Simple linear regression

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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. A graph titled car share fares has trip distance (miles) on the x-axis, and fare (dollars) on the y-axis. Points increases in a line with positive slope. 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 be -0.950. The value of the correlation coefficient would not change. The value of the correlation coefficient would be closer to 0. The value of the correlation coeffi

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? $40 $41.20 $600 $6,235

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 is shown in the scatterplot. The value of r for the scatterplot is -0.847. A graph titled Team attendance has number of losses on the x-axis, and average attendance (thousands) on the y-axis. Points decrease in a line with negative slope. Point are grouped together. Point (2, 15.2) is slightly outside of the line. Which of these data combinations weakens the correlation? 2 losses, 11.9 thousand fans 2 losses, 15.2 thousand fans 5 losses, 10.3 thousand fans 9 losses, 7.7 thousand fans

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 is ŷ = 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 no clear pattern in the residual plot. Yes, there is no clear pattern in the residual plot. No, there is a clear pattern in the residual plot, indicating that the linear model is not appropriate. Yes, his percentage of body fat clearly decreases for the first four months and then increases after that.

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. A graph titled Grabbing Pretzels has handspan (centimeters) on the x-axis, and number of pretzels on the y-axis. A line goes through points (19, 16) and (22, 20). Predictor Coef SE Coef t-ratio p Constant -14.71 4.317 1.689 0.046 Handspan 1.585 0.310 5.114 0.000 S = 3.05 R-Sq = 52.1% R-Sq(Adj) = 51.7% Using the computer output, the slope of the least-squares regression line means for each additional pretzel, the handspan will increase by about 1.585 cm. pretzel, the handspan is predicted to increase by about 1.585 cm. centimeter in handspan, the number of pretzels increases by about 1.585. centimeter in handspan, the number of pretzels is predicted to increase about 1.585.

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and was used to obtain the regression equation ŷ = -0.227x + 50.455, where x represents the price of a bobblehead (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). Which statement best describes the meaning of the y-intercept of the regression line? When the demand for bobbleheads is 0 units, the predicted price is $0. When the demand for bobbleheads is 0 units, the predicted price is $50.455. When the price of a bobblehead is $0, the predicted demand is 50.455 units. This interpretation is not meaningful because a bobblehead cannot have a price of $0. When the price of a bobblehead is $0, the predicted demand is 0.227 units. This interpretation is not meaningful because a bobblehead cannot have a price of $0.

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. A graph titled team attendance has number of losses on the x-axis, and average attendance (thousands) on the y-axis. Points decrease in a line with negative slope. Point are grouped together. Which statement best describes the association shown in the scatterplot? There is no association between losses and attendance. Losses and attendance have a strong, positive association. Losses and attendance have a weak, negative association. Losses and attendance have a strong, negative association.

The fare charged for a rideshare service is a function of the distance traveled. However, the fare differs according to the time of day, availability, and other variables. The distance and fares for 10 rides are shown in the table. The equation of the least-squares regression line is ŷ = 5.21 + 2.33x, where ŷ is the predicted fare and x is the distance. The fare charged for a rideshare service is a function of the distance traveled. However, the fare differs according to the time of day, availability, and other variables. The distance and fares for 10 rides are shown in the table. The equation of the least-squares regression line is y ̂ y ̂=5.21+2.33x , where y ̂"y" ̂ is the predicted fare and xx is the distance. What is the residual for the rideshare cost with a distance of 5 miles? -0.34 0.34 2.33 5.21

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, Temperature Minutes, ln(Temperature) ln(Minutes), Temperature ln(Minutes), ln(Temperature)

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. A graph titled Fuel efficiency has car weight (thousands of pounds) on the x-axis, and fuel efficiency (miles per gallon) on the y-axis. Points decrease in a line with negative slope. Points go through (3, 38), (3.7, 32), and (4.8, 20). Which of the following is a reasonable value for r, given the relationship shown in the scatterplot? -0.197 -0.898 0.528 0.902

Bacteria growth was measured over a one-month period. The number of cells were counted for a certain number of days. A regression analysis was completed and is displayed in the computer output. What is the equation of the least-squares regression line?

C) in(bacteria)=2.077 +0.142(bacteria)

The scatterplot illustrates the relationship between two quantitative variables. A graph shows 5 to 45 on the x-axis and 5 to 30 on the y-axis. The points show an upward trend. The relationship in the scatterplot is weak, positive, and linear. strong, negative, and linear. weak because it contains unusual points. positive and linear with no unu

Given the least-squares regression line, , what is the predicted amount of an unstable element that is left after 6 years? 0.53 gram 1.699 grams 5.468 grams 8.365 grams

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. A 2-column table with 15 rows. Column 1 is labeled Number of Absences with entries 15, 1, 0, 6, 9, 12, 3, 3, 1, 2, 7, 0, 4, 9, 10. Column 2 is labeled G P A with entries 2.1, 4.3, 4.5, 3.2, 4.0, 1.7, 3.8, 2.9, 3.6, 3.4, 2.6, 3.1, 2.8, 2.8, 4.1. Using technology, what is the correlation? -0.56 -0.10 0.10 0.56

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? -0.56 -0.32 0. 32 0.56

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. The average residual is about 3.05 centimeters. The average handspan of a student is 3.05 centimeters. The average number of pretzels a student could grab is 3.05 pretzels.

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 price by $1, the predicted number of pieces increases by 0.08. For each increase in price by $1, the predicted number of pieces increases by 1.20. For each increase in the number of pieces by 1, the predicted price increases by $0.08. For each increase in the number of pieces by 1, the predicted price increases by $1.20.

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? -0.98 -0.96 0.96 0.98

The scatterplot illustrates the relationship between distance and success rate of field-goal attempts for a sample of football kickers. A graph titled Field-goal distance and success rate has distance (yards) on the x-axis, and success rate (percentage) on the y-axis. The points decreases in a line with negative slope. The relationship in the scatterplot is strong and positive. weak and negative. strong and negative. weak and positive.

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The measurements are given in the table. A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38. Using technology, what is the equation for the least-squares regression line? ŷ = -34.13 + 1.98x ŷ = 1.98 - 34.13x ŷ = 17.37 + 0.50x ŷ = 0.50 + 17.37x

At a dome-style football stadium, sports analysts noticed that as the distance of a field-goal attempt increased, the success rate of a field-goal attempt decreased. What are the explanatory variable and response variable for this relationship? Explanatory variable: style of stadium Response variable: distance of field-goal attempt Explanatory variable: style of stadium Response variable: success rate of field-goal attempt Explanatory variable: success rate of field-goal attempt Response variable: distance of field-goal attempt Explanatory variable: distance of field-goal attempt Response variable: success rate of field-goal attempt

When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The relationship between the time and area of the circles was analyzed and is shown in the computer output. What is the equation of the least-squares regression line?

D) log(area)= 0.490+2.004 log(time)

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 exercising Response variable: state of teen's residence Explanatory variable: time spent streaming videos Response variable: time spent exercising Explanatory variable: time spent exercising Response variable: time spent streaming videos Explanatory variable: state of teen's residence Response variable: time spent streaming videos

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 0.91 0.99 1.22

A researcher is studying the relationship between fathers' and sons' heights. He collects a simple random sample of eight pairs of fathers and sons and records their heights as shown in the table. The equation of the least-squares regression line is ŷ = 2.7 + 1.042x, where ŷ is each son's height and x is his father's height. Which shows the residual plot?

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. A graph titled College comparisons has semester tuition (thousands of dollars) on the x-axis, and 4-year graduation rate (percentage) on the y-axis. Points are grouped together in a line with positive slope. 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. The correlation would stay positive and increase. The correlation would stay positive and decrease. The correlation would be negative, rather than positive.

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. A graph titled college comparisons has semester tuition (thousands of dollars) on the x-axis, and 4-year graduation rate (percentage) on the y-axis. Points are grouped together in a line with positive slope. Point (7, 80) is slightly outside of the other points. Which statement best describes how the circled point influences the correlation shown in the scatterplot? A)Because the point lies outside the linear trend, it weakens the correlation. B)Because the point lies above the linear trend, it strengthens the correlation. C)Because the point follows the linear trend, the correlation does not change. D)Because the point lies outside the linear trend, it strengthens 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 computer output displays the regression analysis. Using the computer output, what is the value of r2? 0.521 0.547 1.585 3.05

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? -2.8 -1.4 1.1 1.4

The scatterplot illustrates the relationship between two quantitative variables. A graph shows to 5 on the x-axis and 0 to 12 on the y-axis. The points show a downward trend. Which of the following is an accurate description of the scatterplot? This relationship is weak. This relationship contains two unusual points. This relationship contains more than two unusual points. This relationship has no unu

B) area= 0.010=3.141(time^2)

Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm3, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. What is the equation of the least-squares regression line?

B) volume=-0.013+0262(time)

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). A graph titled hospitals has number of beds on the x-axis, and mean length of stay (days) on the y-axis. Points increases in a line with positive slope. Which statement best explains the relationship between the variables shown? A)Hospitals with more beds cause longer lengths of stay. B)The size of the hospital does not appear the have an influence on length of stay. C)More complex medical cases are often taken by larger hospitals, which increases the lengths of stay for larger hospitals. D)More complex medical cases are often taken by larger hospitals, which decreases the lengths of stay for larger hospitals.

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? 0.145 points 0.72 points 0.861 points 33.55 points

A small technology company started offering shares of stock to investors in 1987. At that time, the price of one share of stock was $0.39. Since then, the company has experienced rapid growth. Twenty-two years later, the price of a single share of stock has risen to over $110. The scatterplot shows the number of years since the initial stock offering in 1987 and the price of the stock. A graph titled stock prices versus years since 1987 has years since 1987 on the x-axis, and stock price (dollars) on the y-axis. Points increase exponentially. A graph titled residuals versus years since 1987 has Residual on the x-axis, and stock price (dollars) on the y-axis. Points decrease, and then curve up. Based on the scatterplot and residual plot, is a linear model appropriate for the growth of stock price? A linear model is appropriate because the regression line fits the scatterplot well. A linear model is not appropriate because the residual plot is centered about zero. A linear model is not appropriate because the residual plot shows a clear pattern. A linear model is not appropriate because the scatterplot shows a clear 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. A graph titled College comparisons has semester tuition (thousands of dollars) on the x-axis, and 4-year graduation rate (percentage) on the y-axis. Points are grouped together in a line with positive slope. Which of the following is an appropriate summary of the scatterplot? There is no relationship between tuition and graduation rate. Colleges with lower tuition tend to have higher graduation rates. Colleges with higher tuition tend to have higher graduation rates.

The Bureau of Labor Statistics is an office within the US Department of Labor. Every three months the bureau releases a report containing jobs and salary data of US workers. One statistic reported is the median weekly salary for full-time workers. The scatterplot shows the growth of median weekly salary, starting in January 2010. An equation of the least-squares for the data in the scatterplot is Median salary hat = 17.327 (year) minus 729.327, where 2010 represents year zero. The value of r for the scatterplot is 0.977. A graph titled median salary versus years since 2010 has years since 2010 on the x-axis, and median salary (dollars) on the y-axis. Points form a line with positive slope. A graph titled residuals versus years since 2010 has years since 2010 on the x-axis, and residual on the y-axis. Points decrease, and then increase. Based on the least-squares regression and residual plot, is a linear model suitable for this data set? A linear model is suitable because the value of r is close to 1. A linear model is suitable because the residual plot shows a curved pattern. A linear model is not suitable because the residual plot shows a clear pattern. A linear model is not suitable because there are more positive residuals than negative residuals.

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? 0.024 2164.1 3860.7 24157.2

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. A regression analysis was completed and is displayed in the computer output. What is the equation of the least-squares regression line?

C) in(volume)= 1.327+2.993 in(time)

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 grade is 0, the predicted number of procrastination days is 0. When the grade is 0, the predicted number of procrastination days is 96.5. When the number of procrastination days is 0, the predicted grade is 3.64 points. When the number of procrastination days is 0, the predicted grade is 96.5 points.

The scatterplot illustrates the relationship between two quantitative variables: number of seeds planted and the crop yield per square foot. A graph titled Number of Seeds and Crop Yield has seeds (per square foot) on the x-axis, and yard (pounds per square foot) on the y-axis. The points curve up to a point, and then curve back down. The relationship in the scatterplot is weak and nonlinear. strong and positive. weak and negative. strong and nonlinear.

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

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. A 2-column table with 10 rows. Column 1 is labeled English (x) with entries 450, 470, 510, 520, 540, 570, 590, 620, 670, 680. Column 2 is labeled Math (y) with entries 490, 480, 500, 580, 550, 540, 610, 590, 620, 650. 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. 0.68, which means for each additional point in the math score, the English score is predicted to increase by 0.68 points. 1.22, which means for each additional point in the English score, the math score is predicted to increase by 1.22 points. 1.22, which means for each additional point in the math score, the English score is predicted to increase by 1.22 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. 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. For each increase in number of procrastination days by 1, the predicted grade decreases by 96.5 points. For each increase in grade by 1 point, the predicted number of procrastination days decreases by 96.5 days. For each increase in grade by 1 point, the predicted number of procrastination days decreases by 3.64 days.

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. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.

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

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. A graph titled Country Wealth has G D P per person (thousands of dollars) on the x-axis, and life expectancy (years) on the y-axis. Points increase with alpha positive slope. Point Jordan is outside of the other points. How does the country of Jordan, labeled in the graph, influence the correlation? This data point weakens the correlation. This data point strengthens the correlation. This data point has no influence on the correlation. Removing this data point would lower the correlation coefficient.

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. A graph titled Arm Span versus Foot Length has arm span (Centimeters) on the x-axis, and foot length (centimeters) on the y-axis. A line goes through (165, 23) and (185, 27). Predictor Coef SE Coef t-ratio p Constant -7.611 2.567 2.965 0.046 Arm span 0.186 0.035 5.377 0.000 S = 1.61 R-Sq = 63.0% R-Sq(Adj) = 62.7% Using the computer output, what is the equation of the least-squares regression line? ŷ = -7.611 + 0.186x ŷ = 0.186 - 7.611x ŷ = 2.567 + 0.035x ŷ = 0.035 + 2.567x

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. The company collected information on several movies and used it to obtain the regression equation ŷ = 0.145x+0.136, where x represents the budget of the movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). Which statement best describes the meaning of the y-intercept of the regression line? When the score of a movie is 0 points, the predicted budget is $0. When the score of a movie is 0 points, the predicted budget is $0.136 million. When the budget of a movie is $0, the predicted rating is 0.136 points. This interpretation is not meaningful, because a movie cannot have a budget of $0. When the budget of a movie is $0, the predicted rating is 0.145 points. This interpretation is not meaningful, because a movie cannot have a budget of $0.

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 rating of a game is 0 points, the predicted time to play is 0 hours. When the rating of a game is 0 points, the predicted time to play is 18.182 hours. 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. When the time to play is 0 hours, the predicted rating is 27.273. This interpretation is not meaningful since a game cannot have a playtime of 0 hours.

A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. A regression equation for this relationship is Height hat = 2.31 (angle) minus 39.389. A graph titled Residuals versus Launch angle has launch angle (Degrees) on the x-axis, and residual on the y-axis. Points decrease, and then curve up. Based on the residual plot shown, is a linear model appropriate for using launch angle to predict height? A linear model is appropriate because the residual plot is curved. A linear model is appropriate because many of the residuals are close to zero. A linear model is not appropriate because the residual plot shows a clear pattern. A linear model is not appropria

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? No, the residuals are relatively large. No, there is a clear pattern in the residual plot. Yes, there is no clear pattern in the residual plot. Yes, about half of the residuals are positive and half are negative.

A student is interested in the depth of the water off the end of the local pier. Starting at midnight, he measures the depth of the water every three hours for an entire day and records the results in the table. The equation of the least-squares regression line is ŷ = 13.0 - 0.259x, where ŷ is the depth of the water and x is the number of hours past m

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. A graph titled Dandie Dinmont Terrier height versus weight has height (inches) on the x-axis, and weight (pounds) on the y-axis. The points curve up. A graph titled Dandie Dinmont Terrier log height versus log weight has log (height) on the x-axis, and log (weight) on the y-axis. The points curve up. Based on the graphs, which type of model is likely appropriate for predicting weight from height? A linear model is appropriate because the graph of the transformed data is roughly linear. A power model is appropriate because the scatterplot of height versus weight appears curved. 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. An exponential model is appropriate because the scatterplot of log height versus log weight has a stronger linear relationship than the scatterplot of the non-transformed data.

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. A graph titled Light Intensity versus Distance has log (distance) on the x-axis, and log (Intensity) on the y-axis. Points curve down exponentially. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, Log distance. Column 2 is labeled coefficient with entries 0.8561, negative 1.4966. Column 3 is labeled S E Coefficient with entries 0.1282, 0.0962. Column 4 is labeled T with entries 6.68, negative 15.56. Column 5 is labeled P with entries 0.001, 0.000. S = 0.0543, r square = 96.4 percent. Using the computer output, the best estimate of the light intensity at 19 centimeters is: 0.0876, because 0.8561 − 1.4966(log 19) = −1.058, and 10−1.058=0.0876 lumens. 0.3472, because 0.8561 − 1.4966(log 19) = −1.058, and e−1.058=0.3472 lumens. 0.3964, because 0.8561(log 19) − 1.4966 = −0.4018, and 10−0.4018=0.3964 lumens. 0.6691, because 0.8561(log 19) − 1.4966 = −0.4018, and e−0.4018=0.6691 lumens.

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. A graph titled l n (F L O P S) versus Years since 1992 has years since 1992 on the x-axis, and l n (F L O P S) on the y-axis. Points increase in a line with positive slope. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, year. Column 2 is labeled coefficient with 3.5246, 0.6498. Column 3 is labeled S E Coefficient with entries 0.1735, 0.0134. Column 4 is labeled T with entries 20.31, 43.32. Column 5 is labeled P with entries 0.000, 0.000. S = 0.3577, r square = 99.9 percent, r square adjusted = 99.9 percent. 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: 13.3 billion FLOPS because ŷ = 06498(15)+305246 = 13.2716 17,334 billion FLOPS because and e9.7604 = 17,334. 580,473 billion FLOPS because and e13.2716= 580,473. 5,759,701,813 billion FLOPS because and 109.7604 = 5,759,701,813.

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. A graph titled log (Circulation) versus Years since 2000 has years since 2000 on the x-axis, and log (circulation) on the y-axis. Points decreases in a line with negative slope. A graph titled Residuals versus years since 2000 has years since 2000 on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. Based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year? A linear model is appropriate because the residual plot does not show a clear pattern. A power model is appropriate because the scatterplot of years and the log of circulation is roughly linear. 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. Both an exponential and a power model would be appropriate because the log of circulation was used to develop the model.

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table. A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38. Using technology, what is the y-intercept and what is its interpretation? The y-intercept is 17.37. When the weight is 0 pounds, the height will be 17.37 inches. The y-intercept is -34.13. When the weight is 0 pounds, the height will be -34.13 inches. The y-intercept is 17.37. When the weight is 0 pounds, it does not make sense to interpret the height. The y-intercept is -34.13. When the weight is 0 pounds, the height is predicted to be -34.13 inches.

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car's stopping distance, in feet, for each volunteer. A graph titled Driving reaction times has reaction time (Seconds) on the x-axis and stopping distance (feet) on the y-axis. Points increase in a line with positive slope. Point (2, 67) is outside of the other points. Which point most likely decreases the correlation shown in the scatterplot? reaction time 0.5 seconds, stopping distance 35 feet reaction time 1.7 seconds, stopping distance 53 feet reaction time 2 seconds, stopping distance 67 feet

Simple linear regression

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