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.

yi = 0 + 1xi

yi = 0 + 1xi + 2xi + 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?

1b1    ib00

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

b1b0    01i

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

greater than 0less 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?

01    ib0b1

Explanation / Answer

The regression model is, yi = 0 + 1xi + i

(a)0, this is y-intercept and it is the fixed cost in the budget that does not change as x increases.

(b) 1, the model shows how cost changes when there are more students in the system.

Budget has to be positive, so the number to be greater than 0.

(c) i, indicates for variations among schools of the same size x.

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