ECO 321HW3.docx - ECO 321 Chengruiwu ID 111327724 2.（a,b） b0=1229.3033(c b1=14.1423 ^ β 1 0 captures the average value of AHE for students in

# ECO 321HW3.docx - ECO 321 Chengruiwu ID 111327724...

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2. a,b b0=1229.3033 b1=14.1423 (c) ^ β 1 0 captures the average value of AHE for students in sample. (d) It appears from the results of the regression that small classes do indeed improve test scores, as the coefficient is positive. The estimated regression coefficient says that, on average, the test score of a small class is 14.1423points larger than the the test score of a regular class. From the date set, the mean is 1233.882 the results of our regression imply that regular classes are on average below the mean and small classes are on average above the mean, since  Unformatted text preview: the average score for small classes is equal to 1229.3033+14.1423=1243.4456. However, notice that, if the true standard deviation of test scores is 73.00992 points, the mean score of small and regular classes is not significantly different from the mean of1233.882. (e) t = β 1 ^ ¿ ¿ SE ¿ β 1 ¿ = 14.1423 2.6 = 5.4 with is larger than Z 1 − α / 2 = z 0.975 = 1:96 . Therefore, the effect is significant at the 5% level. (f) CI ( β 1 ) = β 1 ^ ¿¿ +-SE β 1 ( ¿ ) Z 1 − α / 2 ^ ¿ CI ( β 1 ) = 14.1423+_2.6*1.6= (18.3023,9.98)...
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