t TestĬonfidence intervals and predictions intervals can be constructed around the estimated regression line. The only difference will be the test statistic and the probability distribution used. In simple linear regression, the F test amounts to the same hypothesis test as the t test. The test statistic is then used to conduct the hypothesis, using a t distribution with n-2 degrees of freedom. So, given the value of any two sum of squares, the third one can be easily found. The relationship between them is given by SST = SSR + SSE. Before we can find the r 2, we must find the values of the three sum of squares: Sum of Squares Total (SST), Sum of Squares Regression (SSR) and Sum of Squares Error (SSE). The coefficient of determination, denoted r 2, provides a measure of goodness of fit for the estimated regression equation. The graph of the estimated regression equation is known as the estimated regression line.Īfter the estimated regression equation, the second most important aspect of simple linear regression is the coefficient of determination. The formulas for the slope and intercept are derived from the least squares method: min Σ(y - ŷ) 2. There are two things we need to get the estimated regression equation: the slope (b 1) and the intercept (b 0). Furthermore, it can be used to predict the value of y for a given value of x. It provides a mathematical relationship between the dependent variable (y) and the independent variable (x). In simple linear regression, the starting point is the estimated regression equation: ŷ = b 0 + b 1x.

Simple linear regression equation