$\begin{array}{c|c|c|c|c|c} \overline{\mathrm{x}} & \mathrm{s}_{\mathrm{x}} & \overline{\mathrm{y}} & \mathrm{s}_{\mathrm{y}} & \mathrm{r} & \hat{\mathrm{y}}=\mathrm{b}_{0}+\mathrm{b}_{1 \mathrm{x}} \\ \hline 10 & 5 & ? & ? & -0.8 & \hat{\mathrm{y}}=200-2 \mathrm{x} \end{array}$

A) $\overline{y}$ = 220; $s _ { y }$ = 12.50 B) $\overline{y}$ = 190; $s _ { y }$ = 0.32 C) $\overline{y}$ = 210; $s _ { y }$ = 6 D) $\overline{y}$ = 180; $s _ { y }$ = 12.50 E) $\overline{y}$ = 20; $s _ { y }$ = 2.50 A) $\overline{y}$ = 220; $s _ { y }$ = 12.50 B) $\overline{y}$ = 190; $s _ { y }$ = 0.32 C) $\overline{y}$ = 210; $s _ { y }$ = 6 D) $\overline{y}$ = 180; $s _ { y }$ = 12.50 E) $\overline{y}$ = 20; $s _ { y }$ = 2.50

A golf ball was dropped from 8 different heights.The drop height and the bounce height were recorded. \[\begin{array} { c c } \text { Drop Height } ( \mathrm { cm } ) & \text { Bounce Height } ( \mathrm { cm } ) \\ 96 & 73 \\ 84 & 65 \\ 72 & 55 \\ 60 & 46 \\ 48 & 38 \\ 36 & 29 \\ 24 & 19 \\ 12 & 8 \end{array}\]

A) $\hat{\text { bounce }}$ = 73 - .765 drop B) $\hat{\text { bounce} }$ = -0.335 + 1.305 drop C) $\hat{\text { bounce} }$ = 0.321 + .765 drop D) $\hat{\text { bounce} }$ = 95 - 9.1 drop E) $\hat{\text { bounce} }$ = 0.215 + .866 drop A) $\hat{\text { bounce }}$ = 73 - .765 drop B) $\hat{\text { bounce} }$ = -0.335 + 1.305 drop C) $\hat{\text { bounce} }$ = 0.321 + .765 drop D) $\hat{\text { bounce} }$ = 95 - 9.1 drop E) $\hat{\text { bounce} }$ = 0.215 + .866 drop

\[\begin{array} { c | c | c | c | c | l } \overline { \mathrm { x } } & \mathrm { s } _ { \mathrm { x } } & \overline { \mathrm { y } } & \mathrm { s } _ { \mathrm { y } } & \mathrm { r } & \hat { \mathrm { y } } = \mathrm { b } _ { 0 } + \mathrm { b } _ { 1 \mathrm { x } } \\ \hline 3.0 & 1.2 & ? & 120 & ? & \hat { \mathrm { y } } = - 120 + 60 \mathrm { x } \end{array}\]

A) $\overline{y}$ = 60; r = 0.60 B) $\overline{y}$ = 180; r = -0.60 C) $\overline{y}$ = -117; r = 0.50 D) $\overline{y}$ = -48; r = 0.03 E) $\overline{y}$ = -300; r = 0.50 A) $\overline{y}$ = 60; r = 0.60 B) $\overline{y}$ = 180; r = -0.60 C) $\overline{y}$ = -117; r = 0.50 D) $\overline{y}$ = -48; r = 0.03 E) $\overline{y}$ = -300; r = 0.50

Exam 7: Linear Regression

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 $\hat{\text { bounce }} = - 0.2 + 0.75$ drop.A golf ball dropped from 61 cm bounced a height whose residual is -1.8 cm.What is the bounce height?

(Multiple Choice)

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Question 41

A forester would like to know how big a maple tree might be at age 50 years.She gathers data from some trees that have been cut down,and plots the diameters (in inches)of the trees against their ages (in years).First she makes a linear model.The scatterplot and residuals plot are shown.Do you think the linear model is appropriate? Explain.

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Question 42

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?

(Multiple Choice)

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Question 43

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.

(Multiple Choice)

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Question 44

When checking the "Straight Enough" condition,which is the best graph to look at?

(Multiple Choice)

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Question 45

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.

(Multiple Choice)

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Question 46

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 $\hat{\text { attendance }} = - 2100 + 187$ wins.Predict the average attendance of a team with 400 wins.Explain any possible problems with this prediction.

(Multiple Choice)

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Question 47

=+ 10 5 ? ? -0.8 =200-2

(Multiple Choice)

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Question 48

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 $\mathrm { R } ^ { 2 } = 18.3 \%$ What is correlation between length and price?

(Multiple Choice)

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Question 49

A golf ball was dropped from 8 different heights.The drop height and the bounce height were recorded. Drop Height () Bounce Height () 96 73 84 65 72 55 60 46 48 38 36 29 24 19 12 8

(Multiple Choice)

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Question 50

=+ 3.0 1.2 ? 120 ? =-120+60

(Multiple Choice)

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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 $\hat{\text { bounce }} = 0.3 + 0.74$ drop.A golf ball dropped from 61 cm bounced 46.44 cm.What is the residual for this bounce height?

(Multiple Choice)

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Question 52

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 $\hat{\text { attendance }} = - 2600 + 225$ 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.

(Multiple Choice)

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Question 53

(Multiple Choice)

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Question 54

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 $\mathrm { r } = 0.79$ Interpret this statistic.

(Multiple Choice)

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Question 55

If the linear correlation between shoe size and height is 0.758 and Dave is 2 standard deviations above the mean in shoe size,what would you predict is Dave's height with respect to the mean height?

(Multiple Choice)

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Question 56

Doctors studying how the human body assimilates medication inject some patients with penicillin,and then monitor the concentration of the drug (in units/cc)in the patients' blood for seven hours.First they tried to fit a linear model.The regression analysis and residuals plot are shown.Is that estimate likely to be accurate,too low,or too high? Explain. Dependent variable is: Concentration No Selector R squared $= 90.8 \% \quad$ R squared (adjusted) $= 90.6 \%$ $s = 3.472$ with $43 - 2 = 41$ degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 4900.55 1 4900.55 407 Residual 494.199 41 12.0536 Variable Coefficient s.e. of Coeff t-ratio prob Constant 40.3266 1.295 31.1 S 0.0001 Time -5.95956 0.2956 -20.2 S 0.0001 $Doctors studying how the human body assimilates medication inject some patients with penicillin,and then monitor the concentration of the drug (in units/cc)in the patients' blood for seven hours.First they tried to fit a linear model.The regression analysis and residuals plot are shown.Is that estimate likely to be accurate,too low,or too high? Explain. Dependent variable is: Concentration No Selector R squared = 90.8 \% \quad R squared (adjusted) = 90.6 \% s = 3.472 with 43 - 2 = 41 degrees of freedom \begin{array} { l l r r r } \text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } & 4900.55 & 1 & 4900.55 & 407 \\ \text { Residual } & 494.199 & 41 & 12.0536 & \end{array} \begin{array} { l l l r l } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Constant } & 40.3266 & 1.295 & 31.1 & \text { S } 0.0001 \\ \text { Time } & - 5.95956 & 0.2956 & - 20.2 & \text { S } 0.0001 \end{array}$

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Question 57

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 6993 with a standard deviation of 1400.The correlation between the games won and attendance was 0.47.

(Multiple Choice)

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Question 58

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 $\hat{\text { bounce }} = - 0.1 + 0.70$ drop.Predict the height of the bounce if dropped from 64 cm.

(Multiple Choice)

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Question 59

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 $\mathrm { R } ^ { 2 }$ = 19.00%.What would you predict about the price of the yacht whose length was one standard deviation above the mean?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 71

Exam 7: Linear Regression

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 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.

When checking the "Straight Enough" condition,which is the best graph to look at?

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.

=+ 10 5 ? ? -0.8 =200-2

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 R2=18.3%\mathrm { R } ^ { 2 } = 18.3 \%R2=18.3% What is correlation between length and price?

A golf ball was dropped from 8 different heights.The drop height and the bounce height were recorded. Drop Height () Bounce Height () 96 73 84 65 72 55 60 46 48 38 36 29 24 19 12 8

=+ 3.0 1.2 ? 120 ? =-120+60

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\mathrm { r } = 0.79r=0.79 Interpret this statistic.

If the linear correlation between shoe size and height is 0.758 and Dave is 2 standard deviations above the mean in shoe size,what would you predict is Dave's height with respect to the mean height?

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 bounce ^=−0.1+0.70\hat{\text { bounce }} = - 0.1 + 0.70 bounce ^=−0.1+0.70 drop.Predict the height of the bounce if dropped from 64 cm.

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 R2\mathrm { R } ^ { 2 }R2 = 19.00%.What would you predict about the price of the yacht whose length was one standard deviation above the mean?

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

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 $\mathrm { R } ^ { 2 } = 18.3 \%$ What is correlation between length and price?

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 $\mathrm { r } = 0.79$ Interpret this statistic.

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 $\hat{\text { bounce }} = - 0.1 + 0.70$ drop.Predict the height of the bounce if dropped from 64 cm.

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 $\mathrm { R } ^ { 2 }$ = 19.00%.What would you predict about the price of the yacht whose length was one standard deviation above the mean?