4. Sophia - Introduction to Statistics (3) - Unit 4
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs $4.50 per week to feed, while a Beagle weighs 30 pounds and costs $9.20 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth. $0.18 / lb. $1.60 / lb. $0.31 / lb. $5.64 / lb.
$0.18 / lb.
James takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A guinea pig weighs 3 pounds and costs $3.50 per week to feed, while a Chihuahua weighs 4.8 pounds and costs $6.20 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth. $0.67 / lb. $1.50 / lb. $0.36 / lb. $2.80 / lb.
$1.50 / lb.
Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below. Using the best-fit line, approximately how much money would a 45-year-old teacher make? $50,000 $47,000 $58,000 $55,000
$50,000
Shawna finds a study of American women that has an equation to predict weight (in pounds) from height (in inches): ŷ = -260 + 6.6x. Shawna's mom's height is 68 inches and her weight is 179 pounds. What is the residual of weight and height for Shawna's mom? 921.4 pounds -9.8 pounds 9.8 pounds 188.8 pounds
-9.8 pounds
Sam rolls two dice, one labeled "x" and the other "y." He rolls each of the dice six times and records the (x, y) measurements as follows: Roll"x" die"y" dieRoll 114Roll 223Roll 322Roll 452Roll 544Roll 665 For the "x" die, the mean is 3.3 and the standard deviation is 2.0.For the "y" die, the mean is 3.3 and the standard deviation is 1.2. Using the formula below or Excel, find the correlation coefficient, r, for this set of outcomes Sam rolled. Answer choices are rounded to the nearest hundredth. 0.28 0.23 0.81 0.82
0.28
A clinic has recorded the age, x, versus weight, y, of many babies for their first 12 months of life, and claim the line of best fit is ŷ = 0.60x + 3.3, where y is in kg, and x is in months. A new baby, who is 10 months and weighs 10 kg, is added to the clinic records. What is the residual of the data for this new baby? -0.7 kg 0.7 kg 0.4 kg -0.4 kg
0.7 kg
The table below shows the grade and reading level for 5 students. GradeReading LevelStudent 126Student 2614Student 3512Student 4410Student 514 For grade, the mean is 3.6 and the standard deviation is 2.1.For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth. 1.00 0.92 0.71 0.85
1.00
This scatterplot shows the number of hours a student slept every night and his or her grade point average. The equation for the least-squares regression line to this data is: ŷ = 0.375x + 1.33. What is the predicted GPA for a student who sleeps 2.5 hours per day? Answer choices are rounded to the hundredths place. 2.64 2.27 2.46 2.08
2.27
his scatterplot shows the performance of a pressure sensor using two variables, pressure and voltage The equation for the least-squares regression line to this data set is The predicted value for the voltage for a pressure of 50 MPa is __________. 2580 mV 2502 mV 2582 mV 2481 mV
2502 mV
For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the 7th week? 37 centimeters 39 centimeters 40 centimeters 35 centimeters
37 centimeters
Fred Anderson, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. He has made a scatter plot to depict the relationship between the number of hours and the number of visitors. How many visitors were there during the fourth hour? 20 4 21 1
4
For the data plotted in the scatterplot below, the value was calculated to be 0.5152. Which of the following sets of statements is true? 51.5% of the variation in voltage can be explained by the pressure. The correlation coefficient, r, is -0.718 71.8% of the variation in pressure can be explained by the voltage. The correlation coefficient, r, is -0.718 48.5% of the variation in voltage can be explained by the pressure. The correlation coefficient, r, is -0.265 26.5% of the variation in pressure can be explained by the voltage. The correlation coefficient, r, is -0.265
51.5% of the variation in voltage can be explained by the pressure. The correlation coefficient, r, is -0.718
Gary Sandoval is a photographer who is wondering if there is an association between the number of photographs he takes and percent cloud coverage. His record is shown in the scatterplot. How many photographs did he take when the cloud coverage was 10 percent or more? 550 450 300 750
750
For the data plotted in the scatterplot, the r2 value was calculated to be 0.9846. Which of the following sets of statements is true? 98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969. 98.5% of the variation in yearly income is explained by a nonlinear relationship with age. The correlation coefficient, r, is 0.992. 98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992 98.5% of the variation in age is explained by a nonlinear relationship with yearly income. The correlation coefficient, r, is 0.969.
98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992
he test scores of five students in both math and geography are presented in the table. MathGeographyStudent 176Student 295Student 365Student 488Student 597 The calculation for the correlation, r, for this set of five students is __________ (answer choices are rounded to the hundredths place). A.) 0.32 B.) 0.57 C.) 0.10 D.) 0.45
A.) 0.32
A consulting firm records its employees' income against the number of hours worked in the scatterplot shown below. Using the best-fit line, which of the following predictions is TRUE? A.) An employee will earn about $470 if they work for 15 hours on a project. B.) An employee will earn $730 if they work for 27 hours on a project. C.) An employee will earn $370 if they work for 10 hours on a project. D.) An employee will earn $310 if they work for 7 hours on a project.
A.) An employee will earn about $470 if they work for 15 hours on a project.
Which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? A.) Average annual temperature in the United StatesAnnual sweater sales by an American retailer B.) Age of babyWeight of baby C.) Number of minutes spent exercising Number of calories burned D.) Number of miles drivenNumber of radio stations listened to
A.) Average annual temperature in the United StatesAnnual sweater sales by an American retailer
increased sugar intake leads to higher levels of body fat.Which of the following is NOT necessary to establish causality? A.) Certainty about the mechanism for cause and effect B.) To look for evidence that greater amounts of sugar intake produce higher levels of body fat C.) To consider alternative explanations for the correlation D.) To determine a plausible physical mechanism for cause and effect
A.) Certainty about the mechanism for cause and effect
Tasha found the following scatterplot that shows four different compact cars at different speeds, from 20 to 70 mph. Which answer choice correctly indicates the explanatory variable and the response variable? A.) Explanatory variable: MPHResponse variable: MPG B.) Explanatory variable: MPHResponse variable: Cars C.) Explanatory variable: MPGResponse variable: MPH D.) Explanatory variable: CarsResponse variable: MPG
A.) Explanatory variable: MPHResponse variable: MPG
Steve knows that a correlation between diet and exercise compared to his blood pressure does not, in itself, mean that diet and exercise will lead to lower blood pressure.Which of the following would NOT be a lurking variable in the above scenario? A.) Steve's favorite color B.) Steve's occupation C.) The amount of cigarettes that Steve smokes D.) Steve's stress level
A.) Steve's favorite color
Jack tracked the average amount of time he and his friend spent playing video games each day. He plotted the average for each day and added a best-fit line. Using the best-fit line, which of the following is TRUE? A.) They will likely spend about 64 minutes playing video games on Day 8. B.) They likely spent about 40 minutes playing video games before they started tracking (Day 0). C.) They spent about 41 minutes playing video games on Day 2. D.) They spent 50 minutes playing video games on Day 6.
A.) They will likely spend about 64 minutes playing video games on Day 8.
The following scatterplot shows the 20 top-selling cars with their weight on the horizontal axis and their miles per gallon (mpg) on the vertical axis. The overall direction of this data is __________. The strength of the association is __________. A.) negative; moderately strong B.) positive; moderately strong C.)negative; weak D.)positive; weak
A.) negative; moderately strong
The following table shows the relationship between weight and calories burned per minute for five people. Weight (in pounds)Calories burned per minute1127.251299.151509.8517410.2518211.75Mean149.49.65Standard Deviation29.511.64 Weight is the explanatory variable and has a mean of 149.4 and a standard deviation of 29.51. Calories burned per minute is the response variable and has a mean of 9.65 and a standard deviation of 1.64.The correlation was found to be 0.944.Select the correct slope and y-intercept for the least-squares line (answer choices are rounded to the hundredths place). A.) slope = 0.05y-intercept = 2.18 B.) slope = 16.99y-intercept = 14.55 C.) slope = -0.05y-intercept = 17.12 D.) slope = -16.99y-intercept = 8.23
A.) slope = 0.05y-intercept = 2.18
The weekly feed cost for Dean's domestic shorthair cat is $2. The cat used in a study weighs 10 pounds.Using the equation ŷ = 0.3 + 0.12x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for Dean's domestic shorthair cat? A.)$0.50 B.)$1.46 C.)$1.50 D.)$0.54
A.)$0.50
Robert is wondering if there is an association between the number of hours he studies and the number of semester credits he is enrolled in. The information is shown in the scatterplot below. If Robert is enrolled in five semester credits, how many hours did he study? A.)6 hours B.)9 hours C.)4 hours D.)3 hours
A.)6 hours
By observing a set of data values, Tasha used a calculator for the tire diameter at the tread and circumference data and got an equation for the least-squares line:ŷ = 0.1 + 3.1xBased on this information, select the statement that is TRUE. A.)A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches. B.)A tire with a 32-inch diameter at the tread will have a circumference of 86.9 inches. C.)A tire with a 28-inch diameter at the tread will have a circumference of 99.3 inches. D.)A tire with a 35-inch diameter at the tread will have a circumference of 124.1 inches.
A.)A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches.
The cost of electricity per unit usage can be seen in the scatterplot shown below. Using the best-fit line, which of the following predictions is TRUE? A.)An electricity bill for 16 units would cost $24. B.)An electricity bill for 23 units would cost $38. C.)An electricity bill for 11 units would cost $19. D.)An electricity bill for 9 units would cost $11.
A.)An electricity bill for 16 units would cost $24.
Robert enters data for weight (in pounds) and calories burned per minute into a statistics software package and finds a regression equation of ŷ = 2.2 + 0.05x, where weight is the explanatory variable.Based on this information, select the conclusion about weight and calories burned per minute that is TRUE. A.)For each additional pound of weight, calories burned per minute increases by 0.05 calories. B.)For each additional pound of weight, calories burned per minute increases by 2.2 calories. C.)For each additional pound of weight, calories burned per minute decreases by 0.05 calories. D.)For each additional pound of weight, calories burned per minute stays relatively the same.
A.)For each additional pound of weight, calories burned per minute increases by 0.05 calories.
A data set was graphed using a scatterplot. The correlation coefficient, r, is 0.192.Which of the following statements explains how the correlation is affected? A.)It is affected by inappropriate grouping. B.) It is affected by nonlinearity. C.)It is affected by an influential point. D.)It is not affected.
A.)It is affected by inappropriate grouping.
thirty minutes of exercise per day can reduce your blood pressure.Which of the following is a guideline for establishing causality? A.)Perform a randomized, controlled experiment. B.) Look for evidence that smaller amounts of exercise produce a reduction in blood pressure. C.)Control the number of minutes of exercise and blood pressure to get the same results. D.)Check if lower blood pressure is present or absent when exercise is present or absent.
A.)Perform a randomized, controlled experiment.
A researcher found a study relating the distance a driver can see, y, to the age of the driver, x. When researchers looked at the association of x and y, they found that the coefficient of determination was .Select a conclusion that the researcher can make from this data. A.)The correlation coefficient, r, is -0.736. B.)About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see. C.)The correlation coefficient, r, is -0.271. D.)About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
A.)The correlation coefficient, r, is -0.736.
A researcher found a study relating the mortality rates for women aged 65 to 74, y, to the proportion of calories from sweeteners in their diets, x. When researchers looked at the association of x and y, they found that the coefficient of determination was .Select a conclusion that the researcher can make from this data. A.)The correlation coefficient, r, is 0.697. B.)The correlation coefficient, r, is 0.236. C.)About 51% of the variation in mortality rates is explained by a linear relationship with proportion of calories in sweeteners. D.)About 70% of the variation in proportion of calories in sweeteners is explained by a linear relationship with mortality rates.
A.)The correlation coefficient, r, is 0.697.
By observing a set of data values, Tina used a calculator for the engine speed (rpm) and predicted horsepower (hp) to get an equation for the least-squares line:ŷ = 10 + 30xBased on the data that Tina collected, select the statement that is TRUE. A.)The horsepower associated with an engine speed of 2.5 rpm would be 85 hp. B.)The horsepower associated with an engine speed of 3.5 rpm would be 110 hp. C.)The horsepower associated with an engine speed of 1.5 rpm would be 70 hp. D.)The horsepower associated with an engine speed of 0.5 rpm would be 40 hp.
A.)The horsepower associated with an engine speed of 2.5 rpm would be 85 hp.
Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation. Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. The number of cars on the road Average mileage per vehicle Average income per household The number of citizens in the United States
Average income per household
Shawna reads a study about exercise that includes the following scatterplot. Which answer choice correctly indicates the explanatory variable and the response variable? A.) Explanatory variable: WeightResponse variable: Exercise B) Explanatory variable: WeightResponse variable: Calories burned per minute C.) Explanatory variable: Calories burned per minuteResponse variable: Weight D.) Explanatory variable: ExerciseResponse variable: Calories burned per minute
B) Explanatory variable: WeightResponse variable: Calories burned per minute
Blake enters data for weight (in hundreds of pounds) and miles per gallon of cars into a statistics software package and finds a regression equation of ŷ = 38.5 - 1.4x, where weight is the explanatory variable.Based on this information, select Blake's conclusion about weight and miles per gallon that is TRUE. A.) For each additional 100 pounds of weight, miles per gallon stays relatively the same. B.) For each additional 100 pounds of weight, miles per gallon decreases by 1.4 miles. C.) For each additional 100 pounds of weight, miles per gallon increases by 1.4 miles. D.) For each additional 100 pounds of weight, miles per gallon decreases by 38.5 miles.
B.) For each additional 100 pounds of weight, miles per gallon decreases by 1.4 miles.
A data set was graphed using a scatterplot. The correlation coefficient, r, is 0.845.Which of the following statements explains how the correlation is affected? A.)It is not affected. B.) It is affected by nonlinearity. C.)It is affected by an influential point. D.)It is affected by inappropriate grouping.
B.) It is affected by nonlinearity.
Shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying.Which of the following would NOT be a lurking variable in the above scenario? A.) The low cost and number of soft drink brands available for purchase B.) Musical preferences C.) Body weight D.) The caffeine content of soft drinks
B.) Musical preferences
Which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? A.) Number of miles driven by Paul Number of gallons of gas used by Paul's car B.) Steepness of the Appalachian Trail John's speed while hiking up the Appalachian Trail C.) Swimsuit sales throughout the yearSunscreen sales throughout the year D.) Average Summer temperature in the United States Summer air-conditioning costs for homes in the United States
B.) Steepness of the Appalachian Trail John's speed while hiking up the Appalachian Trail
Which of the following situations describes a multiple regression? A.) Using the square footage to predict the listing price of a home B.) Using the average salary of a homeowner, the number of bedrooms, and the square footage to predict the listing price of a home C.) Using the average salary of a homeowner and the number of bedrooms to predict the listing price and square footage of a home D.) Using the listing price of a home to predict the annual salary of a homeowner, the number of bedrooms, and the square footage
B.) Using the average salary of a homeowner, the number of bedrooms, and the square footage to predict the listing price of a home
Which of the following situations describes a multiple regression? A.) Using job performance to predict the motivational level and IQ scores of an individual B.) Using the motivation level, the amount of social support, and IQ scores to predict the job performance of an individual C.) Using IQ scores to predict the job performance of an individual D.) Using the motivational level and the amount of social support to predict the job performance and IQ scores of an individual
B.) Using the motivation level, the amount of social support, and IQ scores to predict the job performance of an individual
The following table shows the relationship between the weight (in pounds) and the weekly feed cost (in dollars) for five pets. Weight (in pounds)Weekly Feed Cost (in dollars)0.53471983796211Mean24.57.6Standard Deviation25.442.97 Weight is the explanatory variable and has a mean of 24.5 and a standard deviation of 25.44. Weekly feed cost is the response variable and has a mean of 7.6 and a standard deviation of 2.97.The correlation was found to be 0.879.Select the correct slope and y-intercept for the least-squares line (answer choices are rounded to the hundredths place). A.) slope = 7.53y-intercept = 32.73 B.) slope = 0.10y-intercept = 5.15 C.) slope = -7.53y-intercept = 4.27 D.) slope = -0.10y-intercept = 10.05
B.) slope = 0.10y-intercept = 5.15
The weekly feed cost for David's rabbit is $2.20. The rabbit used in a study weighs 9 pounds.Using the equation ŷ = 0.5 + 0.16x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for David's rabbit? A.)$1.35 B.)$0.26 C.)$1.94 D.)$0.85
B.)$0.26
Select the FALSE statement about the correlation coefficient (r). A.)The correlation coefficient quantifies the strength of the linear relationship between two variables. B.)The correlation coefficient r = 0 shows that two variables are strongly correlated. C.)The value of the correlation coefficient lies between -1 and 1. D.)The sign of the correlation coefficient tells us if the pair of variables is positively or negatively associated.
B.)The correlation coefficient r = 0 shows that two variables are strongly correlated.
A scatterplot was created using the weight and weekly feed cost for six pets. Two more pets are added to the scatterplot (shown in blue in the upper left side of the graph). Select the TRUE statement about the two added points. A.) They are outliers in the y-direction only. B.)They are outliers in both the x- and y-direction. C.)They are not outliers. D.) They are outliers in the x-direction only
B.)They are outliers in both the x- and y-direction.
The average height and average weight of five students are presented in the table. Height (in cm)Weight (in kg)Student 117262Student 217365Student 317564Student 417666Student 517765 The calculation for the correlation, r, for this set of five students is __________ (answer choices are rounded to the hundredths place). A.) 0.49 B.) 0.91 C.) 0.70 D.) 0.84
C.) 0.70
Which of the following statements is FALSE? A.)A controlled experiment can give the best evidence for causation. B.) A correlation between -1 and 1 establishes a relationship but not necessarily a causation. C.) A high correlation between the explanatory and response variables is sufficient to prove causation. D.)A correlation coefficient of 1 could mean that the relationship is just a coincidence.
C.) A high correlation between the explanatory and response variables is sufficient to prove causation.
Simone, a veterinary student, recently discovered the following scatterplot produced by the Department of Agriculture. Which answer correctly indicates the explanatory variable and the response variable? A.) Explanatory variable: Food costResponse variable: Animal weight B.) Explanatory variable: Number of animalsResponse variable: Food cost C.) Explanatory variable: Animal weightResponse variable: Food cost D.) Explanatory variable: Type of animalResponse variable: Animal weight
C.) Explanatory variable: Animal weightResponse variable: Food cost
Sam enters data for weight (in pounds) and weekly food cost (in dollars) of pets into a statistics software package and finds a regression equation of ŷ = 0.3 + 0.12x, where weight is the explanatory variable.Based on this information, select Sam's conclusion about food weight and costs that is TRUE. A.) For each additional pound of weight, weekly food costs stay relatively the same. B.) For each additional pound of weight, weekly food costs increase by 30 cents. C.) For each additional pound of weight, weekly food costs increase by 12 cents. D.) For each additional pound of weight, weekly food costs decrease by 12 cents.
C.) For each additional pound of weight, weekly food costs increase by 12 cents.
Smoking causes lung cancer.Which of the following is necessary to establish causality for the above claim? A.) Not considering other possible causes of lung cancer B.) Keeping all variables the same to get duplicate results C.) Looking for cases where correlation between smoking and lung cancer remains while controlling for other variables D.) Using only an observational study to show that smoking causes lung cancer
C.) Looking for cases where correlation between smoking and lung cancer remains while controlling for other variables
Which of the following data sets would most likely have a positive association and a correlation coefficient between 0 and 1? A.) Speed of Frank's vehicleTime it takes Frank to arrive at destination B.) Level of education Head circumference C.) Number of months Lela owns a car Number of scratches on Lela's car D.) Number of school absences Test scores in school
C.) Number of months Lela owns a car Number of scratches on Lela's car
Stephanie knows that a correlation between the number of bars and the number of churches in her city does not, in itself, mean that more bars will lead to a higher number of churches.Which of the following would NOT be a lurking variable in the above scenario? A.) Stephanie's proximity to the center of the city B.) City demographics C.) The number of letters in the street name D.) Population density
C.) The number of letters in the street name
Which of the following situations describes a multiple regression? A.) Using the body height and body weight to predict IQ score and brain volume of an individual B.) Using the IQ score to predict the body height and body weight of an individual C.) Using the brain volume, the body height, and the body weight to predict IQ score of an individual D.) Using the brain volume to predict the IQ score of an individual
C.) Using the brain volume, the body height, and the body weight to predict IQ score of an individual
Glen Sarin is a photographer who is wondering if there is an association between the number of photographs she takes and percent cloud coverage. Her record is shown in the scatterplot. How many photographs did she take when the cloud coverage was 4% or less? A.)150 photographs B.) 1,050 photographs C.)750 photographs D.)900 photographs
C.)750 photographs
Which of the following statements is TRUE? A.) A high correlation indicates that the explanatory variable is a direct cause of the response variable. B.)Having a low correlation is sufficient enough to imply causation. C.)A high correlation can indicate a relationship but cannot prove causation. D.)To imply causation, the correlation must be -1.
C.)A high correlation can indicate a relationship but cannot prove causation.
Why do we square the residuals when using the least-squares line method to find the line of best fit? A.) We don't square the residuals when using the least-squares method. B.)Squaring the residuals makes it easier to identify smaller residuals. C.)It cancels out the effect of having negative and positive residuals. D.)It amplifies the effect of having negative and positive residuals.
C.)It cancels out the effect of having negative and positive residuals.
A scatterplot was created using the miles per gallon and weight of eight cars. Another car is added to the scatterplot (shown in blue in the left side of the graph). Select the TRUE statement about this added point. A.)It is an outlier in the y-direction. B.)It is not an outlier. C.)It is an outlier in the x-direction. D.) It is an outlier in both the x- and y-directions
C.)It is an outlier in the x-direction.
Which of the following statements is TRUE? A.)The least-squares line is the process of minimizing the product of the squared residuals. B.)The least-squares line is the process of minimizing the quotient of the squared residuals. C.)The least-squares line is the process of minimizing the sum of the squared residuals. D.)The least-squares line is the process of minimizing the difference of the squared residuals.
C.)The least-squares line is the process of minimizing the sum of the squared residuals.
Select the statement regarding the correlation coefficient (r) that is TRUE. A.)A correlation coefficient of 1 implies a weak correlation between two variables. B.) The correlation coefficient cannot be calculated for all scatterplots. C.)The sign of the correlation coefficient might change when we combine two subgroups of data. D.) The correlation coefficient describes the direction of the association between two variables, but not the strength.
C.)The sign of the correlation coefficient might change when we combine two subgroups of data.
The following scatterplot shows the 20 top-selling cars with their weight on the horizontal axis and their miles per gallon (mpg) on the vertical axis. The overall direction of this data is __________. The strength of the association is __________. A.)negative; weak B.)positive; weak C.)negative; strong D.)positive; strong
C.)negative; strong
Which of the following is NOT a guideline for establishing causality? Check if the effect is present or absent when the response variable is present or absent. Look for cases where correlation remains while other factors vary. Check if the effect is present or absent when the explanatory variable is present or absent. Perform a randomized, controlled experiment.
Check if the effect is present or absent when the response variable is present or absent.
Which statement is true regarding correlation? Correlation is a quantitative measure of the form between two variables, as seen on a scatterplot. Correlation can be used to determine the direction of the relationship between two variables. Correlation can only be negative. Correlation can only be positive.
Correlation can be used to determine the direction of the relationship between two variables.
Which statement about correlation is FALSE? Correlation is a quantitative measure of the strength of a linear association between two variables. Correlation is a quantitative measure of the strength of a non-linear association between two variables. A correlation of -1 or 1 corresponds to a perfectly linear relationship. Correlation is measured by r, the correlation coefficient which has a value between -1 and 1.
Correlation is a quantitative measure of the strength of a non-linear association between two variables
A local shop's weekly sales of ice cream and sunglasses are presented in the table. Ice CreamSunglassesMonday35Tuesday46Wednesday57Thursday79Friday89 The calculation for the correlation, r, for this set of five data points is __________ (answer choices are rounded to the hundredths place). A.) 0.94 B.) 0.77 C.) 0.88 D.) 0.98
D.) 0.98
A researcher found a study relating the value of a car, y, to the age of the car, x. When researchers looked at the association of x and y, they found that the coefficient of determination was .Select a conclusion that the researcher can make from this data. A.)About 40% of the variation in the age of the car is explained by a linear relationship with the value of the car. B.)The correlation coefficient, r, is 0.025. C.)The correlation coefficient, r, is 0.842. D.) About 16% of the variation in the value of the car is explained by a linear relationship with the age of the car.
D.) About 16% of the variation in the value of the car is explained by a linear relationship with the age of the car.
The following table shows the relationship between the weight (in hundreds of pounds) and the miles per gallon (mpg) for five cars. Weight (in hundreds of pounds)Miles per gallon (mpg)532927131517142011Mean12.819.8Standard Deviation6.029.15 Weight is the explanatory variable and has a mean of 12.8 and a standard deviation of 6.02. Miles per gallon is the response variable and has a mean of 19.8 and a standard deviation of 9.15.The correlation was found to be -0.959.Select the correct slope and y-intercept for the least-squares line (answer choices are rounded to the hundredths place). A.) slope = 1.46y-intercept = 14.71 B.) slope = -0.63y-intercept = 27.86 C.) slope = 0.63y-intercept = 25.27 D.) slope = -1.46y-intercept = 38.49
D.) slope = -1.46y-intercept = 38.49
The weekly feed cost for Dianna's iguana is $2.10. The iguana used in a study weighs 11 pounds.Using the equation ŷ = 0.4 + 0.15x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for Dianna's iguana? A.)$0.72 B.)$2.05 C.)$1.38 D.)$0.05
D.)$0.05
Mr. Carl Burl, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. He has made a scatterplot to depict the relationship between the number of hours and the number of visitors. How many visitors came to his exhibition in the first 3 hours? A.)7 visitors B.)6 visitors C.)22 visitors D.)16 visitors
D.)16 visitors
By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line:ŷ = 2.2 + 0.05xBased on the information gathered by Thomas, select the statement that is TRUE. A.)A person weighing 149 pounds can burn 9.8 calories per minute. B.)A person weighing 125 pounds can burn 8.3 calories per minute. C.)A person weighing 173 pounds can burn 10.7 calories per minute. D.)A person weighing 134 pounds can burn 8.9 calories per minute.
D.)A person weighing 134 pounds can burn 8.9 calories per minute.
Which of the following statements is TRUE? A.)Low correlation implies causation. B.)A high correlation means that the response variable is caused by the explanatory variable. C.)To imply causation, the correlation must be 1. D.)High correlation does not always establish causation.
D.)High correlation does not always establish causation.
A data set was graphed using a scatterplot. The correlation coefficient, r, is 0.813.Which of the following statements explains how the correlation is affected? A.) It is affected by nonlinearity. B.)It is affected by inappropriate grouping. C.)It is not affected. D.)It is affected by an influential point.
D.)It is affected by an influential point.
A scatterplot was created using the miles per gallon and weight of 20 cars. Another car is added to the scatterplot (shown in blue in the lower part of the graph). Which statement is TRUE regarding the added point? A.)It is not an outlier. B.)It is an outlier in the x-direction. C.) It is an outlier in both the x- and y-directions. D.)It is an outlier in the y-direction.
D.)It is an outlier in the y-direction.
Select the statement about the correlation coefficient (r) that is TRUE. A.)The correlation coefficient cannot be calculated by hand. A statistical software must be used. B.) The correlation coefficient r = 0.75 shows a very strong positive relationship between two variables. C.)The stronger the strength of association, the lower the value of the correlation coefficient. D.)The correlation coefficient is always between -1 and +1.
D.)The correlation coefficient is always between -1 and +1.
Which of the following statements is FALSE? A.)The least-squares line is the most common way to find the line of best fit. B.) Squaring the residuals prevents positive and negative residuals from canceling out. C.)The least-squares line should minimize residuals. D.)The difference of the squared residuals is used to calculate the least-squares line.
D.)The difference of the squared residuals is used to calculate the least-squares line.
The following scatterplot relates the life expectancy of animals to their heart rate. Ignoring humans (which are labeled "Man" in the scatterplot), which two conclusions can be made from the scatterplot? A.)The overall direction of the data is positive. B.)The strength of the association is weak. C.) The overall direction of the data is nonlinear. D.)The strength of the association is moderate. E.)The strength of the association is strong. F.)The overall direction of data is negative.
E.)The strength of the association is strong. F.)The overall direction of data is negative.
This scatterplot shows the performance of a pressure sensor using two variables, pressure and voltage Which answer choice correctly indicates the explanatory variable and the response variable of the scatterplot? Explanatory variable: PressureResponse variable: Voltage Explanatory variable: PressureResponse variable: Pressure Sensor Explanatory variable: VoltageResponse variable: Pressure Sensor Explanatory variable: VoltageResponse variable: Pressure
Explanatory variable: PressureResponse variable: Voltage
The scatterplot below shows the performance of a thermocouple. Which answer choice correctly indicates the explanatory variable and the response variable for the scatterplot? Explanatory variable: Temperature Response variable: Thermocouple performance Explanatory variable: Temperature Response variable: Voltage Explanatory variable: Voltage Response variable: Thermocouple performance Explanatory variable: Voltage Response variable: Temperature
Explanatory variable: Temperature Response variable: Voltage
This scatterplot shows the performance of a pressure sensor using two variables, pressure and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot. Form: Linear Direction: Positive Strength: Moderate Form: Non-Linear Direction: Negative Strength: Strong Form: LinearDirection: NegativeStrength: Weak Form: Non-Linear Direction: Positive Strength: Weak
Form: LinearDirection: NegativeStrength: Weak
This scatterplot shows the performance of an electric motor using the variables speed of rotation and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot. Form: The data points appear to be in a straight line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are closely concentrated. Form: The data points are arranged in a curved line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are far apart from each other. Form: The data points appear to be in a straight line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are closely concentrated.
Form: The data points appear to be in a straight line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are closely concentrated.
Which of the following statements is true? Only a correlation equal to -1 implies causation. High correlation does not necessarily imply causation. Only a correlation equal to 1 implies causation. A correlation equal to 1 or -1 implies causation.
High correlation does not necessarily imply causation.
For what reason may the correlation in this scatterplot be affected? It is impossible to determine. It may be affected by an influential point. It may be affected by inappropriate grouping. It may be affected by non-linearity.
It may be affected by non-linearity.
Which of the following is NOT a guideline for establishing causality? Look for cases where correlation exists between the variables of a scatterplot. Keep all variables the same to get duplicate results. Perform a randomized, controlled experiment. Take into consideration all the other possible causes.
Keep all variables the same to get duplicate results.
Stacey finds a scatterplot that shows data for nine schools. It relates the percentage of students receiving free lunches to the percentage of students wearing a bicycle helmet. The plot shows a strong negative correlation. Stacey recalls that correlation does not imply causation. In this example, Stacey sees that increasing the percentage of free lunches would not cause children to use their bicycle helmets less. Identify the lurking variable that is causing Stacey's observed association. The number of bikes at each school Helmet brands School budget Parents' annual salary
Parents' annual salary
For ten students, a teacher records the following scores of two assessments, Quiz 1 and Test. Quiz 1 (x)Test (y)15201215101214181010813612151016181315Mean11.914.3Standard Deviation3.33.5 The correlation of Quiz 1 and Test is 0.568. Given the information below, what is the slope and y-intercept for the least-squares line of the Quiz 1 scores and Test scores? Answer choices are rounded to the hundredths place. Slope = 0.60 y-intercept = 3.32 Slope = 0.54 y-intercept = 7.87 Slope = 0.54 y-intercept = 4.18 Slope = 0.60 y-intercept = 7.16
Slope = 0.60 Y-intercept = 7.16
Jaime finished analyzing a set of data with an explanatory variable x and a response variable y.He finds that the mean and standard deviation for x are 5.43 and 1.12, respectively. The mean and standard deviation for y are 10.32 and 2.69, respectively.The correlation was found to be 0.893. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. Slope = 2.14y-intercept = -16.65 Slope = 0.37y-intercept = 1.61 Slope = 2.14y-intercept = -1.30 Slope = 0.37y-intercept = 8.31
Slope = 2.14y-intercept = -1.30
Using the provided scatterplot, select the correct direction of the blue outlier. The outlier is in neither the x- nor y- direction. The outlier is in both the x- and y- direction. The outlier is in the x-direction. The outlier is in the y-direction.
The outlier is in the y-direction.
Data for weight (in pounds) and age (in months) of babies is entered into a statistics software package and results in a regression equation of ŷ = 17 + 0.8x. What is the correct interpretation of the slope if the weight is the response variable and the age is the explanatory variable? The weight of a baby decreases by 17 pounds, on average, when the baby's age increases by 1 month. The weight of a baby decreases by 0.8 pounds, on average, when the baby's age increases by 1 month. The weight of a baby increases by 17 pounds, on average, when the baby's age increases by 1 month. The weight of a baby increases by 0.8 pounds, on average, when the baby's age increases by 1 month
The weight of a baby increases by 0.8 pounds, on average, when the baby's age increases by 1 month
Data for weight (in kilograms) and height (in inches) of babies is entered into a statistics software package and results in a regression equation of ŷ = 1.2x - 20.7. What is the correct interpretation of the slope if the weight is the response variable and the height is the explanatory variable? The weight of a baby decreases by 1.2 kilograms, on average, when the baby's height increases by 1 inch. The weight of a baby increases by 1.2 kilograms, on average, when the baby's height increases by 1 inch. The weight of a baby decreases by 20.7 kilograms, on average, when the baby's height increases by 1 inch. The weight of a baby increases by 20.7 kilograms, on average, when the baby's height increases by 1 inch.
The weight of a baby increases by 1.2 kilograms, on average, when the baby's height increases by 1 inch.
In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. Which of the following statements is TRUE? The researchers proved that exercise causes weight loss. 93% of the high school students studied lost weight. The researchers proved that exercise causes weight loss, but only for high school students. There is a strong positive linear association between weight loss and exercise, but the researchers have not proven causation.
There is a strong positive linear association between weight loss and exercise, but the researchers have not proven causation
A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be __________. between 1 and 2 between -1 and -2 between 0 and 1 between 0 and -1
between 0 and -1
A correlation coefficient between number of miles driven and number of gallons of gas used is most likely to be __________. between 1 and 2 between 0 and 1 between 0 and -1 between -1 and -2
between 0 and 1
