Question

1, Which one of the following equations contains the true error term? Pick 1

		Y-hat =  α+ β X
		None of the above
		Y-hat = a+ b X
		Y = α+ β X + ε
		All of the above
		Y = a+ b X + e

2,

After running a regression, we calculate the coefficient of determination r² = 0.94. How to interpret this r²? Pick 1

		The variation of Y is 94%.
		94% of variation in Y is explained by the model.
		If model changes by 1, Y changes by 94%.
		The probability of accurately predicting Y is 94%.
		None of the above.

3,

Suppose the estimated slope is b=5, and the standard error of the slope is s_b=2. Based on b and s_b, you calculate the p-value for the slope is 0.067. Can you reject the null hypothesis? Pick 1

		If the alpha (significance level) is 0.1, we can reject the null hypothesis
		If the alpha (significance level) is 0.05, we can reject the null hypothesis
		If the alpha (significance level) is 0.01, we can reject the null hypothesis
		Not enough information to make the decision
		More than one answers are correct

4,

What is the main point of the Ludwig and Philips article on Head Start? Pick all that applies

		Statistical significance is irrelevant to interpreting data.
		The only correct way to interpret data is to do cost-benefit analysis.
		If a program's impact is not statistically significant, then it is not a good program.
		You cannot say that a program is ineffective just because its impact is insignificant in your study; you may not have enough power to rule out important impacts. You need to examine whether the data plausibly support the idea that the program has a large enough impact to matter.

Answer 1

1) The correct equation is Y = α+ β X + ε

2) Here the coefficient of determination r² interpreted as 94% of variation in Y is explained by the model.

3) Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

For "If the alpha (significance level) is 0.1, we can reject the null hypothesis" this statement

p value = 0.067 < 0.1 so we used first rule.

That is we reject null hypothesis

so correct option is first statement "If the alpha (significance level) is 0.1, we can reject the null hypothesis"