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I want to predict shop sales from a set of independent variables which consists of shop attributes like floor space, no. of stuff of a specific store (continuous variables) and also location of the store which is a categorical variable (binary coding) like east west south. I have some questions.

  1. If I run stepwise regression for variable selection and if one of the included dummy variable gets dropped , what does that mean?

  2. Is it necessary to include interaction terms with dummy variables and continuous variables if they are significant? I am asking this because my motive is to predict sales.

  3. Should I include interaction terms before running stepwise regression?

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    $\begingroup$ Stepwise regression is generally not a preferred technique. $\endgroup$ – rnso Mar 29 '15 at 1:22
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  1. If by dummy variables you're referring to multiple binary variables that make up one categorical predictor, each of them needs to be in the model for each other dummy to be meaningful. In stepwise regression either they are all in or all out, but not piecemeal. Are you doing this by hand or something? All stats packages I'm familiar with treat multilevel categoricals properly in this respect, and shouldn't consider dummy variables independently for model specification.

  2. Again, you can't include interactions with some dummy variables of a single categorical predictor but not others. All in or all out. The test of whether the interaction needs to be included is a comparison between a model without interactions with all dummies and a model with interactions with all dummies. If the interaction is significant, you should keep it in any case. Just be aware that the interpretation of the "main effects" changes drastically when interactions are included in models.

  3. If doing backwards stepwise regression, include the interaction terms.

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  • $\begingroup$ Thanks for your reply Sir, I am relatively new to regression. Sir can you just explain me how will you interprete main effects in the model considering interaction terms are significant. Assuming you have 2 independent variables one continous like floor space and another categorical like "type of the outlet" having 3 levels Hypermarket, Supermarket , Grocery. Dependent variable is Shop turnover which is metric. So my question is how will I interpete the main effect assuming interaction effect to be significant? Will it be any specific interpretation or normal interpretation for main effects ? $\endgroup$ – ankan Jan 19 '15 at 12:30
  • $\begingroup$ Also are you suggesting I can use backward selection for a model with categorical and many continuous variables, also interactions, and the model will automatically treat categorical variables in a different manner: suppose I use PROC GLM for instance $\endgroup$ – ankan Jan 19 '15 at 12:38
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    $\begingroup$ As soon as interactions are in the model, the interpretation of the "main effects" changes. For simplicity, let's assume you have two independents, one continuous, and the other categorical having only two levels (it gets more complicated with 3 or more), and we can use the ones you list above (say the levels are Hypermarket and Supermarket). Once the interaction is in the model, the interpretation of main effect is the "slope" when the other term is equal to 0. $\endgroup$ – tim.farkas Jan 22 '15 at 14:58
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    $\begingroup$ read Data Analysis: A Model Comparison Approach. Excellent and very accessible textbook on regression. $\endgroup$ – tim.farkas Jan 22 '15 at 15:11
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    $\begingroup$ If you are using PROC GLM as you indicated, since you are new to regression, then you need to understand how dummy coding works in GLM. You will need to make sure you set the "PARAM=" statement to obtain the coding you are working with if you want to have an accurate interpretation of your results (depending on what you are doing). $\endgroup$ – StatsStudent Aug 8 '15 at 18:13

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