Single Equation Linear Regression Analysis

By rule of thumb, a t-value of greater than 2. If the t-value indicates that the b coefficient is statistically significant, this means that the independent variable or X number of patrol cars deployed should be kept in the regression equation, since it has a statistically significant relationship with the dependent variable or Y average speed in mph.

If the relationship was not statistically significant, the value of the b coefficient would be statistically speaking indistinguishable from zero. F F is a test for statistical significance of the regression equation as a whole. It is obtained by dividing the explained variance by the unexplained variance. By rule of thumb, an F-value of greater than 4. If F is significant, than the regression equation helps us to understand the relationship between X and Y. For our example above, say we obtained the following values: Consulting a t-table, we find that the coefficient is statistically significant.

This means that the independent variable X number of patrol cars deployed should be kept in the regression equation, since it has a statistically significant relationship with the dependent variable Y average speed in mph. This means that the regression equation is helping us to understand the relationship between X and Y. The independent variable can be called an exogenous variables, predictor variables or regressors. More about the uses of regression.

Three major uses for regression analysis are 1 causal analysis, 2 forecasting an effect, and 3 trend forecasting. Other than correlation analysis , which focuses on the strength of the relationship between two or more variables, regression analysis assumes a dependence or causal relationship between one or more independent variables and one dependent variable. Firstly, the regression might be used to identify the strength of the effect that the independent variable s have on a dependent variable.

Typical questions are what is the strength of relationship between dose and effect, sales and marketing spend, age and income. Secondly, it can be used to forecast effects or impact of changes. That is, the regression analysis helps us to understand how much the dependent variable change with a change in one or more independent variables. Typical questions are, "how much additional Y do I get for one additional unit X?

The regression analysis can be used to get point estimates.


Lesson 1: Simple Linear Regression