For my Aggregate Engel Curve assignment, I ran OLS test to see if National Real GDP per capita has a significant impact on consumption spending of gambling. I was originally going to use a cross sectional data analysis, but gambling is only legal in 24 of the 50 states so, I went with a time series approach using data from 20092015. I also picked time series because even though gambling is not legal everywhere, all states still have some form of legal gambling, which is why I chose to look at data from Commercial Gambling and Lottery ticket consumption. The Commercial Gambling is your basic casino trip, and I still used this data because there are no barriers for anyone from any state to enter these casinos or play the lottery (except for ages 18+) and that is where I thought that using national income would be a better explanatory variable on my data. All data numbers were measured in billions (USD).
To start off my data, I ran a regression analysis for Real GDP per capita and Commercial Gambling expenditure (total per year), then ran another regression for both coefficients, Commercial Gambling, and Lottery ticket sales. When running the first analysis, Commercial gambling was statistically significant with a pvalue of 0.0013. This meant that as income rose so did spending on Commercial Gambling, however, when running the regression for both, I found that they were not statistically significant. My reasoning for this was that when looking at Real GDP as income rises, compared against a single gambling event had a positive correlation (which can be seen from the Rsquared values of my analysis), but when another gambling event was added, it showed how spending for one dropped (Commercial Gambling) and more went to the second event (Lottery). This was just my take on it though, of course several variables take into play such as age of household, transportation costs, geographic location, and median household income.
Commercial Gambling only:
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The AUTOREG Procedure
Ordinary Least Squares Estimates
Fit Summary
Ordinary Least Squares Estimates  
SSE  309516.773  DFE  5 
MSE  61903  Root MSE  248.80385 
SBC  98.6349617  AIC  98.7431414 
MAE  183.536902  AICC  101.743141 
MAPE  1.16479804  HQC  97.4060606 
DurbinWatson  1.2795  Total RSquare  0.8944 
Parameter Estimates
Parameter Estimates  
Variable  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
Variable Label 
Intercept  1  1377  2181  0.63  0.5555  
Commercial  1  387.7134  59.5939  6.51  0.0013  Commercial 
For both Coefficients:
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The AUTOREG Procedure
Ordinary Least Squares Estimates
Fit Summary
Ordinary Least Squares Estimates  
SSE  206958.234  DFE  4 
MSE  51740  Root MSE  227.46331 
SBC  97.7634049  AIC  97.9256744 
MAE  138.683857  AICC  105.925674 
MAPE  0.89564805  HQC  95.9200533 
DurbinWatson  1.9107  Total RSquare  0.9294 
Parameter Estimates
Parameter Estimates  
Variable  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
Variable Label 
Intercept  1  11148  7221  1.54  0.1975  
Commercial  1  166.9237  397.6935  0.42  0.6962  Commercial 
Lottery  1  159.3078  113.1520  1.41  0.2319  Lottery 
So, even though these were not statistically significant in the second test, the total RSquare value is still high, which shows that rises in income have a positive correlation with increased consumer expenditure on gambling. This shows that my aggregate Engel curve estimation does still have a positive relationship, and to further see the correlation between the variables and Real GDP I ran a correlation test in SAS which gave Commercial Gambling a .9457 and Lottery sales a .96242 which is a strong relationship.
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The CORR Procedure
Variables Information
3 Variables:  GDP Commercial Lottery 
Simple Statistics
Simple Statistics  
Variable  N  Mean  Std Dev  Sum  Minimum  Maximum  Label 
GDP  7  15555  698.77343  108883  14595  16597  GDP 
Commercial  7  36.56714  1.70443  255.97000  34.28000  38.54000  Commercial 
Lottery  7  65.97571  5.99054  461.83000  58.25000  73.87000  Lottery 
Pearson Correlations
Pearson Correlation Coefficients, N = 7 Prob > r under H0: Rho=0 

GDP  Commercial  Lottery  
GDP
GDP 
1.00000

0.94570
0.0013 
0.96242
0.0005 
Commercial
Commercial 
0.94570
0.0013 
1.00000

0.99057
<.0001 
Lottery
Lottery 
0.96242
0.0005 
0.99057
<.0001 
1.00000

Finally, I ran a hypothesis test to see if the 2 coefficients were equal in importance for my analysis comparison to Real GDP increases. I set both coefficients equal, and at the 5% level of significance the two coefficients were not of equal importance. This relates back to the scenarios listed above on how gambling is legal some places and not others, and that there are several different types of gambling methods. Overall, I was not shocked by the findings about increases in income do have increases in gambling expenditure. I wish I would have found more data on the household income of ages 18+ only and compared that to overall household incomes, which may have presented different results.
Test:
Test 1
Results
Test 1 Results for Dependent Variable GDP  
Source  DF  Mean Square 
F Value  Pr > F 
Numerator  1  21169  0.41  0.5572 
Denominator  4  51740 
Data on Commercial and Lottery Gambling provided by: State Gaming Regulatory Agency.
Data on Real GDP per capita provided by: Organization for Economic Cooperation and Development.