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• 7.53 Mustafa Telab
  
• Brett Davidoff
  
• 8.21 - Alexis Mekueko

Click here to sign-up for a presentation slots. There are two time slots (12 to 1:30pm and 8 to 9:30pm) on three different days (December 1st, 3rd, and 8th).

You are required to attend ONLY ONE of those time slots. You will do your presentation, watch the other presentations, and provide peer feedback (will be shared anonymously afterward).

Presentations should be no more than 10 minutes.

• Overview slide

  • Context on the data collection
  • Description of the dependent variable (what is being measured)
  • Description of the independent variable (what is being measured; include at least 2 variables)
  • Research question

• Summary statistics

• Include appropriate data visualizations.

• Statistical output

  • Include the appropriate statistics for your method used.
  • For null hypothesis tests (e.g. t-test, chi-squared, ANOVA, etc.), state the null and alternative hypotheses along with relevant statistic and p-value (and confidence interval if appropriate).
  • For regression models, include the regression output and interpret the R-squared value.

• Conclusion

  • Why is this analysis important?
  • Limitations of the analysis?

• Data is presented to support the conslusions using the appropriate analysis (i.e. the statistical method chosen supports the research question).

• Suitable tables summarize data in a clear and meaningful way even to those unfamiliar with the project.

• Suitable graphics summarize data in a clear and meaningful way even to those unfamiliar with the project.

• Data reviewed and analyzed accurately and coherently.

• Proper use of descriptive and/or inferential statistics.

cor.test(elections$buch, elections$bush)

## 
##  Pearson's product-moment correlation
## 
## data:  elections$buch and elections$bush
## t = 6.455, df = 65, p-value = 1.574e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4527668 0.7522709
## sample estimates:
##       cor 
## 0.6250012

model1 <- lm(buch ~ bush, data = elections)
summary(model1)

## 
## Call:
## lm(formula = buch ~ bush, data = elections)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -911.30  -46.11  -26.05   12.01 2608.01 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.697e+01  5.446e+01   0.863    0.392    
## bush        4.920e-03  7.622e-04   6.455 1.57e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 353.9 on 65 degrees of freedom
## Multiple R-squared:  0.3906, Adjusted R-squared:  0.3813 
## F-statistic: 41.67 on 1 and 65 DF,  p-value: 1.574e-08

cor.test(log(elections$buch), log(elections$bush))

## 
##  Pearson's product-moment correlation
## 
## data:  log(elections$buch) and log(elections$bush)
## t = 19.222, df = 65, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8760098 0.9515894
## sample estimates:
##       cor 
## 0.9221706

model2 <- lm(log(buch) ~ log(bush), data = elections)
summary(model2)

## 
## Call:
## lm(formula = log(buch) ~ log(bush), data = elections)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.97038 -0.24247  0.00825  0.25452  1.65752 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.55079    0.38903  -6.557 1.04e-08 ***
## log(bush)    0.75620    0.03934  19.222  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4672 on 65 degrees of freedom
## Multiple R-squared:  0.8504, Adjusted R-squared:  0.8481 
## F-statistic: 369.5 on 1 and 65 DF,  p-value: < 2.2e-16

model3 <- lm(log(buch) ~ log(bush), data = elections[-50,])
summary(model3)

## 
## Call:
## lm(formula = log(buch) ~ log(bush), data = elections[-50, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.97136 -0.22384  0.02279  0.26959  1.00652 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.31657    0.35470  -6.531 1.23e-08 ***
## log(bush)    0.72960    0.03599  20.271  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4203 on 64 degrees of freedom
## Multiple R-squared:  0.8652, Adjusted R-squared:  0.8631 
## F-statistic: 410.9 on 1 and 64 DF,  p-value: < 2.2e-16

Obtain the predicted vote count for Palm Beach given the fitted model without

new <- data.frame(bush = elections$bush[50])

The difference between predicted on the original scale and the observed vote count

elections$buch[50] - exp(predict(model3, new))

##        1 
## 2809.498

Prediction Confidence Interval for log(vote count)

predict(model3, new, interval='prediction', level=.95)

##        fit      lwr      upr
## 1 6.392757 5.532353 7.253162

Prediction Confidence Interval on the original scale

exp(predict(model3, new, interval='prediction',level=.95))

##        fit     lwr      upr
## 1 597.5019 252.738 1412.564

elections$buch[50]

## [1] 3407

Therefore, what we can say is that it is likely that Palm Beach is a different community.

Wand, J.N., Shotts, K.W., Sekhon, J.S., Mebane, W.R., Herron, M.C., & Brady, H.E. (2001). The Butterfly Did It: The Aberrant Vote for Buchanan in Palm Beach County, Florida. American Political Science Reviw, 95(4).

Smith, R.L. (2002). A Statistical Assessment of Buchanan’s Vote in Palm Beach County. Statistical Science, 17(4).

Regression Analysis - 1.3.3 - 2000 Elections in Florida (Youtube)