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To do this, you need to activate the respective test in the Test assumptions sub-tab. The normality of the residuals can be checked by analyzing certain charts or by running a Shapiro- Wilk test on the residuals. Use the various tests displayed in the linear regression results to check retrospectively that the underlying hypotheses have been correctly verified. One must verify two main assumptions for linear regression regarding the residuals: How to validate linear regression assumptions? The variables are then removed from the model using the same procedure as for stepwise selection.
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If the probability is greater than the "Probability of removal", the variable is removed. After the third variable is added, the impact of removing each variable that is present in the model after it has been added is evaluated (still using the t statistic). If a second variable is such that the probability associated with its t is less than the "Probability for entry", it is added to the model. Stepwise: The selection process starts by adding the variable with the largest contribution to the model (the criterion used is Student's t statistic).Furthermore, the user can choose several "criteria" to determine the best model: Adjusted R², Mean Square of Errors (MSE), Mallows Cp, Akaike's AIC, Schwarz's SBC, Amemiya's PC. Best model: This method allows you to select the best mode among all the models that can handle a number of variables varying from "Min variables" to "Max Variables".It is possible to select only the most important ones using one of the four methods available in XLSTAT: Not all variables are important or significant in the linear regression model. Going further: variable selection in linear regression The linear regression hypotheses are that the errors e i follow the same normal distribution N(0,s) and are independent.
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Since the model is found by using the ordinary least squares (OLS) method (the sum of squared errors e i² is minimized), many wonder: is OLS the same as linear regression? Not really, OLS is simply the name of the method that enables us to find the regression line equation. Where y i is the value observed for the dependent variable for observation i, x ki is the value taken by variable k for observation i, and e i is the error of the model. The linear regression equation is written for observation i as follows: The principle of linear regression is to model a quantitative dependent variable Y through a linear combination of p quantitative explanatory variables, X 1, X 2, …, X p. A distinction is usually made between simple regression (with only one explanatory variable) and multiple regression (several explanatory variables) although the overall concept and calculation methods are identical. Linear regression is undoubtedly one of the most frequently used statistical modeling methods.