Least squares coefficient estimators

The population regression line is useful theoretical construct, but for applications we need to determine an estimate of the model using available data. Suppose that we have n pairs of observations

. We would like to find the straight line that best fits these points. To do this we need estimators of unknown coefficients and of the population regression line.

We obtain the coefficient estimators, a and b using equations derived by using the least squares procedure. As shown in Figure 3.2 there is a deviation, between the observed, and the predicted value, , on the estimated regression equation for each value of x, where .

Some of the will be positive and some negative. We then compute a mathematical function that represents the effect of squaring all of the residuals and computing the sum of the squared residuals. This function- whose left side is labeled SSE –includes the coefficients, a and b. The quantity SSE is defined as the “Error Sum of Squares”. The coefficient estimators a and b are selected as the estimators that minimize the Error Sum of Squares.

Дата добавления: 2015-08-05