months. Collecting data from the last 18 monthly electric bills, the amount of each bill is plotted against the mean temperature for each month. The logs of both the mean monthly temperature and the electric bill are taken in order to develop a linear model. Based on the scatterplot and residual plot, which type of model is most suitable for modeling electric bills based on mean monthly temperature?

A power model is appropriate because the scatterplot of log temperature and log bill is roughly linear, and the residual plot shows no distinct pattern.

Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm3, is reported at different time intervals, measured in seconds and is displayed in scatterplot A. Two transformations of the data are shown in the second and third graphs. Scatterplot B displays the relationship between time and the log of volume. Scatterplot C displays the relationship between the log of time and the log of volume. Which model best represents the relationship between time and volume?

A power model would best represent the relationship because scatterplot C is fairly linear.

One method used to measure the speed of supercomputers is the number of floating-point mathematical operations the computer can perform in one second. This is often referred to by the acronym FLOPS. For many years since 1992, the number of FLOPS performed by the largest supercomputer available that year was recorded. Based on the three graphs shown, which type of model is most appropriate for comparing years to FLOPS?

An exponential model could be appropriate because the scatterplot of years and ln(operations) is roughly linear. The next step is to look at the residual plot.

A forest management agency collects measurements from beech trees in a public park. The age of many of the trees is known, and the basal area—the area of land occupied by the trunks of the trees—is also measured. A least-squares equation that compares the basal area to the age of each tree is given by . Based on the residual plot shown, is a linear model appropriate for comparing tree age to basal area?

Because the residual plot does not show a clear pattern, a linear model is appropriate.

One statistic used to measure a country's wealth is its gross domestic product (GDP). A higher GDP indicates greater wealth in the country. A researcher compared the GDP per person for 12 countries with the life expectancy of that country. The data for the 12 countries are shown in the scatterplot. The value of r for the scatterplot is 0.608. Which of the following statements accurately describes the relationship shown in the scatterplot?

Countries with higher GDPs tend to have higher life expectancies.

Exercise science researchers collecting data within their state noticed that teens who spend more time streaming videos spend less time exercising. What are the explanatory variable and response variable for this relationship?

Explanatory variable: time spent streaming videos Response variable: time spent exercising

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. Which statement best describes the meaning of the slope of the regression line?

For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards.

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = -3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the slope of the regression line?

For each increase in number of procrastination days by 1, the predicted grade decreases by 3.64 points.

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. Which statement best describes the meaning of the slope of the regression line?

For each increase in the number of pieces by 1, the predicted price increases by $0.08.

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph. What effect will the circled point have on the slope of the least-squares regression line?

It will increase the value of the slope because its residual is a large positive value.

An official for a regional baseball league examines attendance data for teams in the league. For each team in the league, the number of losses and the average game attendance are shown in the scatterplot. The value of r for the scatterplot is -0.847. Which statement best describes the association shown in the scatterplot?

Losses and attendance have a strong, negative association.

Data were recorded for the temperature of a cup of coffee over a 30 minute period. It is known that the temperature of hot coffee will cool to room temperature following an exponential model. Which of the following would linearize the data for temperature and minutes?

Minutes, ln(Temperature)

Jim has started a new exercise program. He has monthly checkups where his percentage of body fat is measured. Jim records his body fat percentage and the number of months he has been on the exercise program. He collects data for 10 months and finds a linear model to give the relationship between the time spent exercising and his percentage of body fat. The equation of the line isŷ = 17 - 1.25x, where ŷ is his percentage of body fat and x is the time spent exercising (in months). The residual plot is shown. Based on the residual plot, is the linear model appropriate?

No, there is a clear pattern in the residual plot, indicating that the linear model is not appropriate.

In the decathlon event at large track meets, male athletes compete in a total of 10 events. Their combined performance in each of the events is used to determine the winner. Two of the events are the 200-meter dash and the javelin throw. For 12 athletes at a large international competition, performances in these events are recorded and placed in a scatterplot. The performance for one athlete from Latvia is labeled in the graph. How does this point influence the correlation of the scatterplot?

This data point weakens the correlation.

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels (this point is circled on the graph) What effect will the circled point have on the standard deviation of the residuals?

This point will increase the value of the standard deviation of the residuals because it has a large positive residual.

In the decathlon event at large track meets, male athletes compete in a total of 10 events. Their combined performance in each of the events is used to determine the winner. Two of the events are the 200-meter dash and the javelin throw. For 12 athletes at a large international competition, performances in these two events are recorded and placed in a scatterplot. The value of r for this scatterplot is 0.369. Which of the following best describes the relationship between the variables in the scatterplot?

Those with higher 200-meter times tend to have longer javelin distances. The relationship is moderate.

A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a game and how well that game is rated among board game players. Information was collected on several board games and was used to obtain the regression equation ŷ = 27.273x + 18.182, where x represents time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). Which statement best describes the meaning of the y-intercept of the regression line?

When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game cannot have a playtime of 0 hours.

During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. What is the explanatory variable for this relationship?

number of seeds planted per square foot