Model Fitting

The questions listed below are designed for discussion and preparation. When reviewing these questions, try to illustrate your points with specific examples/cases from what we have seen in class.

  1. If the \(R^2\) value for a simple regression is 0.80, does this mean that 80% of the changes in the dependent variable are caused by changes in the independent variable?
  2. List two ways to make regression estimates more precise.
  3. What do you learn form a regression calculation if the estimated slope is zero?
  4. What do you use the t statistic of the slope coefficient for?
  5. Why are the extrapolation predictions (i.e., for values of the independent variables outside the sample range) especially difficult?
  6. Does a correlation of zero indicate that there is no relation between two vari ables?
  7. If you have only two observations, will you be able to get a high \(R^2\) value? Will you be able to obtain precise estimates of the slope and intercept?
  8. What does the graph of a regression equation with two independent variable look like?
  9. Is it correct to say that in a multiple regression the independent variable with the largest coefficient has the greatest effect on the dependent variable?
  10. What happens to regression calculations if an important independent variable is left out?
  11. Suppose two the independent variables in your regression are perfectly correlated. Explain intuitively why this creates problems for the regression calculation.
  12. Will adding another independent variable make the \(R^2\) value for the regression go up or down?
  13. What do you learn form a regression model where the \(R^2\) value is zero?