Prestige <-
  read.table('http://math.uttyler.edu/nathan/classes/statistics/data/prestige.data',header=TRUE)

attach(Prestige)
### Up to this point:
plot(education,prestige)
m1 <- lm(prestige ~ education)
abline(m1)
summary(m1)

plot(income,prestige)
m2 <- lm(prestige ~ income)
abline(m2)
summary(m2)


### How do we combine these?

## prestige_i = b_0 + b_1 income + b_2 education + e_i

m3 <- lm(prestige ~ income + education)
summary(m3)


#Call:
#lm(formula = prestige ~ income + education)
#
#Residuals:
#      Min        1Q    Median        3Q       Max 
#-19.40399  -5.33079   0.01542   4.98027  17.68893 
#
#Coefficients:
#              Estimate Std. Error t value Pr(>|t|)    
#(Intercept) -6.8477787  3.2189771  -2.127   0.0359 *  
#income       0.0013612  0.0002242   6.071 2.36e-08 ***
#education    4.1374444  0.3489120  11.858  < 2e-16 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
#
#Residual standard error: 7.81 on 99 degrees of freedom
#Multiple R-squared: 0.798,	Adjusted R-squared: 0.7939 
#F-statistic: 195.6 on 2 and 99 DF,  p-value: < 2.2e-16 

#H0: intercept=0 vs H1: intercept =/= 0, with all other terms in model
# i.e. H0: b_0 = 0 vs H1: b_0 =/= 0

# p.value = .0359 -- reject H0

#H0: income_slope = 0 vs H1: income_slope =/= 0, with all other terms in model
# i.e. H0: b_1 = 0 vs H1: b_1 =/= 0

# p.value = 2.36e-08 = .0000000236 -- reject H0

summary(lm(prestige ~ income + education + census))

summary(lm(prestige ~ census))