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A school district is interested in effects of charter schools on standardized test scores (0-100). They run three studies: (Model 1) parents can choose to send students to Charter School, (Model 2) parents can choose to send students to Charter School but we also want to consider that the average income of the parents may be a factor, and (Model 3) a sample of students are randomly assigned (Experiment).

    Standardized Student Test Scores
    Model 1    Model 2    Model 3 (Experiment)
Intercept    75***
(10.2)    67***
(8.2)    83***
Charter School    12**
(2.5)    4
(6)    -7***
Average Parental Income    —    10**
(2)    —
R2    0.17    0.53    0.15
# of students    375    375    165
    Significance p<0.1*,'<0.05**,'<0.01***
– Charter School: 1 if student participated, 0 if they went to a public school
– Average Parental Income: 1 if >$100,000 (high income), 0 if <$100,000 (low income)

1.    What are the explanatory variables and outcome variables for each of the three models

2.    What is interpretation of intercept in each of the three models?

3.    What is the interpretation of the R-squared in each of the three models? Which model would be best based on the R-squared?

4.    In Model 2, what is the predicted student test score of a charter school student from a low-income family? Show all of your work.

5.    In Model 3 what is the Average Treatment Effect (ATE)? Construct a 95% confidence interval around the average treatment effect and interpret it. Show all of your work.

6.    Does the evidence presented in Models 1-3 support the effectiveness of charter schools in increasing student test scores? Why or why not?


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