What is the significance of regression

To determine how well the regression line obtained fits the given data points, F-test of overall significance is conducted. The issues involved in the F-test of overall significance are many and mathematics involved is rigorous, especially when more than two variables are involved.

This study describes in details how the test can be conducted and finally gives the simplified approach of test using an online calculator. Users Online: Kothari CN. Quantitative Techniques. Vohra ND. Quantitative Techniques in Management.

Statistical Methods in Medical Research. Massachusetts: Blackwell Science; Sullivan LS. Essentials of Biostatistics Workbook. London: Jones and Bartlett Learning; Comparison of some common tests for normality.

Int J Probabil Statist ;, Regression Analysis with Applications. London: Chapman and Hall; Harris M, Taylor G. Medical Statistics Made Easy. New Yolk: Springer-Verlag; Su H, Berenson ML. Comparing tests of homoscedasticity in simple linear regression. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.

The topics covered, length of sessions, food provided, and the cost of a ticket are our independent variables. Administering surveys to your audiences of interest is a terrific way to establish this dataset. Your survey should include questions addressing all of the independent variables that you are interested in. To begin investigating whether or not there is a relationship between these two variables, we would begin by plotting these data points on a chart, which would look like the following theoretical example.

Plotting your data is the first step in figuring out if there is a relationship between your independent and dependent variables. Our dependent variable in this case, the level of event satisfaction should be plotted on the y-axis, while our independent variable the price of the event ticket should be plotted on the x-axis. Once your data is plotted, you may begin to see correlations.

But how can we tell the degree to which ticket price affects event satisfaction? To begin answering this question, draw a line through the middle of all of the data points on the chart. This line is referred to as your regression line, and it can be precisely calculated using a standard statistics program like Excel.

The regression line represents the relationship between your independent variable and your dependent variable. Excel will even provide a formula for the slope of the line, which adds further context to the relationship between your independent and dependent variables.

If X is our increase in ticket price, this informs us that if there is no increase in ticket price, event satisfaction will still increase by points. Regression lines always consider an error term because in reality, independent variables are never precisely perfect predictors of dependent variables. This makes sense while looking at the impact of ticket prices on event satisfaction — there are clearly other variables that are contributing to event satisfaction outside of price.

Unlike t-tests that can assess only one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously. The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model.

In Minitab statistical software , you'll find the F-test for overall significance in the Analysis of Variance table. If the P value for the F-test of overall significance test is less than your significance level, you can reject the null-hypothesis and conclude that your model provides a better fit than the intercept-only model.

Typically, if you don't have any significant P values for the individual coefficients in your model, the overall F-test won't be significant either. However, in a few cases, the tests could yield different results. For example, a significant overall F-test could determine that the coefficients are jointly not all equal to zero while the tests for individual coefficients could determine that all of them are individually equal to zero.

In the intercept-only model, all of the fitted values equal the mean of the response variable. Therefore, if the P value of the overall F-test is significant, your regression model predicts the response variable better than the mean of the response.