Linear Regression: The Two Variable Model Shaun Bray Math 480 April 24, 2013
Goal for Today: • What is regression? • Population Regression Function (PRF) • Sample Regression Function (SRF) • The Method of Ordinary Least Squares • How to interpret regression function
What is Regression Analysis? • Concerned with the study of the relationship between one variable (dependent) and one or more other variables (independent). • Examples: • Quantity demanded of a commodity in terms of the price of the commodity, income of the consumer, and prices of competing commodities. • Sales of a product related to advertising expenditure incurred.
Regression analysis may have one of the following objectives: • To estimate the mean value of the dependent variable, given the values of the independent variables. • To test hypotheses about the nature of dependence. • Predict the mean value of the dependent variable, given the value(s) of the independent variables(s) beyond the sample range. • A combination of one or more of these objectives.
Sample Regression Function (SRF) • The PRF is relatively easy to find if we have data of an entire population. • In practice, this is hardly ever the case, so we often look for a sample of a population. • The task here is to estimate the PRF on the basis of the sample information.
Conclusion • What is regression analysis and what are its objectives? • Population and Sample Regression Functions • The Method of Ordinary Least Squares