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.

(a) Write a population regression model to describe this relationship.

(b) 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?

(c) Which parameter in your model shows how total cost changes when there are more students in the system? Do you expect this number to be greater than 0 or less than 0?

(d) 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?

Explanation / Answer

a)

y=b0+b1x

Annual Budget=b0+b1*Number of Students

b)

Here, b0 would represent the fixed cost in the budget

c)

Here, b1 would represent the parameter that would make the total cost to change i.e. total cost would change as more number of students are added. This number should ideally be greater than 0.

d)

Ideally for a good model, there should be no multicollinearity and there should be homoscedasticity. If all of the data given fits the above two assumptions, it should be considered a good regression model.

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