Week 4 Discussion

Linear Regression

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Linear regression is one form of bivariate regression, meaning that it involves two variables. The

simple regression model tries to �t a straight line to a set of data points consisting of one independent

variable (known as the x value) and one dependent variable (known as the y value). The model's

parameters are denoted by Greek letters such as α_0,α_1,and ε.

There are a number of assumptions that must be met in order for a simple regression model to be a

reasonable choice for modeling the relationship between two variables. Probably the easiest

assumption to understand is that the relationship between the independent variable and the

dependent variable needs to be a linear relationship. For example, if we plotted lots of values that were

created by using the equation y = x2, and then attempted to predict a straight line that approximated

those points, you would have very little success in trying to model data points that had much variability

in terms of the values of the independent variable. While a linear model might work over a very small range of x values, it would not work well over a wider range of values.

Other assumption violations which can cause unpredictable results include the assumption that the

errors (between the straight line estimate and the actual data) are independent (meaning that the

straight line estimates things just about equally well for all data points), the assumption that the

variance within the data is constant, and the assumption that all of the errors are approximately

normally distributed.

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The supplemental material entitled "Linear Regression Models" shows you both the most general form

of the model (which will include an error term) and the form of the model which is most often used

(which does not explicitly include the error term, but understand that there will be errors that must be

analyzed).

Additional Materials

View a Pdf Transcript of Linear Regression Models 

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