Chapter 10, Problem 24E

To determine

To explain: The population regression model.

Answer to Problem 24E

Solution: The regression model is $\underset{\_}{y={\beta }_0+{\beta }_{1}x+\epsilon }$.

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:

$y={\beta }_0+{\beta }_{1}x+\epsilon$

Where y represents the annual budget, x represents the number of students and ${\beta }_0+{\beta }_{1}x$ represents the average response.

(a)

To determine

To explain: The fixed parameter of the model.

Answer to Problem 24E

Solution: The fixed parameter is $\underset{\_}{{\beta }_0}$.

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.

Answer to Problem 24E

Solution: The required parameter is $\underset{\_}{{\beta }_1}$.

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.

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 $x$.

Answer to Problem 24E

Solution: The required term is $\underset{\_}{\epsilon }$.

Explanation of Solution

The term $\epsilon$ 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 $x$.