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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?