ODU Coefficients Standard Error T Stat and P Value Regression Analysis

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Description

Overview: 

In week 3 you worked with a data set on restaurant sales (173 observations). You will use this data set to perform regression analysis. You will focus on 3 specifications of the model detailed below. In a cohesive and well-organized report, you will perform analysis and discuss findings. You must provide results table(s), in the fashion discussed in the handout on presenting regression results. You will also be asked to reflect on what is not being controlled for that could be important, so that your client understands that there might be some omitted variables causing bias in results. 

You will format your discussion in a manner similar to the example provided to you in the module. The quality of your analysis, the quality of your writing, and the professionalism of your report will be factored into your grade. Use the technical writing tips discussed earlier and follow the examples in the handouts of how to set up tables and communicate findings. 

NOTE: Before starting, please change variable names as follows (for ease of grading). As you were instructed to do in a previous module, be sure that you have created variables in the affirmative, so SWAM is SWAM YES, where 1=yes and 0=no.

  • Gross Sales (remember that this is average WEEKLY sales when you interpret)
  • SWAM
  • Franchise
  • Website
  • Road Frontage
  • Competitors
  • Marketing %
  • Meals Tax
  • Food Types of American, Asian, Mexican, Italian, Other  (one will be the omitted category).

ALSO, ALLOW ME TO MAKE ONE MORE CLARIFICATION BEFORE YOU START. LET’S ASSUME THAT THE AVERAGE WEEKLY SALES IS BEFORE MEALS TAX. IN OTHER WORDS, RESTAURANTS WITH A MEALS TAX WILL NOT HAVE THIS MEALS TAX INFLUENCING THEIR SALES DATA. THIS ALLOWS US TO COMPARE APPLES TO APPLES, IN THIS SENSE. I DO NOT WANT THIS ISSUE TO CAUSE ANY CONFUSION. IT IS TRUE THAT IF OUR SALES DATA REFLECTED THE TAX (FOR SOME RESTAURANTS THAT HAVE THE TAX AND NOT OTHERS), THIS WOULD NOT BE AS CLEAN. 

YOU CLIENT WANTS TO SEE WHAT CAN BE LEARNED IN A MORE SOPHISTICATED ANALYSIS, WHICH REGRESSION ALLOWS FOR. THE FOLLOWING 5 THINGS NEED TO BE ADDRESSED IN YOUR REPORT: 

A. EXPECTED SIGN:

Create a table providing variable name, definition of each variable, expected sign in regression (+, -, or ?), and the relevant hypothesis test (either one-tailed or two-tailed) for your analysis. This informs the reader about your apriori assumptions and type of test conducted. Be sure to offer some motivation.  

B. MODEL 1:

The investors think that weekly average gross sales is potentially impacted by if SWAM, if a franchise, if restaurant has a website, if it has road frontage, if it has a meal tax, # of competitors, % spent on marketing, and type of food (USE AMERICAN AS OMITTED CATEGORY IN YOUR CATEGORICAL VARIABLE). You will perform this analysis and inform the investors of what is learned. 

C. MODELS 2A and 2B: 

The investors want to know if variables impact average weekly gross sales the same way (in sign and magnitude of effect) when looking at only American food restaurants vs. when looking at only Non-American food restaurants (so looking at all other types of food together as one category). You will perform this analysis and inform the investors of what is learned. 

D. MODEL 3: 

Expanding on model 1, investors want to know if 2 variables– Number of Competitors & Marketing %— have a nonlinear effect (quadratic) on sales. Starting with model 1, you will add the required variable and inform the investors of what is learned.

Remember, there is an EXCEL HELP handout in the module that overviews how to create a quadratic term. 

E. OTHER INFLUENCES: 

The investors want to know what other things might be impacting restaurant sales that they have not data on, things that might be omitted variables in the analysis. Help the investors better understand what other variables should potentially be added to the analysis (and why) for a more thorough study. Be thorough and detailed in your discussion. 

Audience: 

Your audience is your client, who is still being assisted by a former student of Dr. Marks’ with a background in statistics and regression. While you can speak to the former student (you do not need to explain regression), you must be certain you are also making the findings of your report accessible to the investors. 

Also, for assessment purposes, you must show a mastery of the topics covered, so your overriding objective is to show coaches that you understand the concepts, are applying tests correctly, and are interpreting accurately. You will need to provide intuitive explanations of your analysis and the conclusions and key takeaways for someone not that well versed in regression. But you do not have to explain what regression analysis is, etc. Assume that level of knowledge. 

Be sure you carefully and accurately:

  • discuss results of the F-test, 
  • explain the R2 measures,
  • convert p-values if required (one-tailed)
  • discuss statistical significance of coefficients (with both p-values and t-tests where you compare t-stat to t-critical and explain what they convert to if one-tailed test). SEE HANDOUT FOR EXAMPLES OF EFFICIENT WAYS TO DO THIS.
  • interpret coefficients for significant results and discuss insignificant results,

               Link to T-Table #1

            Links to an external site.Link to T-Table #2            Links to an external site.

Lecture: Help for Data Analysis #3 (42 mins)https://longwood.hosted.panopto.com/Panopto/Pages/…2.) Comparing Sub-Groups with Regression (19 mins)https://longwood.hosted.panopto.com/Panopto/Pages/…3.) Watch me generate regression results in Excel (11 mins)https://longwood.hosted.panopto.com/Panopto/Pages/…

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