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Question 3 If there is omitted variable bias in our model, then: We cannot say that X causes changes in Y. Our estimates are consistent. E[u|X1,X2,...,Xk]=0 There is at least one variable omitted from the model that is correlated with at least one of our Xs. We cannot assume the conditional mean assumption is true. Our estimates are biased. Question 4 For our estimates of the population parameters to be consistent in a multivariable regression model, we need which of the following assumptions to be true? The variance of the error, u, given every value of every X, is constant. There is no perfect multicollinearity. The errors, u, are normally distributed. There is no imperfect multicollinearity. E[u | X1,X2,...,Xk]=0 The sample is randomly selected from the population of interest. There are no large outliers in X1, X2, ..., Xk, or Y. Question 8 What do you conclude from questions 5-7? We cannot reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero. We do not have enough evidence to conclude that increasing the student-teacher ratio will cause test scores to decrease. We conclude that an increase in the student-teacher ratio has a statistically significant negative relationship with test scores. We conclude that there is no statistically significant relationship between the student-teacher ratio and test scores. We fail to reject the null hypothesis at the 5% level. We can reject the null hypothesis at the 5% level, but we fail to reject at the 1% level. We can reject the null hypothesis at the 5% level. We conclude that increasing the student-teacher ratio will cause test scores to decrease. We can reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero. Now we also control for expenditures per pupil (Expn) because we think our previous model might have suffered from omitted variable bias (OVB): TestScore=649.6-0.29STR -0.656PctEL+3.87*Expn The standard error for beta0hat is 15.5. The standard error for beta1hat is 0.48. The standard error for beta2hat is 0.32. The standard error for beta3hat is 1.59. What can you conclude about OVB? Beta1hat suffered from positive bias in model 1. STR and Expn are positively correlated. Beta1hat suffered from negative bias in model 1. STR and Expn are negatively correlated. STR and Expn are uncorrelated. Beta1hat did not suffer from any bias in model 1.

Question 3
If there is omitted variable bias in our model, then:
We cannot say that X causes changes in Y.
Our estimates are consistent.
E[u|X1,X2,...,Xk]=0
There is at least one variable omitted from the model that is correlated with at least one of our Xs.
We cannot assume the conditional mean assumption is true.
Our estimates are biased.

Question 4
For our estimates of the population parameters to be consistent in a multivariable regression model, we need which of the following assumptions to be true?
The variance of the error, u, given every value of every X, is constant.
There is no perfect multicollinearity.
The errors, u, are normally distributed.
There is no imperfect multicollinearity.
E[u | X1,X2,...,Xk]=0
The sample is randomly selected from the population of interest.
There are no large outliers in X1, X2, ..., Xk, or Y.

Question 8
What do you conclude from questions 5-7?
We cannot reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero.
We do not have enough evidence to conclude that increasing the student-teacher ratio will cause test scores to decrease.
We conclude that an increase in the student-teacher ratio has a statistically significant negative relationship with test scores.
We conclude that there is no statistically significant relationship between the student-teacher ratio and test scores.
We fail to reject the null hypothesis at the 5% level.
We can reject the null hypothesis at the 5% level, but we fail to reject at the 1% level.
We can reject the null hypothesis at the 5% level.
We conclude that increasing the student-teacher ratio will cause test scores to decrease.
We can reject the null hypothesis at the 5% level because the 95% confidence interval does not contain zero.

Now we also control for expenditures per pupil (Expn) because we think our previous model might have suffered from omitted variable bias (OVB):
TestScore=649.6-0.29*STR -0.656*PctEL+3.87*Expn
The standard error for beta0hat is 15.5. The standard error for beta1hat is 0.48. The standard error for beta2hat is 0.32. The standard error for beta3hat is 1.59.

What can you conclude about OVB?
Beta1hat suffered from positive bias in model 1.
STR and Expn are positively correlated.
Beta1hat suffered from negative bias in model 1.
STR and Expn are negatively correlated.
STR and Expn are uncorrelated.
Beta1hat did not suffer from any bias in model 1.

Added by Christopher R.

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