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.
- 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?
- List two ways to make regression estimates more precise.
- What do you learn form a regression calculation if the estimated slope is zero?
- What do you use the t statistic of the slope coefficient for?
- Why are the extrapolation predictions (i.e., for values of the independent variables outside the sample range) especially difficult?
- Does a correlation of zero indicate that there is no relation between two vari ables?
- 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?
- What does the graph of a regression equation with two independent variable look like?
- 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?
- What happens to regression calculations if an important independent variable is left out?
- Suppose two the independent variables in your regression are perfectly correlated. Explain intuitively why this creates problems for the regression calculation.
- Will adding another independent variable make the \(R^2\) value for the regression go up or down?
- What do you learn form a regression model where the \(R^2\) value is zero?