A:
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 appropriate assumptions and type of test conducted. Be sure to offer some motivation.The table is below:
Model1:
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.
Model2A 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.
Coefficient = American food and Non-American food (2 regression analysis was run)
For American Food
For non-American food
Result for both regression testing
Model3:
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.
Quadratic results for Competitors
Quadratic results for Marketing %
B:
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.
Link for the T-Table for hypothesis testing
https://statisticsbyjim.com/hypothesis-testing/t-distribution-table/
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)
- interpret coefficients for significant results and discuss insignificant results,
- make relevant comparisons where required,
- fully address any other questions asked.
- No more than 3.5 pages
- Single spaced, 1” margin
Examples
The examples below refer to results where explanatory variables and the dependent variablewere measured in %. Your interpretation will likely be different if your dependent variable is not measured in %.
Two of the variables related to the racial composition of each district were found to be significant at the 99% level of confidence and had a positive impact on voter turnout. A 10% increase in the proportion of the population that is white raises voter participation by 2.7% (p=.0062; t=6.15>tc=2.33) and a 10% increase in the proportion of the population that is black increases participation by 2.3% (p=.002; t=4.30>tc=2.59), holding all else constant.
If something is statistically significant but has an unexpected sign (opposite of your hypothesis), we would still consider it to be a result (since maybe your initial hypothesis is incorrect). But it should be noted in the discussion. An example is below (without actual p-values and t/critical t reported so be sure you do that).
However, median income had an unexpected sign. The result suggests that, holding all else constant, increased median income decreases voter turnout rates, a result significant at the 95% level of confidence (P=x; t=x>tc=y). A $1000 increase in median income decreases voter turnout by .3%.
