library(readr)
br2 <- read_delim("br2.csv", delim = ";",    escape_double = FALSE, trim_ws = TRUE)
                 

# select only traditional houses 
table(br2$Traditional)

# sub data with traditional style 

br2_traditional <-subset(br2, Traditional==1)

# lm price vs sqft for traditional styple houses 

mod1<-lm(price ~ sqft , data=br2_traditional)
coef(mod1)

# (Intercept)         sqft 
# -28407.55866     73.77195 

summary(mod1)

confint(mod1, level= 0.95)

# Ho: beta2=0
# H1: beta2>=0 (unilateral test with 1 rej area on the right)

# compare p-value with alpha=0.01
# p.value=0.00000
# alpha=0.01 
# p-value<alpha --> we reject the null hyp (coef is sign and positive )



# linear regression model PRICE=b1+b2Traditional 

mod2<-lm(price ~ Traditional, data = br2 )
coef(mod2)
# b2=-24706.88 (price of houses in traditional style is -24706.88 less than the houses in not trad style)
# [-39.000; + 10000] --> coeff NOT sign
# [-39.000; - 10000] --> coeff IS Sign
# [+ 10000; + 39000] --> coeff IS sign

# if 0 value is included in the bound, then the coeff (var x ) is NOT significant in explaing the variable y

confint(mod2, level=0.95)

summary(mod2)

# hipotesis test 
# Ho: beta2=0
# H1  beta2>=0

# plvalue=0.00097
# alpha=0.01 

# conclusion: reject null Hyp 

# ci interpretation = price differencial betw trad and non trad houses range from -39 tousand dollars to - 10 tousand dollars (more or less)