Question

The economist now uses regression analysis to address the same issue as in the previous questions. The dependent variable is the change in full time equivalent employees per NJ fast food restaurant before and after the change in the minimum wage. The explanatory variables include the fast food brand and whether the restaurant is company owned or a franchise. Some of the regression results are below

Regression Statistics
Multiple R	0.17
R Square	0.03
Adjusted R Square	0.02
Standard Error	9.25
Observations	399
ANOVA
	df	SS
Regression	5	977.79
Residual	393	33661.89
Total	398	34639.68
	Coefficients	Standard Error
Intercept	-3.92	1.58
Burger King Dummy	2.78	1.34
KFC Dummy	2.72	1.43
Wendys Dummy	1.79	1.64
NJ dummy	2.76	1.18
company owned dummy	-0.01	1.11

1. What does this regression tell us?
2. How might we improve our understanding of the relationship between the minimum wage and employment levels?

Answer 1

In this multiple regression case,

we are checking how the data of NJ Fast Food restaurant (acting as dependent variable) regressed with other food chains.

this small value of R =0.17 indicates that this dependent variable is less correlated with all the other variables,the multiple regression equation is less likely to predict its observed value.   

s^2 due to regression =977.79/5=195.558

s^2 due to residuals=33661.89/393=85.654

f value calculated=195.558/85.654=2.283

which is greater than f value tabulated,and so we can improve our understanding by change its p value.