Exam 4: Linear Regression With One Regressor

Imagine that you had discovered a relationship that would generate a scatterplot very similar to the relationship Y_i = $x _ { i } ^ { 2 }$ , and that you would try to fit a linear regression through your data points. What do you expect the slope coefficient to be? What do you think the value of your regression R² is in this situation? What are the implications from your answers in terms of fitting a linear regression through a non-linear relationship?

If the three least squares assumptions hold, then the large sample normal distribution of $\hat { \beta }$ ₁ is

Binary variables

Assume that there is a change in the units of measurement on both Y and X. The new variables are Y^*= aY and X^* = bX. What effect will this change have on the regression slope?

You have analyzed the relationship between the weight and height of individuals. Although you are quite confident about the accuracy of your measurements, you feel that some of the observations are extreme, say, two standard deviations above and below the mean. Your therefore decide to disregard these individuals. What consequence will this have on the standard deviation of the OLS estimator of the slope?