Regression

Notes for Simple Regression:

• What have we seen so far?

o Two major classes of time series methods- decomposition and exponential smoothing

o In each method we looked at methods appropriate for different patterns and conditions

o In each case data was given in some chronological time frame and hence time series

• Here we are looking at forecasts differently- a forecast here is expressed as a function of a certain number of factors (variables) that influence its outcome

• The underlying theme is that the factors (explanatory variables or independent variables) explain the behavior of the forecast or dependent variable

• By experimenting with different combinations of inputs (explanatory variables) and their effect on the output (forecast variable), one gets a better understanding of the situation

• In this way explanatory models can be geared toward intervention i.e. influencing the future by decisions made today

• Simple regression

• Multiple Regression

• Econometric modeling

• Time series and cross-sectional regression

• Least Squares Estimation

Using a sales vs. time example show how different lines can be fitted

Y = a +bX +e

a, b are intercept and slope

e the error is the deviation of the observation from the linear relationship

The objective is to find the values of a and b so the line Y(hat) = a + bX presents the best fit

e = Y –Y(hat)

SSE = e12 + e22 +…….

The line of best fit is the line that provides the minimum SSE

• Correlation Coefficient

o Correlation is a measure of linear association, so careful about non-linear relationships

o Small sample (n> 30)

o King Kong Effect (extreme values and skewness)

• Simple regression and correlation coefficient

Coefficient of determination R2 = SSR/SST (show with diagram)

• Residuals, Outliers, and...