Question

Governor Brown charges you to study whether or not the use of computers in the classroom for elementary school students improves academic performance in California.

(a) The office of Governor Brown provides you with data on district-level average test scores and on the fraction of schools in each district that use computers in the classroom. Based on these data, describe the regression model you would use to measure the effectiveness of computers in the classroom. Make sure to explain how to interpret each regression coefficient.

(b) Explain why the data and regression model in (a) may not be informative about the causal effect of computers on student achievement.

(c) Describe an identification strategy that could be successful to measure the causal effect of computers on student achievement. What assumption(s) associated with the identification strategy would be necessary?

This is a purely qualitative question..

Answer 1

a) The appropriate regression equation we'll like to use is

y=a+bx where

y= district level average test scores (response)

x=amount of computer usage(predictor)

a=constant

b=regression coefficient which represents the mean change in the response given a one unit change in the predictor.

The sign of each coefficient indicates the direction of the relationship between a predictor variable and the response variable. A positive sign indicates that as the predictor variable increases, the response variable also increases. (there is a positive effect of computer usage on the test scores). A negative sign indicates that as the predictor variable increases, the response variable decreases. (the effect is negative)

b) The reason on why the above regression model is not completely informative is, the data consists of the fraction of schools in each district that use computers in the classroom. But only the fraction will not help in providing the required result. It should be amount of computer usage(x) corresponding to each average test score of the district(y).

c) IDENTIFICATION STRATEGY : We would analyse the data in two ways for this purpose. First, we'd choose a sample of schools of the district and provide equal amount of computers for the learning purpose to each of the school. Then we'd build a regression model as described in part (a) and test for the effect.

Next, we'd restrict the use of computer in the same schools and allow learning only by classroom teaching. Hence build a regression model where response variable is same but predictor variable will be extent of classroom teaching. Then we'll test for the same.

Finally, by observing the difference in the test scores in both the cases, we'll draw valid inferences regarding the effect of computer usuage on teaching.

ASSUMPTIONS :

1) There will be no effect of other study methods or courses a student may opt during the learning process. Only effect of computer usage is the concern here.

2) Both analysis should be conducted on the same schools so that the IQ difference of students does not affect the result.