Use the data in BENEFITS to answer this question. It is a school-level data set at the K–5 level on average teacher salary and benefits. See Example 4.10 for background.

(i) Regress lavgsal on bs and report the results in the usual form. Can you reject

H₀: β_bs = 0 against a two-sided alternative? Can you reject H₀: β_bs = – 1 against

H₁: β_bs > – 1? Report the p-values for both tests.

(ii) Define lbs = log(bs). Find the range of values for lbs and find its standard deviation.

How do these compare to the range and standard deviation for bs?

(iii) Regress lavgsal on lbs. Does this fit better than the regression from part (i)?

(iv) Estimate the equation

lavgsal = β₀ + β₁bs + β₂ lenroll + β₃lstaff + β₄lunch + u

and report the results in the usual form. What happens to the coefficient on bs? Is it now statistically different from zero?

(v) Interpret the coefficient on lstaff. Why do you think it is negative?

(vi) Add lunch² to the equation from part (iv). Is it statistically significant? Compute the turning point (minimum value) in the quadratic, and show that it is within the range of the observed data on lunch. How many values of lunch are higher than the calculated turning point?

(vii) Based on the findings from part (vi), describe how teacher salaries relate to school poverty rates.

In terms of teacher salary, and holding other factors fixed, is it better to teach at a school with lunch = 0 (no poverty), lunch = 50, or lunch = 100 (all kids eligible for the free lunch program)?