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What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 8 randomly selected games are shown below.   Attendance 14 44 21 13 22 43 38 16 Runs 5 13 9 8 8 13 9 6   Find the correlation coefficient:  r=r=    Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? ρ μ r  == 0 H1:H1: ? μ ρ r   ≠≠ 0     The p-value is:    (Round to four decimal places) Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.  r2r2 =  (Round to two decimal places)  (Round to two decimal places)  Interpret r2r2 :   Given any fixed attendance, 78% of all of those games will have the predicted number of runs scored. There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 78%. There is a 78% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game. 78% of all games will have the average number of runs scored.   The equation of the linear regression line is:    ˆyy^ =  + xx   (Please show your answers to two decimal places)     Use the model to predict the runs scored at a game that has an attendance of 21,000 people. Runs scored =  (Please round your answer to the nearest whole number.)       Interpret the slope of the regression line in the context of the question:   For every additional thousand people who attend a game, there tends to be an average increase of 0.19 runs scored. The slope has no practical meaning since the total number runs scored in a game must be positive. As x goes up, y goes up. Interpret the y-intercept in the context of the question: The best prediction for a game with 0 attendance is that there will be 4 runs scored. If the attendance of a baseball game is 0, then 4 runs will be scored. The average runs scored is predicted to be 4. The y-intercept has no practical meaning for this study.

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 8 randomly selected games are shown below.   Attendance 14 44 21 13 22 43 38 16 Runs 5 13 9 8 8 13 9 6   Find the correlation coefficient:  r=r=    Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? ρ μ r  == 0 H1:H1: ? μ ρ r   ≠≠ 0     The p-value is:    (Round to four decimal places) Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.  r2r2 =  (Round to two decimal places)  (Round to two decimal places)  Interpret r2r2 :   Given any fixed attendance, 78% of all of those games will have the predicted number of runs scored. There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 78%. There is a 78% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game. 78% of all games will have the average number of runs scored.   The equation of the linear regression line is:    ˆyy^ =  + xx   (Please show your answers to two decimal places)     Use the model to predict the runs scored at a game that has an attendance of 21,000 people. Runs scored =  (Please round your answer to the nearest whole number.)       Interpret the slope of the regression line in the context of the question:   For every additional thousand people who attend a game, there tends to be an average increase of 0.19 runs scored. The slope has no practical meaning since the total number runs scored in a game must be positive. As x goes up, y goes up. Interpret the y-intercept in the context of the question: The best prediction for a game with 0 attendance is that there will be 4 runs scored. If the attendance of a baseball game is 0, then 4 runs will be scored. The average runs scored is predicted to be 4. The y-intercept has no practical meaning for this study.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2BGP
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What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 8 randomly selected games are shown below.

 

Attendance 14 44 21 13 22 43 38 16
Runs 5 13 9 8 8 13 9 6

 

Find the correlation coefficient:  r=r=    Round to 2 decimal places.

The null and alternative hypotheses for correlation are:
H0:H0: ? ρ μ r  == 0
H1:H1: ? μ ρ r   ≠≠ 0    
The p-value is:    (Round to four decimal places)

Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.

  • There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance.
  • There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance.
  • There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful.
  • There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.

 r2r2 =  (Round to two decimal places)  (Round to two decimal places)

 Interpret r2r2 :  

  • Given any fixed attendance, 78% of all of those games will have the predicted number of runs scored.
  • There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 78%.
  • There is a 78% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game.
  • 78% of all games will have the average number of runs scored.

 

The equation of the linear regression line is:   
ˆyy^ =  + xx   (Please show your answers to two decimal places)  

 

Use the model to predict the runs scored at a game that has an attendance of 21,000 people.
Runs scored =  (Please round your answer to the nearest whole number.)  

 

 

Interpret the slope of the regression line in the context of the question:  

  • For every additional thousand people who attend a game, there tends to be an average increase of 0.19 runs scored.
  • The slope has no practical meaning since the total number runs scored in a game must be positive.
  • As x goes up, y goes up.


Interpret the y-intercept in the context of the question:

  • The best prediction for a game with 0 attendance is that there will be 4 runs scored.
  • If the attendance of a baseball game is 0, then 4 runs will be scored.
  • The average runs scored is predicted to be 4.
  • The y-intercept has no practical meaning for this study.

 

 

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