The following table gives details on the model. These results indicate whether a variable brings significant information or not, once all the other variables are already included in the model. The next tables display the Type I and Type III SS. Therefore, we can conclude with confidence that the two variables do bring a significant amount of information. Given the fact that the probability corresponding to the F value is lower than 0.0001, it means that we would be taking a lower than 0.01% risk in assuming that the null hypothesis (no effect of the two explanatory variables) is wrong. In other words, it's a way of asking yourself whether it is valid to use the mean to describe the whole population, or whether the information brought by the explanatory variables is of value or not. The results enable us to determine whether or not the explanatory variables bring significant information (null hypothesis H0) to the model. It is important to examine the results of the analysis of variance table (see below). These effects could be gender, geographical region, life habits, etc. The remainder of the variability is due to some effects (other explanatory variables) that have not been included in this analysis. In this particular case, 63 % of the variability of the Weight is explained by the Height and the Age. The closer to 1 the R², the better the fit. The R² (coefficient of determination) indicates the % of variability of the dependent variable which is explained by the explanatory variables. The first table displays the goodness of fit coefficients of the model. How to interpret the results of a multiple linear regression in XLSTAT? Go to the Outputs tab and activate the Type I/III SS option in order to display the corresponding results. Since the column title for the variables is already selected, leave the Variable labels option activated. The quantitative explanatory variables are the "Height" and the "Age". The Dependent variable (or variable to model) is here the "Weight". In the ribbon, select XLSTAT > Modeling data > Linear Regression This dataset is also used in the two tutorials on simple linear regression and ANCOVA. The Linear Regression method belongs to a larger family of models called GLM (Generalized Linear Models), as do the ANOVA. Here, the dependent variable is the weight, and the explanatory variables are height and age: we have two of them so we choose multiple linear regression. Using simple linear regression, we want to find out how the weight of the children varies with their height and age, and to verify if a linear model makes sense. They concern 237 children, described by their gender, age in months, height in inches (1 inch = 2.54 cm), and weight in pounds (1 pound = 0.45 kg). Introduction to Experimental Ecology, New York: Academic Press, Inc. How to run multiple linear regression in XLSTAT? Dataset for running a multiple linear regression If you want to establish the linear relationship between only two variables, do not hesitate to check our tutorial on simple linear regression. Multiple linear regression enables you to predict a variable depending on several others, on the basis of a linear relationship inferred by a supervised learning algorithm. Not sure this is the modeling feature you are looking for? Check out this guide. Linear regression is based on Ordinary Least Squares (OLS). This tutorial will help you set up and interpret a multiple linear regression in Excel using the XLSTAT software.
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