Question

Suppose SAT score and high school graduating class size (hsize, scaled in terms of 100 students) are correlated and the unobserved factors denoted by u. Then SAT = B + Bhsize+u. ss df - • reg sat hsize Source Model 324242.826 Residual 1 80049603.5 Total 1 80373846.3 1 4.135 MS 324242.826 19359.0335 19432.7481 Number of obs F(1, 4135) Prob > F R-squared Adj R-squared Root MSE 4.137 16.75 0.0000 4,136 0.0038 139.14 sat hsize _cons Coef. 5.098593 1016.056 Std. Err. 1.245825 4.104317 t ? 247.56 P>It 0.000 0.000 [95% Conf. Interval] 2.656106 7.541079 1008.01 1024.103 i) Interpret the coefficient on hsize. What kinds of factors are possibly contained in u? Would you expect the model to satisfy the assumption that E(uhsize) = 0? Why? iii) =0 at 5% significance level? What is the t-statistic for Can you reject H, : this null? What is R, in other words, how much variation in SAT for these 4137 students is explained by hsize? Is this big or small?

Answer 1

i) the coefficient of size means how much change in SAT score is caused by one unit change in hszie(high school graduating class size). here it means if graduating class size goes up by 100, the SAT score goes up by the value of the coefficient of hsize.

ii) the term u may contain effects of all the other factors which are influencing SAT scores other than the high school graduating class size. some of them may be:

1. how many hours one student studies per day on average

2. how motivated the students are

3. what are the ambitions of the students

4. how much of the students are actually appearing for SAT.

Yes. E(u|hsize) is expected to be zero. for simplicity, we are taking only one factor 2. how motivated the students are. some students may be more motivated and some of them may be less motivated. hence overall effect of motivation may comes to zero.

iii) the t score is cofficient/standard error=5.098593/1.245825=4.092543495

we reject the null hypothesis that beta1=0 as the probability of the score is 0.000 which is less than 5%.

iv) the R² here is 1-model SS/total SS=1-324242.826/80373846.3=0.996

hence R² is big.

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