Suppose that there is a linear relationship between the number of students x in

Question

Suppose that there is a linear relationship between the number of students x in a school system and the annual budget y. Write a population regression model to describe this relationship.

mu hat = b0 + b1xi

yi = 0 + 1xi

yi = 0 + 1xi + 2xi + i

y = b0 + b1xi + i

yi = 0 + 1xi + i

(a) Which parameter in your model is the fixed cost in the budget (for example, the salary of the principals and some administrative costs) that does not change as x increases?

1

b1     

i

0

b0

(b) Which parameter in your model shows how total cost changes when there are more students in the system?

b0

i     

b1

0

1

Do you expect this number to be greater than 0 or less than 0?

greater than 0

less than 0     

(c) Actual data from various school systems will not fit a straight line exactly. What term in your model allows variation among schools of the same size x?

i

0     

1

b0

b1

Explanation / Answer

Suppose that there is a linear relationship between the number of students x in a school system and the annual budget y. Write a population regression model to describe this relationship.

yi = 0 + 1xi + i

(a) Which parameter in your model is the fixed cost in the budget (for example, the salary of the principals and some administrative costs) that does not change as x increases?

0

(b) Which parameter in your model shows how total cost changes when there are more students in the system?

1

Do you expect this number to be greater than 0 or less than 0?

greater than 0

(c) Actual data from various school systems will not fit a straight line exactly. What term in your model allows variation among schools of the same size x?

i

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