1. Teacher Salaries and School Characteristics (Computer Exercise), 

(i) Download the dataset benefits4.dta and report the sample mean, minimum and maximum values for each variable.

(ii) Estimate the equation lavgsal = β₀+ β₁bs + u                      (1)

by OLS and report the results in the usual form.

(iii) Test H₀ : β₁ = -1 against H₁ : β₁ > -1 using a 5% significance level.

(iv) Estimate the equation:

lavgsal = β₀ + β₁bs +β₂lenroll + β₃lstaff + β₄poor + u

and report the results in the usual form. What happens to the coefficient on bs when the additional explanatory variables are added to the model? Is β₁ statistically different from zero (against a two-sided alternative) at the 5% level of significance?

(v) What is the interpretation of the coefficient on lstaf f ? Why do you think it is negative?

(vi) From the model in (iv), obtain the predicted lavgsal when bs = 0.34, lenroll = 5.93, lstaf f = 4.32 and poor = 36. Run a regression which allows you to put a 90% confidence interval around the predicted value (this is a 'conditional' or 'within sample' prediction). Report the confidence interval.

(vii) Now consider a prediction for an individual. Construct the 90% confidence interval for the predicted lavgsal for an individual teacher when bs = 0.34, lenroll = 5.93, lstaf f = 4.32 and poor = 36 (this is an 'unconditional' prediction). Comment on the width of this confidence interval compared to that in (vi).

(viii) Add poor² to the model in (iv). Compute the turning point in the quadratic, and show that this point lies in the observed data for poor. How many observations have poor higher than the calculated turning point?

(ix) Based on your findings from part (viii) describe how teacher salaries relate to school poverty rates. In terms of teacher salary, and holding other factors constant, is it better to teach at a school with poverty = 0, poverty = 50 or poverty = 100? Explain.

(x) Does the model in (viii) provide a good explanation of lavgsal? Does the model capture causal effects? Explain your reasoning.

Note: The benefit4.dta data set can be downloaded from the unit Blackboard website. This file has 901 observations and 5 variables. The variables correspond to:

1. lavgsal (log( average teacher salary)),

2. bs (average benefits / average salary for the school),

3. lenroll (log(total student enrollment)),

4. lstaf f (log(staff / 1000 students),

5. poor (percent of the student population from low socio-economic backgrounds).