Submitted By fina03032015
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Q1.
(a) Degree of freedom = n – k – 1 = 33 – 3 – 1 = 29
Critical t score c0.025 = 2.045
95% CI for F = 733 2.045 * 253 = 215.615 to 1250.385
This is statistically significant at 5% since the interval does not include 0.
(Check: computed t = 733/253 = 2.89 > 2.045) 95% CI for S = -.805 2.045 * .752 = -2.34284 to .73284
This is NOT statistically significant at 5% since the interval includes 0.
(Check: computed t = -.805/.752 = - 1.07048 > - 2.045)
95% CI for A = 74 2.045 * 12.4 = 48.642 to 99.358
This is statistically significant at 5% since the interval does not include 0.
(Check: computed t = 74/12.4 = 5.968 > 2.045)
(b)
All three estimates are expected to be positive. The fact that one of them has the wrong sign (βS) may reflect negative omitted variable bias. Multicollinearity obviously is a problem and may be responsible for the wrong sign of βS too. Variable S looks irrelevant but it should be relevant in theory. Its small t-stat may be due to omitted variable or multicollinearity.
Q2. Using the intuition from simple case of omitted variable:
(a) y = apple consumption, x1 = price of banana, x2 = price of orange yt = 0 + 1 x1,t + 2 x2,t + ut
If we leave out x2, bias on β1 depends on (1) whether x1 and x2 are correlated in the sample which mostly likely is positive (e.g. inflation), and whether price of orange has positive or negative effect on the annual consumption of apple in the population (sign of 2) which should be positive too (law of demand).
Bias is (+) (+) = (+)

(b) y = student grades on the midterm, x1 = hours studies for the midterm x2 = hours slept before the midterm If we leave out x2, bias on β1 depends on (1) whether x1 and x2 are correlated in the sample which mostly likely is negative, and (2) whether hours slept before the midterm has positive or negative effect on the midterm grade in...

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