Group Members: Kaelyn Lemon, Zora Yezi Yang
We compiled and analyzed data on used cars of the model Audi A6. The use of the word “car” in this project refers specifically to pre-owned Audi A6s. We chose to describe the cars in terms of the following variables:
Model -the type of Audi A6, for example 3.0T or 3.2T
Mileage -the mileage of the car
Year -the model year of the car, for example 2009
Zip.Code -the center of the search radius from which the cases were found. 02118 corresponds to Boston, 90210 corresponds to Los Angeles, 55105 corresponds to Saint Paul, and 30322 corresponds to Atlanta
Cost -the price of the car in US dollars
Color -the color of the car: Black (black and brown), Blue, White (white, beige, tan, bronze, and gold), and Gray (gray and silver)
We also added the variable Age, which is equal to Year-2013, so that the newest cars (Year 2013) are Age 0, and Age increases as a car gets older.
dataSource = "https://docs.google.com/spreadsheet/pub?key=0AnEWI_gMkW2ndDljYWk1TUMxNWdzeUVlOTNSX3dDRWc&output=csv"
cars = fetchGoogle(dataSource)
cars=transform(cars, Age=2013-Year)
xyplot(Cost~Year, data=cars, ylab="Cost ($)", xlab="Year")
As cars get older (Year is smaller), Cost decreases.
xyplot(Cost~Mileage, data=cars, ylab="Cost ($)", xlab="Mileage")
Cost and Mileage have a very similar relationship to Cost and Year: as Mileage increases (the car gets older), Cost decreases.
bwplot(Cost~Color, data=cars)
Color affects the Cost of a car in that the median cost of Blue and Gray cars is lower than the medium cost of Black and White cars. However, all colors are available within roughly the same ranges of cost.
bwplot(Cost~Model, data=cars)
densityplot(~Year, groups=Model, data=cars, auto.key=TRUE)
The Model of a car affects the Cost in that models 2.7T and 2.8T have the lowest median cost while models 3.0T and 2.0T have the highest median cost. This appears to be explained by the fact that models 2.7T and 2.8T are model types of older cars, 3.2T and 4.2T are mostly model types of cars of average age, and the greatest number of 3.0T cars are newer cars while 2.0T is a model only found in the newest cars. Thus, Model corresponds to Year.
bwplot(Cost~Zip.Code, data=cars)
Boston (02118) and Saint Paul (55105) tend to have slightly cheaper cars than Los Angeles (90210) and Atlanta (30322).
tally(~Color|Zip.Code, data=cars)
## Zip.Code
## Color z02118 z30322 z55105 z90210
## Black 0.38824 0.33333 0.24490 0.38318
## Blue 0.16471 0.06667 0.18367 0.08411
## Gray 0.40000 0.41333 0.34694 0.37383
## White 0.04706 0.18667 0.22449 0.15888
## Total 1.00000 1.00000 1.00000 1.00000
Each city has roughly the same percentage of cars that are a specific color, although Boston appears to have comparatively fewer White cars, and Atlanta and Los Angeles appear to have comparatively fewer Blue cars.
densityplot(~Year, groups=Color, data=cars, auto.key=TRUE)
On average, the distribution of Years for a specific Color are very similar for all colors. However, Black and White are comparatively less frequent for cars of average age (around Year 2005), and Black is much more frequent for newer cars.
This is suprising because we did not expect the frequency of Color to depend on Year. We would have assumed that the preference of some colors over another would be constant and therefore lead to the same distribution by Year for each Color.
Here you'll give a few models, giving the model coefficients and interpreting them using language that might make sense to a well-educated car buyer.
mod1 = lm( Cost ~ Age, data=cars)
coef(mod1)
## (Intercept) Age
## 44432 -3726
confint(mod1)
## 2.5 % 97.5 %
## (Intercept) 43552 45313
## Age -3870 -3582
The average cost of a new car (Year 2013) is $44,432 , and the cost decreases by $3726 for every year older a car is.
mod2 = lm( Cost ~ Mileage, data=cars)
coef(mod2)
## (Intercept) Mileage
## 46324.5607 -0.3092
confint(mod2)
## 2.5 % 97.5 %
## (Intercept) 45137.6911 47511.4302
## Mileage -0.3245 -0.2939
The average cost of a car driven zero miles is $46324.56. The cost of a car decreases by $0.31 per mile driven.
mod3 = lm( Cost ~ Age+Mileage, data=cars)
coef(mod3)
## (Intercept) Age Mileage
## 45923.9877 -2551.1783 -0.1117
confint(mod3)
## 2.5 % 97.5 %
## (Intercept) 45057.9351 4.679e+04
## Age -2851.9676 -2.250e+03
## Mileage -0.1375 -8.591e-02
The average cost of a new car (Year 2013) with zero miles is $45,923.99 , and the cost decreases by $2551 for every year older the car gets and decreases by $0.11 for every mile it is driven.
mod4 = lm( Cost ~ Zip.Code, data=cars)
coef(mod4)
## (Intercept) Zip.Codez30322 Zip.Codez55105
## 22905 7044 -1337
## Zip.Codez90210
## 7330
confint(mod4)
## 2.5 % 97.5 %
## (Intercept) 19696 26114
## Zip.Codez30322 2357 11731
## Zip.Codez55105 -6644 3969
## Zip.Codez90210 3032 11629
The average cost of a car in Boston is $22905. The average cost of a car in Atlanta is $29949 ($7044 more than Boston). The average cost of a car in Saint Paul is $21568 ($1337 less than Boston). The average cost of a car in Los Angeles is $30235 ($7330 more than Boston).
mod8=lm(Cost~Mileage*Zip.Code, data=cars)
coef(mod8)
## (Intercept) Mileage
## 4.630e+04 -3.307e-01
## Zip.Codez30322 Zip.Codez55105
## 2.104e+03 -2.376e+03
## Zip.Codez90210 Mileage:Zip.Codez30322
## -1.528e+02 1.873e-04
## Mileage:Zip.Codez55105 Mileage:Zip.Codez90210
## 6.189e-02 2.799e-02
confint(mod8)
## 2.5 % 97.5 %
## (Intercept) 4.354e+04 4.906e+04
## Mileage -3.650e-01 -2.964e-01
## Zip.Codez30322 -1.477e+03 5.685e+03
## Zip.Codez55105 -6.720e+03 1.969e+03
## Zip.Codez90210 -3.445e+03 3.139e+03
## Mileage:Zip.Codez30322 -4.684e-02 4.721e-02
## Mileage:Zip.Codez55105 1.325e-02 1.105e-01
## Mileage:Zip.Codez90210 -1.488e-02 7.087e-02
xyplot(Cost~Mileage, groups=Zip.Code, data=cars)
modelvalues=makeFun(mod8)
plotFun(modelvalues(Zip.Code="z55105", Mileage=x)~x, add=TRUE)
plotFun(modelvalues(Zip.Code="z02118", Mileage=x)~x, add=TRUE)
plotFun(modelvalues(Zip.Code="z90210", Mileage=x)~x, add=TRUE)
plotFun(modelvalues(Zip.Code="z30322", Mileage=x)~x, add=TRUE)
The average cost of a car with zero miles in Boston is $46,300, and the cost will decrease by $0.33 for every mile driven. The average cost of a car with zero miles in Atlanta is $48,404, and the cost will decreases by $0.33 for every mile driven. The average cost of a car with zero miles in Saint Paul is $43,924, and the cost will decrease by $0.27 for every mile driven. The average cost of a car with zero miles in Los Angeles is $46,147.20, and the cost will decrease by $0.30 f0r every mile driven.
mod5=lm(Cost~Color, data=cars)
coef(mod5)
## (Intercept) ColorBlue ColorGray ColorWhite
## 30533 -7576 -6719 -1376
confint(mod5)
## 2.5 % 97.5 %
## (Intercept) 27701 33364
## ColorBlue -13240 -1912
## ColorGray -10633 -2806
## ColorWhite -6607 3856
The average cost of a black car is $30533. The average cost of a Blue car is $22957 ($7576 less than a Black car). The average cost of a Gray car is $23814 ($6719 less than a Black car). The average cost of a White car is $29157 ($1376 less than a Black car).
mod6=lm(Year~Color, data=cars)
coef(mod6)
## (Intercept) ColorBlue ColorGray ColorWhite
## 2009.1532 -1.8559 -1.4564 -0.6314
confint(mod6)
## 2.5 % 97.5 %
## (Intercept) 2008.431 2009.8755
## ColorBlue -3.301 -0.4112
## ColorGray -2.455 -0.4582
## ColorWhite -1.966 0.7030
The average Year for a Black car is 2009. The average Year for a Blue car is 2007. The average Year for a Gray car is halfway between 2007 and 2008. The average Year for a White car is halfway between 2008 and 2009.
mod7=lm(Cost~Age*Color, data=cars)
coef(mod7)
## (Intercept) Age ColorBlue
## 44666.708 -3674.207 -168.834
## ColorGray ColorWhite Age:ColorBlue
## -1319.469 1159.200 -103.197
## Age:ColorGray Age:ColorWhite
## -9.153 -47.976
confint(mod7)
## 2.5 % 97.5 %
## (Intercept) 43295.4 46038.0
## Age -3932.7 -3415.8
## ColorBlue -3370.1 3032.5
## ColorGray -3383.9 745.0
## ColorWhite -1367.0 3685.4
## Age:ColorBlue -594.9 388.6
## Age:ColorGray -359.3 341.0
## Age:ColorWhite -476.8 380.9
The average cost of a new Black car (Year 2013) is $44,666.71 , and the cost decreases by $3674.21 for every year older the car becomes. The average cost of a new Blue car (Year 2013) is $44,497.88 , and the cost decreases by $3777.41 for every year older the car becomes. The average cost of a new Gray car (Year 2013) is $43,347.24 , and the cost decreases by $3683.36 for every year older the car becomes. The average cost of a new White car (Year 2013) is $43,507.51 , and the cost decreases by $3626.23 for every year older the car becomes.
We did not find any outliers that had a strong influence on our coefficients. When our data was grouped by Zip Code or Color, the 95% confidence intervals showed the model coefficients to be less precise. This could relate to the differing number of cases for each level of these two categories.