Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
8th Edition
ISBN: 9781464158933
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 10, Problem 24E
To determine

To explain: The population regression model.

Expert Solution
Check Mark

Answer to Problem 24E

Solution: The regression model is y=β0+β1x+ε_.

Explanation of Solution

According to the question, response is the Annual budget and explanatory variable is the number of students. The regression model which represents the linear relationship can be written as:

y=β0+β1x+ε

Where y represents the annual budget, x represents the number of students and β0+β1x represents the average response.

(a)

To determine

To explain: The fixed parameter of the model.

(a)

Expert Solution
Check Mark

Answer to Problem 24E

Solution: The fixed parameter is β0_.

Explanation of Solution

The intercept does not change with the change in explanatory variable. That is why it can be considered as the fixed parameter of the regression model.

(b)

To determine

To explain: The changing parameter of the model.

(b)

Expert Solution
Check Mark

Answer to Problem 24E

Solution: The required parameter is β1_.

Explanation of Solution

The slope tells the amount of change in annual budget when the number of students increases. That is why it can be considered as the changing parameter of the regression model.

To determine

To explain: Whether it is expected to be a number greater than 0 or less than 0.

Expert Solution
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Answer to Problem 24E

Solution: Yes, it is greater than 0.

Explanation of Solution

The slope tells the amount of change in annual budget when the number of students increases. The number will be greater than zero.

(c)

To determine

To explain: The variation among schools of same size x.

(c)

Expert Solution
Check Mark

Answer to Problem 24E

Solution: The required term is ε_.

Explanation of Solution

The term ε is known as the error term of the model. The error term allows the unaccounted variations in the model when the explanatory variables are constant. That is why it represents the variation among schools of same size x.

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