Deck 7: Linear Regression

Question 1

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= 0.3 + 0.71 drop.Interpret the meaning of the y-intercept.

A)According to the model,a ball dropped from 0.71 cm high will bounce 0 cm.(This may not actually happen. )
B)According to the model,a ball dropped from 0.3 cm high will bounce 0 cm.(This may not actually happen. )
C)According to the model,a ball dropped from 0 cm high will bounce 0.71 cm.(This may not actually happen. )
D)According to the model,a ball dropped from 0.71 cm high will bounce 0.3 cm.(This may not actually happen. )
E)According to the model,a ball dropped from 0 cm high will bounce 0.3 cm.(This may not actually happen. )

Answer 1

According to the model,a ball dropped from 0 cm high will bounce 0.3 cm.(This may not actually happen. )

Question 2

A)

= 0.6 + 14.2x
B)

= 2 + 1.69x
C)

= -4 + 2x
D)

= 14.2 + 0.6x
E)

= 20.05 + 0.15x

Answer 2

= 14.2 + 0.6x

Question 3

A random sample of 150 yachts sold in the Canada last year was taken.A regression analysis to predict the price (in thousands of dollars)from length (in metres)was completed.A linear model is appropriate.What are the units of the slope?

A)Slope is yachts per dollar.
B)Slope is metres per dollar.
C)Slope is dollars per metre.
D)Slope is metres per thousand dollars.
E)Slope is thousands of dollars per metre.

Answer 3

Slope is thousands of dollars per metre.

Question 4

A)

= 79.40 - 24.00x
B)

= 40.00 + 2.47x
C)

= -24.00 + 79.40x
D)

= -112.60 + 40.00x
E)

= 7.45 - 0.01x

Question 5

A)Model is appropriate.
B)Model may not be appropriate.The spread is changing.
C)Model is not appropriate.The relationship is nonlinear.

Question 6

A)Model is not appropriate.The relationship is nonlinear.
B)Model is appropriate.
C)Model may not be appropriate.The spread is changing.

Question 7

A)Model may not be appropriate.The spread is changing.
B)Model is appropriate.
C)Model is not appropriate.The relationship is nonlinear.

Question 8

A)

= 12.25;

= 0.90
B)

= -46;

= 11.50
C)

= 49;

= -14.25
D)

= 11;

= 1.80
E)

= 2.75;

= 0.45

Question 9

A)2
B)4
C)3
D)9
E)7

Question 10

A)Model is not appropriate.The relationship is nonlinear.
B)Model is appropriate.
C)Model may not be appropriate.The spread is changing.

Question 11

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.Do you think the slope is positive or negative? Why?

A)Negative.Larger homes should use less electricity.
B)Positive.The larger the number of houses the more electricity used.
C)Negative.Smaller homes should use less electricity.
D)Positive.More square feet indicates more houses.
E)Positive.Larger homes should use more electricity.

Question 12

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.What units does the slope have?

A)Slope is kilowatt-hours per square foot.
B)Slope is kilowatt-hours per house.
C)Slope is square feet per kilowatt-hour.
D)Slope is square feet per house.
E)Slope is houses per kilowatt-hour.

Question 13

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet)of 135 homes.A regression to predict the amount of electricity used (in kilowatt-hours)from size was completed.The residuals plot indicated that a linear model is appropriate.What are the variables and units in this regression?

A)Amount of electricity used (in kilowatt-hours)is y and size (in square feet)is x.
B)Amount of electricity used (in kilowatt-hours)is y and number of homes is x.
C)Size (in square feet)is y and amount of electricity used (in kilowatt-hours)is x.
D)Size (in square feet)is y and number of homes is x.
E)Number of homes is y and amount of electricity used (in kilowatt-hours)is x.

Question 14

A)

= 220;

= 12.50
B)

= 190;

= 0.32
C)

= 210;

= 6
D)

= 180;

= 12.50
E)

= 20;

= 2.50

Question 15

Consider the four points (20,20), (30,50), (40,30),and (50,60).The least squares line is
= 5 + 50x.Explain what "least squares" means using these data as a specific example.

A)The line

= 5 + 50x minimizes the sum of the vertical distances from the points to the line.
B)The line

= 5 + 50x minimizes the sum of the squared vertical distances from the points to the line.
C)The line

= 5 + 50x minimizes the sum of the squared horizontal distances from the points to the line.
D)The line

= 5 + 50x minimizes the square of the standard deviation.
E)The line

= 5 + 50x minimizes the sum of the squared difference between the x and y values.

Question 16

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.The model is
= 1,248 + 0.6 size.Explain what the slope of the line says about the electricity usage and home size.

A)On average,the amount of electricity used increases by 1,248 kilowatt-hours when the size of the house is increased by a square foot.
B)On average,the size of the house increases by 1,248 feet for every kilowatt-hour used.
C)On average,the amount of electricity used is 0.6 kilowatt hours less than the size of the house.
D)On average,the amount of electricity used increases by 0.6 kilowatt-hours when the size of the house is increased by a square foot.
E)On average,the size of the house increases by 0.6 feet for every kilowatt-hour used.

Question 17

A)Model may not be appropriate.The spread is changing.
B)Model is appropriate.
C)Model is not appropriate.The relationship is nonlinear.

Question 18

A)Model may not be appropriate.The spread is changing.
B)Model is not appropriate.The relationship is nonlinear.
C)Model is appropriate.

Question 19

A)

= 60;r = 0.60
B)

= 180;r = -0.60
C)

= -117;r = 0.50
D)

= -48;r = 0.03
E)

= -300;r = 0.50

Question 20

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= -0.3 + 0.69 drop.Explain what the slope of the line says about the bounce height and the drop height of the ball.

A)On average,the bounce height will be 0.69 cm less than the drop height.
B)On average,the drop height increases by 0.69 cm for every extra cm of bounce height.
C)On average,the bounce height increases by -0.3 cm for every extra cm of drop height.
D)On average,the bounce height increases by 0.69 cm for every extra cm of drop height.
E)On average,the drop height increases by -0.3 cm for every extra cm of bounce height.

Question 21

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression to predict the average attendance from the number of games won has an
= 31.4%.The residuals plot indicated that a linear model is appropriate.What is the correlation between the average attendance and the number of games won.

A)0.099
B)0.560
C)0.314
D)0.686
E)0.828

Question 22

A random sample of 150 yachts sold in Canada last year was taken.A regression to predict the price (in thousands of dollars)from length (in feet)has an
= 19.00%.What would you predict about the price of the yacht whose length was one standard deviation above the mean?

A)The price should be 1 SD above the mean in price.
B)The price should be 0.436 SDs above the mean in price.
C)The price should be 1 SD below the mean in price.
D)The price should be 0.900 SDs above the mean in price.
E)The price should be 0.872 SDs above the mean in price.

Question 23

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression to predict the average attendance from the number of games won has an r = 0.79.Interpret this statistic.

A)Negative,fairly strong linear relationship.62.41% of the variation in average attendance is explained by the number of games won.
B)Negative,weak linear relationship.4.41% of the variation in average attendance is explained by the number of games won.
C)Positive,weak linear relationship.4.41% of the variation in average attendance is explained by the number of games won.
D)Positive,fairly strong linear relationship.79% of the variation in average attendance is explained by the number of games won.
E)Positive,fairly strong linear relationship.62.41% of the variation in average attendance is explained by the number of games won.

Question 24

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= 0.4 + 0.72 drop.A golf ball dropped from 64 cm bounced 1 cm less than expected.How high did it bounce?

A)86.94 cm
B)45.08 cm
C)47.48 cm
D)66.12 cm
E)45.48 cm

Question 25

The relationship between the selling price (in dollars)of used Ford Escorts and their age (in years)is analyzed.A regression analysis to predict the price from the age gives the model
= 14,210 - 1,348 age.You want to sell a 17 year old Escort.Use the model to determine an appropriate price.Explain any problems.

A)-$22,916 You won't sell a car for a negative amount.The model doesn't give meaningful prices for Escorts this old.
B)$11 The car should be worth more than this.
C)-$37,126 There are no problems with this prediction.
D)$22,916 There is no way the car is worth this much.
E)-$8,706 You won't sell a car for a negative amount.The model doesn't give meaningful prices for Escorts this old.

Question 26

Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an
= 85.8%.Why doesn't the model explain 100% of the variation in the price of an Escort?

A)The model was calculated incorrectly.It should explain all the variation in price.
B)The model is only right 85.8% of the time.
C)14.2% of the time the buyer is getting ripped off by an unscrupulous seller.
D)The prices of all used Ford Escorts were not used.
E)There are other factors besides age that affect the price.These include things such as mileage,options,and condition of the car.

Question 27

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression to predict the average attendance from the number of games won has an
= 30.4%.The residuals plot indicated that a linear model is appropriate.Write a sentence summarizing what
Says about this regression.

A)Differences in average attendance explain 30.4% of the variation in the number of games won.
B)In 30.4% of games won the attendance was at least as large as the average attendance.
C)The number of games won explains 69.6% of the variation in average attendance.
D)The number of games won explains 30.4% of the variation in average attendance.
E)Differences in average attendance explain 69.6% of the variation in the number of games won.

Question 28

A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.The model is
= 1,240 + 0.5 size.How much electricity would you predict would be used in a house that is 2,372 square feet?

A)54 kilowatt-hours
B)2,264.00 kilowatt-hours
C)1,186 kilowatt-hours
D)2,426 kilowatt-hours
E)3,612.5 kilowatt-hours

Question 29

A random sample of records of electricity usage of homes gives the amount of electricity used and size (in square feet)of 135 homes.A regression to predict the amount of electricity used (in kilowatt-hours)from size has an R-squared of 71.3%.The residuals plot indicated that a linear model is appropriate.Write a sentence summarizing what
Says about this regression.

A)Size differences explain 28.7% of the variation in electricity usage.
B)Differences in electricity usage explain 71.3% of the variation in the size of house.
C)Size differences explain 71.3% of the variation in the number of homes.
D)Size differences explain 71.3% of the variation in electricity usage.
E)Differences in electricity usage explain 28.7% of the variation in the number of house.

Question 30

Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an
= 88.2%.Describe the relationship

A)Positive,strong linear relationship.As the age increases the price goes up.
B)Negative,weak linear relationship.As the age decreases the price goes down.
C)Positive,weak linear relationship.As the age increases the price goes down.
D)Negative,strong linear relationship.As the age increases the price goes down.
E)Negative,strong linear relationship.As the age increases the price stays the same.

Question 31

The relationship between the number of games won during one season by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model
= -2,100 + 187 wins.Predict the average attendance of a team with 400 wins.Explain any possible problems with this prediction.

A)13 people.There are other factors besides number of games won.
B)72,700 people.A team doesn't play that many games and their arenas probably can't hold that many people.
C)5,380 people.There is no problem with this prediction.
D)76,900 people.A team doesn't play that many games and their arenas probably can't hold that many people.
E)74,800 people.It is only an estimate.

Question 32

A random sample of 150 yachts sold in Canada last year was taken.A regression to predict the price (in thousands of dollars)from length (in metres)has an
= 15.2%.What would you predict about the price of the yacht whose length was two standard deviations below the mean?

A)The price should be 0.780 SDs below the mean in price.
B)The price should be 0.390 SDs below the mean in price.
C)The price should be 1 SD below the mean in price.
D)The price should be 1.842 SDs below the mean in price.
E)The price should be 1 SD above the mean in price.

Question 33

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= -0.1 + 0.70 drop.Predict the height of the bounce if dropped from 64 cm.

A)44.9 cm
B)91.57 cm
C)44.7 cm
D)64.6 cm
E)44.8 cm

Question 34

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= 0.3 + 0.74 drop.A golf ball dropped from 61 cm bounced 46.44 cm.What is the residual for this bounce height.?

A)-1 cm
B)0.74 cm
C)46.14 cm
D)1 cm
E)2 cm

Question 35

A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.The model is
= 1,287 + 0.3 size.The people in a house that is 2,347 square feet used 500 kilowatt-hours less than expected.How much did they use?

A)1,491.1 kilowatt-hours
B)3,134.3 kilowatt-hours
C)-82.9 kilowatt-hours
D)3,533.33 kilowatt-hours
E)1,204.1 kilowatt-hours

Question 36

A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.The residuals plot indicated that a linear model is appropriate.The model is
= 1,218 + 0.3 size.What would a negative residual mean for people living in a house that is 2,495 square feet?

A)They are using more electricity than expected.
B)Their house is bigger than expected.
C)Their house is smaller than expected.
D)They are using the least amount of electricity of all of the houses sampled.
E)They are using less electricity than expected.

Question 37

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model
= -2,100 + 193 wins.Predict the average attendance of a team with 58 wins.

A)11 people
B)9,094 people
C)13,294 people
D)11,194 people
E)-1,849 people

Question 38

Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an
= 87.7%.Write a sentence summarizing what
Says about this regression.

A)The age of the car explains 87.7% of the variation in price.
B)The price of the car explains 87.7% of the variation in age.
C)The age of the car explains 12.3% of the variation in price.
D)The age of the car explains 9.36% of the variation in price.
E)The price of the car explains 12.3% of the variation in age.

Question 39

A random sample of 150 yachts sold in Canada last year was taken.A regression to predict the price (in thousands of dollars)from length (in metres)has an
= 18.3%.What is correlation between length and price?

A)0.428
B)0.033
C)0.667
D)0.904
E)0.183

Question 40

The relationship between the selling price (in dollars)of used Ford Escorts and their age (in years)is analyzed.A regression analysis to predict the price from the age gives the model
= 14,458 - 1,472age.Predict the price of an Escort that is 8 years old.

A)$11,776
B)$10
C)$26,234
D)$12,994
E)$2,682

Question 41

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model
= -3,000 + 176 wins.One team averaged 4,240 fans at each game.They won 57 times.Calculate the residual and explain what it means.

A)17,272 people.The team averaged 17,272 less fans than would be predicted for a team with 57 wins.
B)2,792 people.The team averaged 2792 more fans than would be predicted for a team with 57 wins.
C)-2,792 people.The team averaged 2792 less fans than would be predicted for a team with 57 wins.
D)4,223 people.On average the team will have 4,223 extra people.
E)7,032 people.The team were expected to average 7,032 people for each game.

Question 42

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model
= -2,600 + 225 wins.One team averaged 14,865 fans at each game and won 49 times.Calculate the residual for this team and explain what it means.

A)14,853 people.On average the team will have 14,853 extra people.
B)-6,440 people.The team averaged 6440 less fans than would be predicted for a team with 49 wins.
C)28,490 people.The team averaged 28,490 more fans than would be predicted for a team with 49 wins.
D)6,440 people.The team averaged 6440 more fans than would be predicted for a team with 49 wins.
E)8,425 people.The team were expected to average 8,425 people for each game.

Question 43

The relationship between the price of yachts (y)and their length (x)is analyzed.The mean length was 41 metres with a standard deviation of 11.The mean price was $84,000 with a standard deviation of 14,000.The correlation between the price and the length was 0.41.

A)

= 31,800 + 1,270 length
B)

= 70,800 + 0.000322 length
C)

= -962,000 + 547 length
D)

= -4,040,000 + 622 length
E)

= 62,605+ 522 length

Question 44

Two different tests are designed to measure employee productivity and dexterity.Several employees are randomly selected and tested with these results.

A)

= 2.36 + 2.03 Dexterity
B)

= 6.08 + 1.56 Dexterity
C)

= 75.3 - 0.329 Dexterity
D)

= 10.7 + 1.53 Dexterity
E)

= 5.05 + 1.91 Dexterity

Question 45

A golf ball was dropped from 8 different heights.The drop height and the bounce height were recorded.

A)

= 73 - .765 drop
B)

= -0.335 + 1.305 drop
C)

= 0.321 + .765 drop
D)

= 95 - 9.1 drop
E)

= 0.215 + .866 drop

Question 46

Ten Jeep Cherokee classified ads were selected.The age and prices of several used Ford Escorts are given in the table.

A)

= 7.05 -0.000319 age
B)

= -3110 + 22000 age
C)

= 21979 - 3108 age
D)

= 17200 - 891 age
E)

= 19000 - 3000 age

Question 47

The relationship between the number of games won by an NHL team (x)and the average attendance at their home games (y)is analyzed.The mean number of games won was 70 with a standard deviation of 16.The mean attendance was 6,993 with a standard deviation of 1,400.The correlation between the games won and attendance was 0.47.

A)

= 4114 + 41.125 wins
B)

= 2,360 + 66.1 wins
C)

= 6,990 + 0.00537 wins
D)

= 868 + 87.5 wins
E)

= -2,890 + 141 wins

Question 48

Managers rate employees according to job performance and attitude.The results for several randomly selected employees are given below.

A)

= 100.3 - 0.453 Attitude
B)

= 92.3 - 0.669 Attitude
C)

= 2.81 + 1.35 Attitude
D)

= -47.3 + 2.02 Attitude
E)

= 11.7 + 1.02 Attitude

Question 49

Ten students in a tutor program at Carleton University were randomly selected.Their grade point averages (GPAs)when they entered the program were less than 9.5.The following data were obtained regarding their GPAs on entering the program versus their current GPAs.

A)

= 0.711 + 0.346E
B)

= 0.873 + 0.627E
C)

= 2.51 + 0.529E
D)

= 1.54 + 0.8566E
E)

= 0.0065 + 0.879E

Question 50

A sociology student does a study to determine whether people who exercise live longer.He claims that someone who exercises 7 days a week will live 15 years longer than someone who doesn't exercise at all.

A)Predictions based on a regression line are for average values of x and y.The actual average life expectancy changes every year so an accurate prediction is impossible.
B)There is nothing wrong with the interpretation.
C)Predictions based on a regression line are for average values of y for a given x.The actual life expectancy will vary around the prediction.
D)The

Has to be greater than 90% to make a statement like this.
E)A linear model is inappropriate for sociology studies.

Question 51

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= 0.5 + 0.71 drop.A golf ball company is trying to show that its new ball will increase your driving distance.If the new ball is dropped from several heights would the company rather see positive or negative residuals.Explain.

A)Negative.The ball isn't bouncing as high as expected so you would more likely be able to hit it longer.
B)Positive.This would mean the ball is bouncing more than expected and you would more likely be able to hit it longer.
C)Positive.This would mean the ball is being dropped from higher distances so you would more likely be able to hit it longer.
D)Neither.The ball should bounce the same as expected otherwise it wasn't manufactured properly.
E)Negative.This would mean the ball is bouncing more than expected and you would more likely be able to hit it longer.

Question 52

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm. )The regression analysis gives the model
= -0.2 + 0.75 drop.A golf ball dropped from 61 cm bounced a height whose residual is -1.8 cm.What is the bounce height?

A)1.8 cm
B)59.45 cm
C)59.2 cm
D)47.35 cm
E)43.75 cm

Question 53

Ten Ford Escort classified ads were selected.The age and prices of several used Ford Escorts are given in the table.

A)

= 11291 - 1578 age
B)

= 7200 - 692 age
C)

= 7.05 -0.000616 age
D)

= -1580 + 11300 age
E)

= 10000 - 1600 age

Question 54

A biology student does a study to investigate the association between the amount of sunlight and the number of roses on a rosebush in one summer.(The
Value is 58%)He claims that the amount of sunlight determines 58% of the number of roses on a rosebush in one summer.

A)The

Has to be greater than 90% to make a statement like this.
B)The amount of sunlight accounts for 58% of the variation in the number of roses.It does not determine the number of roses.
C)The amount of sunlight will increase the number of roses 58% of the time.
D)The amount of variation in sunlight changes 58% of the time.This tells us nothing about the number of roses.
E)There is nothing wrong with the interpretation.

Question 55

A psychologist does an experiment to determine whether an outgoing person can be identified by his or her handwriting.She claims that the
Of 89% shows that this linear model is appropriate.

A)

Does not tell whether the model is appropriate,but measures the strength of the linear relationship.High

Could also be due to an outlier.
B)This

Means that 89% of the dependent values will fall within one standard deviation of the mean and tells nothing about the appropriateness of the model.
C)An

This high means there is a very weak linear association and the model is probably inappropriate.
D)

Does not tell whether the model is appropriate,but gives the percentage of data points that are close to the model.You can sometimes have a high

With a nonlinear relationship.
E)There is nothing wrong with the interpretation.

Question 56

The relationship between the cost of a taxi ride (y)and the length of the ride (x)is analyzed.The mean length was 4.6 km with a standard deviation of 1.1.The mean cost was $8.70 with a standard deviation of 2.0.The correlation between the cost and the length was 0.81.

A)

= 0.336 + 1.82 length
B)

= 1.93 + 1.47 length
C)

= -113 + 26.5 length
D)

= 6.65 + 0.446 length
E)

= -458 + 101 length

Question 57

Ten students in a graduate program at Carleton University were randomly selected.Their grade point averages (GPAs)when they entered the program were between 11.5 and 12.0.The following data were obtained regarding their GPAs on entering the program versus their current GPAs.

A)

= 10.51 + 0.329E
B)

=12.23 + 0.746E
C)

= 11.42 + 0.0312E
D)

= 13.81 + 0.497E
E)

= 12.91 + 0.0212E