give the SAS variable names for the respective output statistics. The format of the OUTPUT statement is: OUTPUT OUT=(data set name) option=name1 option=name2 …, where the options might be P for predicted values, RSTUDENT or R for studentized or raw residuals, respecively, or L95M and U95M for lower and upper 95% confidence intervals on the estimated model. Examples of these would be predicted values, raw or studentized residuals, confidence intervals, etc. OUTPUT: The OUTPUT statement will save requested regression statstics to a new SAS data set. These, in order, result in the fit of a model with no intercept, requesting REG use various model selection procedures when multiple regressor variables are present, and providing a list of regressor variables that must be included in all models tested. Examples of these might be NOINT, SELECTION, and INCLUDE. The last category of options are used to specify the model itself. Examples include R, DW, and INFLUENCE, for a preliminary residual analysis, the Durbin-Watson statistic, and influence statistics, respectively. The second type of options are diagnostic. In simple linear regression, we define a linear relationship between a continuous dependent response, \(y_i\), and an independent continuous regressor variable, \(x_1\) as: Likewise, readers interested in fixed or mixed nonlinear modeling are referred to the specific tutorials on those subjects. While much of the theoretical background and diagnostics still apply to these models, the details and considerations of setting these models up in SAS are covered elsewhere. Application of mixed model methodology to linear regression is also possible. Some additional knowledge of SAS may be useful for understanding certain aspects of this tutorial and the readers are referred to: Data Step and Graphics and Plotting. To learn more about the assumptions of multiple linear regression and how to treat them in SAS, check out the link below.This document is an introduction to estimating and diagnosing simple and multiple linear regression fixed effect models in SAS. Fix: If outliers are influential, consider excluding them or applying robust regression methods.Check: Plot the standardized residuals against the predicted values look for points that deviate substantially from the others.Outliers: Identify extreme data points that may exert a significant influence on the model. Fix: If multicollinearity is detected, consider removing or combining correlated predictors.Check: Calculate the variance inflation factor (VIF) for each predictor VIF values above 5 or 10 indicate potential multicollinearity.Multicollinearity: Predictor variables should not be highly correlated with each other. Fix: Consider transforming variables or using polynomial terms to achieve linearity.Check: Plot the residuals against each predictor variable residuals should show a random scatter pattern around zero.Linearity: The relationship between the dependent variable and each independent variable should be approximately linear. Note : Check P-value of Q statistics and LM tests. Model dependent_variable = variable1 categorical_variable / archtest Fix: If heteroscedasticity is present, consider transforming the dependent variable or using weighted least squares. Check: Plot the residuals against the predicted values residuals should be evenly spread around zero, with no cone-like shape. Homoscedasticity means the variability of residuals should be constant across all levels of the predictors. Whereas, PROC GLM does not support these techniques. Automated variable selection: PROC GLMSELECT supports BACKWARD, FORWARD, STEPWISE variable selection techniques.Whereas, PROC REG does not support CLASS statement. Handling categorical and continuous variables: PROC GLMSELECT supports categorical variables selection with CLASS statement.The benefits of using PROC GLMSELECT over PROC REG and PROC GLM for building a linear regression model are as follows: To understand the output of the linear regression model, refer this section. Ods output ParameterEstimates = estimates Whereas the PROC GLM can handle both the categorical and continuous independent variables. However, PROC REG is specialized for linear regression analysis with one or more continuous independent variables. The PROC GLM has many similarities with the PROC REG procedure in terms of building a regression model. The p-value for both the independent variables is less than 0.05, which means they are statistically significant. The regression equation can be formed based on the parameter estimates Housing Price = 139989 + 63.65716*(square footage) + 5769.28237*(distance from city center)
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