Suppose you have developed a regression model to explain the relationship between y and x 1 , x 2 , and x 3 . The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x 1 ≤ 55, .5 ≤ x 2 ≤ 1, and 1,000 ≤ x 3 ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x 1 = 30, x 2 = .6, and x 3 = 1,300, or when x 1 = 60, x 2 = .4, and x 3 = 900? Why?

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Answer 1

Textbook Question

Chapter 12, Problem 12.134LM

Suppose you have developed a regression model to explain the relationship between y and x₁, x₂, and x₃. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x₁ ≤ 55, .5 ≤ x₂ ≤ 1, and 1,000 ≤ x₃ ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x₁ = 30, x₂ = .6, and x₃ = 1,300, or when x₁ = 60, x₂ = .4, and x₃ = 900? Why?

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

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Answer 2

Textbook Question

Chapter 12, Problem 12.134LM

Suppose you have developed a regression model to explain the relationship between y and x₁, x₂, and x₃. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x₁ ≤ 55, .5 ≤ x₂ ≤ 1, and 1,000 ≤ x₃ ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x₁ = 30, x₂ = .6, and x₃ = 1,300, or when x₁ = 60, x₂ = .4, and x₃ = 900? Why?

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

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Answer 3

Textbook Question

Chapter 12, Problem 12.134LM

Suppose you have developed a regression model to explain the relationship between y and x₁, x₂, and x₃. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x₁ ≤ 55, .5 ≤ x₂ ≤ 1, and 1,000 ≤ x₃ ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x₁ = 30, x₂ = .6, and x₃ = 1,300, or when x₁ = 60, x₂ = .4, and x₃ = 900? Why?

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

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Answer 4

Textbook Question

Chapter 12, Problem 12.134LM

Suppose you have developed a regression model to explain the relationship between y and x₁, x₂, and x₃. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5 ≤ x₁ ≤ 55, .5 ≤ x₂ ≤ 1, and 1,000 ≤ x₃ ≤ 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x₁ = 30, x₂ = .6, and x₃ = 1,300, or when x₁ = 60, x₂ = .4, and x₃ = 900? Why?

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Answer 8

Expert Solution & Answer

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

For which set of values the error of prediction would be small for predicting y using the least squares regression equation.

Answer 12

Answer to Problem 12.134LM

The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Answer 13

Explanation of Solution

Given info: The independent variables in the study are x1,x2 and x3 . The ranges for each of the independent variables are 5≤x1≤55 , 0.5≤x2≤1 and 1,000≤x3≤2,000 . The response variable in the regression model is y, the range of y is 10≤y≤100 . The two set of values mentioned are x1=30,x2=0.6 and x3=1,300 , x1=60,x2=0.4 and x3=900

Justification:

When the values of the independent variables in the study are closer or equal to the values of sample means then the error of prediction would be small and if the values of the independent variables in the study are further to the values of sample means then the error of prediction would be large.

The independent variables are x1,x2 and x3 . Consider the values x1=60,x2=0.4 and x3=900 , it can be observed that all the values of the independent variables x1,x2 and x3 are not within the range of the variables; this implies that the values x1=60,x2=0.4 and x3=900 would be far away from the value of sample means. Hence, the error of prediction would be large.

Consider the values x1=30,x2=0.6 and x3=1,300 , it can be observed that all the values of the independent variables x1,x2 and x3 are within the range of the variables this implies that the values x1=30,x2=0.6 and x3=1,300 would be closer from the value of sample means. Hence, the error of prediction would be less.

Thus, The error of prediction would be small for predicting y using the least squares regression equation for the values x1=30,x2=0.6,x3=1,300 .

Answer 14

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Answer to Problem 12.134LM

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