Daily 13 - Mar 04

Class Performance

Students: 91 | Mean: 3.71 | Median: 4 | SD: 0.60

Scores ranged from 0 to 4 out of 4 points.

Correct Answer

The unconditional expectation of y is a constant, while the conditional expectation of y given x is a function of x.

Common Errors

Writing “function” for the first blank — Several students wrote “function” instead of “constant.” The unconditional expectation E[Y] is a single number (constant), not a function.
Using notation instead of key terms — Some students wrote E(Y) and E(Y|X) rather than stating “constant” and “x.” The question asks what these objects are, not their notation.
Unclear or swapped blanks — A few students wrote vague letters (N, M) or provided the same answer for both blanks without distinguishing constant from function of x.

Correct Answer

The average return to another year of schooling is 5.2 (equivalently 5.21%, 0.0521, or 0.052).

Common Errors

Providing a formula instead of a number — One student wrote a fraction expression rather than the numeric value from Figure 6.
No widespread errors — The vast majority of students correctly identified the 5.2% return from Figure 6. This was the strongest question overall.
Rounding differences — Some students wrote 5.2, others 5.21 or 5.21%. All equivalent representations were accepted.

Correct Answer

The estimated return to schooling is statistically significant at the 5% level.

Common Errors

No common errors — Nearly all students correctly identified “is” as the answer. This was the highest-scoring question.
Elaborating beyond the answer — Some students added extra context (e.g., “yes, both are significant”). As long as “is” was clearly indicated, full credit was awarded.

Correct Answer

The population regression coefficients minimize the MSE (mean squared error) between the outcome and the regression approximation.

Common Errors

Writing “mean standard error” — One student confused “squared” with “standard.” MSE stands for mean squared error, not mean standard error.
Writing incorrect abbreviations — A few students wrote abbreviations that did not match MSE, likely due to handwriting confusion or misremembering the term.
Writing “measurement square error” — One student used the wrong first word. The correct term is specifically “mean squared error.”

Strengths: Return to schooling (5.2%) identified correctly | Statistical significance well understood | MSE widely known.

Review:

Unconditional expectation is a constant, conditional expectation is a function of x — know the distinction
MSE = mean squared error — not “mean standard error” or other variations
State the concept, not just the notation — writing E(Y) doesn’t convey “constant”; say what it is