So I've been looking at this homework for hours and cannot figure it out. Any help would be appreciated! When is the rule of thumb for significance, t > 2 , be precisely the same as a formal test for significance at the 95% confidence level? (For what sample size?) 2. Suppose that β1 = 10 with a standard error of 4. What is the probability that the estimated effect ˆ β1 is negative? 3. Suppose that β1 = 13 with a standard error of 10. What is the probability that the estimated effect ˆ β1 appears statistically significant? 4. Suppose that a regression produces ˆ β = 0.57 with a standard error of 6.97. Would these results be unusual if the true β = 0? Explain. 5. Suppose that a regression contains N = 23 observations and two β coefficients, β0 and β1 . The estimate of β1 is 73.3 with a standard error of 9.2 . Construct a 95% confidence interval for β1 . (Hint: use tα 2,N−K .) 6. Suppose that we estimate the relationship between a consumer’s QUANTITY (demanded) and PRICE of a good, using a double-log form: ln(QUANTITYi ) = β0 + β1 ln(PRICEi ) + ui We estimate ˆ β1 = −0.86 with a standard error of 0.05 . The sample has N = 100 observations. a. Test the hypothesis that demand is unit elastic (against the alternative that it is not unit elastic). b. Calculate the probability that demand is elastic (that is, β1 < −1) given the available information.

closed as off-topic by EnergyNumbers, Kenny LJ, denesp, Adam Bailey, Herr K. Dec 6 at 20:24

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