CHAPTER 4 INTRODUCTION TO FORECASTING WITH REGRESSION METHODS

1. The first step in evaluating a regression model is to determine whether the sign of the estimated slope term makes sense. The second step is to test whether or not the slope term is significantly different from zero. The appropriate statistical test to determine this is a t-test since the true regression error variance is generally unknown. The third check of regression is to evaluate what percent of the variation in the dependent variable is explained by variation in the independent variable. This is given by the R-squared (coefficient of determination) in regression output. Fourth, the regression model should be evaluated for serial correlation. The Durbin-Watson statistic is used in this regard. The problem of serial correlation is common to time-series data and leads to the problem of spurious regression, i.e., misleading regression statistics.

2. Putting the data in graphic form may help the analyst determine patterns in the data such as trend and seasonality. In addition, whether a linear or nonlinear model would be the most appropriate, and whether there are outliers in the data. Graphic displays are generally helpful in evaluating whether seasonal, cyclical, and trend components are in the data.

3. In evaluating regression models, we test whether the slope term is significantly different from zero to determine if there is a statistical relationship between the dependent and independent variables. If the slope term is zero, the regression line is horizontal indicating that the value of Y is independent of the value of X. We do not usually test the comparable hypothesis for the intercept because the intercept is the value that the dependent variable would have if X = 0, and is rarely of interest since X = 0 is usually not within the relevant range of the data.

4. a) The t-ratio for the slope coefficient is:

b/(standard error of b) = 805/258 = 3.12.

This indicates that experience is a statistically significant determinant