//Regression With Categorical Variables
//created by John M. Quick
//http://www.johnmquick.com
//December 15, 2009

> #read data into variable
> datavar <- read.csv("dataset_nflQbSalary.csv")

> #attach data variable
> attach(datavar)

> #display all data
> datavar
         TEAM   QB TOTAL CONF
1       49ERS  900 17256  NFC
2       BEARS 3000 23074  NFC
3     BENGALS 1050 20666  AFC
4       BILLS  650 24249  AFC
5     BRONCOS  500 21992  AFC
6      BROWNS  967 19413  AFC
7  BUCCANEERS  675 19545  NFC
8   CARDINALS 1450 20397  NFC
9    CHARGERS 1200 18698  AFC
10     CHIEFS 1100 25859  AFC
11      COLTS 2000 22022  AFC
12    COWBOYS 1750 28349  NFC
13   DOLPHINS 1400 23738  AFC
14     EAGLES  425 19325  NFC
15    FALCONS 2250 25642  NFC
16     GIANTS 1600 23258  NFC
17       JETS  800 19063  AFC
18      LIONS 1525 24644  NFC
19     OILERS 1700 21399  AFC
20    PACKERS 1500 23245  NFC
21   PATRIOTS 2250 23294  AFC
22    RAIDERS 1300 20390  AFC
23       RAMS 1500 24378  NFC
24   REDSKINS 1450 20780  NFC
25     SAINTS 1200 23695  NFC
26   SEAHAWKS 1250 25348  AFC
27   STEELERS 3500 30131  AFC
28    VIKINGS 1250 23246  NFC

> #represent a categorical variable numerically using as.numeric(VAR)
> #dummy code the CONF variable into NFC = 1 and AFC = 0
> dCONF <- as.numeric(CONF) - 1

> #use the plot() function to create a box plot
> #what does the relationship between conference and team salary look like?
> plot(CONF, TOTAL, main="Team Salary by Conference", xlab="Conference", ylab="Salary ($1,000s)")

> #what are the mean and standard deviation of conference?
> mean(dCONF)
[1] 0.5
> sd(dCONF)
[1] 0.5091751
> #this makes senseÉ there are an even number of teams in both conferences and they are coded as either 0 or 1!
> #what is the correlation between total team salary and conference?
> cor(dCONF, TOTAL)
[1] 0.007019319

> #create a linear model using lm(FORMULA, DATAVAR)
> #predict team salary using quarterback salary and conference
> linearModel <- lm(TOTAL ~ QB + dCONF, datavar)
> #generate model summary
> summary(linearModel)

Call:
lm(formula = TOTAL ~ QB + dCONF, data = datavar)

Residuals:
    Min      1Q  Median      3Q     Max 
-3977.2 -1960.9  -221.3  1669.4  5003.6 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 19099.3562  1183.1760  16.142 9.88e-15 ***
QB              2.4849     0.6945   3.578  0.00145 ** 
dCONF        -102.5585   947.5246  -0.108  0.91467    
---
Signif. codes:  0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 

Residual standard error: 2505 on 25 degrees of freedom
Multiple R-squared: 0.3387,	Adjusted R-squared: 0.2858 
F-statistic: 6.402 on 2 and 25 DF,  p-value: 0.005688 

> #input the categorical values to split the linear model into two representations
> #the original model: TOTAL = 19099 + 2.5 * QB - 103 * dCONF
> #substitute 0 for dCONF to derive the AFC model: TOTAL = 19099 + 2.5 * QB
> #substitute 1 for dCONF to derive the NFC model: TOTAL = 18996 + 2.5 * QB
> #what is the predicted salary for a team with a quarterback salary of $2,000,000 in the AFC and NFC conferences?
> #AFC prediction
> 19099 + 2.5 * 2000
[1] 24099
> #NFC prediction
> 18996 + 2.5 * 2000
[1] 23996