Consider the following regression model:
Yi = α + βix1i + β2x2i + εi
a) Suppose that β2 was equal to zero. You are given a sample of data for the variables x1, x2 and y. You are then asked to fit a regression line to the data. In simple Ordinary Least Squares regression, the fitted line must always go through a particular point, which is found from the x and y data. What is the point in question?
b) Suppose that β2 was now not equal to zero. A researcher using the regression model finds that the values of the term εi are correlated with one another. The researcher argues that this shows that the model is properly specified as the terms follow a coherent pattern. Is this a reasonable approach? Explain your answer.
c) The researcher then estimates the model again, but uses a different set of data with 12 observations. The intercept term, seems to be zero. Is this cause for concern? Explain your answer.
d) You are given the following statistics about the regression:
The t statistic for the first independent variable is -2.3 and the estimate is 4.5. The t statistic for the second independent variable is -0.5 and the estimate is 5.1. The t statistic for the intercept term is 1.5. The R squared is 0.7 and the F statistic is 2.4. Test the overall significance of the model at the 5% level.
e) The researcher would like to create another regression model and use data from people who are currently students. Then he would use extrapolation to predict what the dependent variable would be for older people. Is this approach valid? Explain your answer.