The table shows the cumulative number of home runs hit by Luis Gonzalez up to th
ID: 3134800 • Letter: T
Question
The table shows the cumulative number of home runs hit by Luis Gonzalez up to the All-Star break in 2006.
1)
(a) Create a linear regression model for these data. (Round your coefficients to three decimal places.)
H(g) = ______________________
2) Choose the correct letter that corresponds to the practical and meaning of the problem above about the slope:
a) The slope means that on average Luis Gonzalez hit 0.053 home runs each game.
b) The slope means that on average Luis Gonzalez hit 0.094 home runs each game.
c) The slope means that on average Luis Gonzalez hit 0.52 home runs each game.
d) The slope means that on average Luis Gonzalez hit 0.201 home runs each game.
e) The slope means that on average Luis Gonzalez hit 0.162 home runs each game.
3) Choose the correct letter that corresponds to the practical and meaning of the problem above about the vertical intercept:
a) The vertical intercept means that at game 0 Luis Gonzalez had hit 3.297 home runs which is of course unreasonable.
b) The vertical intercept means that at game 0 Luis Gonzalez had hit 2.392 home runs which is of course unreasonable.
c) The vertical intercept means that at game 0 Luis Gonzalez had hit 1.791 home runs which is of course unreasonable.
d The vertical intercept means that at game 0 Luis Gonzalez had hit 2.695 home runs which is of course unreasonable.
e) The vertical intercept means that at game 0 Luis Gonzalez had hit 1.393 home runs which is of course unreasonable.
4)
(c) Use the linear regression model to predict the number of home runs hit by Luis Gonzalez by the 110th game of the season. (Round your answer to two decimal places.)
____________
5) Choose the correct letter:
Is this an example of interpolation or extrapolation?
a) interpolation
b) extrapolation
Explain. (choose the correct letter)
a) Because we are estimating a value inside the number of games values provided in the table of data.
b) Because we are estimating a value outside the number of games values provided in the table of data.
6)
(d) Use the linear regression model to predict the number of home runs hit by Luis Gonzalez by the final game of the season, game 162. (Round your answer to two decimal places.)
___________
7)Choose the correct letter:
Is this an example of interpolation or extrapolation?
a) interpolation
b) extrapolation
Explain. (choose the correct letter)
a) Because we are estimating a value inside the number of games values provided in the table of data.
b) Because we are estimating a value outside the number of games values provided in the table of data.
8) (choose the correct letter)
Based on the coefficient of determination, do you think the interpolation or extrapolation values you found are accurate?
a) The values are accurate.
b) The values are not very accurate.
GameNumber
g Cumulative
Number of Home
Runs Hit
H 4 1 5 2 12 3 13 4 16 5 76 6 87 7
Explanation / Answer
1) Y = 2.39 + 0.0529 X
Regression Analysis: Y versus X
The regression equation is
Y = 2.39 + 0.0529 X
2) Correct Answer: (a)
a) The slope means that on average Luis Gonzalez hit 0.053 home runs each game
3) Correct Answer : (b)
The vertical intercept means that at game 0 Luis Gonzalez had hit 2.392 home runs which is of course unreasonable.
4) The linear regression model to predict the number of home runs hit by Luis Gonzalez by the 110th game of the season is 8.209
since Y = 2.39 + 0.0529 X = 2.39 + 0.0529(110) = 8.209
5) Correct Answer b) extrapolation
Since 110 is not in the Game number and it is out side from our data
Correct Answer: b) Because we are estimating a value outside the number of games values provided in the table of data.
6) The linear regression model to predict the number of home runs hit by Luis Gonzalez by the final game of the season, game 162 is 10.9598
since Y = 2.39 + 0.0529 X = 2.39 + 0.0529(162) = 10.9598
7) Correct Answer b) extrapolation
Since 162 is not in the Game number and it is out side from our data
Correct answer (b)
b) Because we are estimating a value outside the number of games values provided in the table of data
8) Correct Answer: (a)
a) The values are accurate
rxy = 0.863475 and Coeffecient of determination r2xy = 0.745589
It is high correlation between the two variables. Therefore The values are accurate.
Game Cumulative Number Number of Home g Runs Hit H X Y X^2 Y^2 XY 4 1 16 1 4 5 2 25 4 10 12 3 144 9 36 13 4 169 16 52 16 5 256 25 80 76 6 5776 36 456 87 7 7569 49 609 Total: 213 28 13955 140 1247Related Questions
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