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STAT 331 ProjectAuto sales vs Oil Prices
Team Members
Salman Asif, Jawed Karim, Umer Iqbal,
Gautam Karwa, Nicky Chen, Chulmin Lee
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Introduction Purpose of project
Analyze the relationship between autosales and oil prices, electronic goodssales and sports sales
Regressors
Electronic sales and sports goods sales
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Source of Data
Our datasets are U.S. monthly auto sales for retail, U.S.monthly gasoline price, U.S. monthly electronics sales,and U.S. monthly sporting goods sales from Jan, 1992 to
Aug, 2008. The gasoline price is U.S. city average.
Source: U.S. Census, and U.S. Bureau of LaborStatistics
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Analysis Selection of model
Based on R-squared
Methods used in the analysis Estimation and Significance of Regressors
Residual Diagnostics
Prediction intervals
Plots and visuals
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Proposed Model AUTO SALES = 0 + 1x OIL PRICE +
2x ESALES + 3x SSALES + ei
Where AUTO SALES = Monthly auto sales in US ($ Millions)
OIL PRICES = Average monthly oil prices ($/gallon)
ESALES = Electronic goods sales ($ Millions)
SSALES = Sports goods sales ($ Millions)
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Diagnostics Homoscedasity
Residual vs Fitted plot
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Diagnostics Homoscedasity
Scatter plot of residuals
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Diagnostics Auto Correlation
DW test
Durbin-Watson testdata: AutoSales ~ Gasoline + Electronic + Sporting
DW = 0.8647, p-value < 2.2e-16
alternative hypothesis: true autocorrelation is greater than 0
Significant p-value
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Diagnostics Auto Correlation
The runs test
Runs Test - Two sided
data: l$residuals
StandardizedRuns
Statistic = -5.8129, p-value = 6.14e-09
Significant p-value
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Diagnostics Auto Correlation
ACF plot
0 5 10 15 20
0.0
0.2
0.4
0.6
0.8
1.0
Lag
ACF
ACF plot of residuals
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Diagnostics Normality
Histogram of Residuals
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Diagnostics Normality
QQ Plot
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Diagnostics Normality
Shapiro-Wilk Test
Shapiro-Wilk normality test
data: l$residuals
W = 0.9259, p-value = 1.608e-08
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Normalizing the Residuals Shapiro-Wilk Test
Shapiro-Wilk normality testdata: L$residuals
W = 0.9939, p-value = 0.6147
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Normalizing the Residuals Histogram of Residuals
Histogram of Residuals
Residuals
Frequency
-6000 -4000 -2000 0 2000 4000
0
10
20
30
40
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Normalizing the Residuals QQ plot
-3 -2 -1 0 1 2 3
-6000
-4000
-2000
0
2000
4000
Normal Q-Q Plot
Theoretical Quantiles
SampleQuantiles
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Results of Diagnostics Homoscedasticity
Residuals are not Homoscedastic
Correlation Residuals are Correlated
Normality
Residuals are Normal
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Implications Observed that increase in electronic
goods sales and/or sports sales
causes an increase in auto sales Decrease in oil prices results in
increase in Auto sales
Most Important Regressor is Oil Prices
Proposed model is useful forpredicting auto sales
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Pros and cons of Model Pros
R-squared value is high
Regressors are significant Model has good predictive value
Cons
Residuals are not homoscedastic and not
uncorrelated
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Conclusions Oil Prices very good at predicting auto
sales
Positive relationship between autosales and electronic goods andsporting goods
Proposed model fits the data very
well Residuals are normal but not
homoscedastic and uncorrelated
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Recommendations Increase our sample size
Add more regressors
Perform variance-stabilizingtransformations
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Questions?