Linear Regression
Linear regression creates a linear model to fit paired numerical data. It allows for prediction of one characteristic from the knowledge of the other. There are several methods for creating and testing the efficiency of a linear model.
Least Squares Method
This method calculated a line that fits the data by minimizing the squares of their deviations from it. The model takes the form
where a and b are
Correlation Coefficient Method
This method uses the value of the correlation coefficient and the sample variances to determine b.
The intercept a is still calculated by
Intercept
At test can be used to test the hypothesis that the population regression coefficient (ßo) is equal to zero. The test statistic is
Where syx is the standard error
If the test statistic lies outside of the critical value from the t table with n-2 degrees of freedom, the hypothesis that the regression coefficient is zero is rejected.
Predicting
When predicting a value, a confidence interval for that value can be calculated by
