Q2

#PART A
plot(auction$Price~auction$Age)
model <- lm(auction$Price~auction$Age)
summary(model)
abline(model)

#PART B
#Least squares estimate of the intercept:-381.860
#Least squares estimate of the slope: 11.808
#estimated error variance: 249.6^2 = 62300.16

#PART C
# When age if the clock increases by one year, the price increases or decreases by 11.808 pounds sterling.

#PART D
# 62.37% of variation in the response is explained by the values of the predictor.

#PART E
#The F-statistic is 46.42 (2dp) for testing H0: beta1 = 0 versus H1: beta1 is the slope term in the model.
# very large F statistic means
#The corresponding p-value is 2.115e-07, hence we have very strong evidence against the null meaning
# This

#PART F
sqrt(46.42)
# = 6.813222 = observed t test statistic that is equivalent to the Ftest considered in part e
# the computation ofthe p value for the test to be modified to the one sided alternative H1: beta1 > 0
#
6.813222/2

anova(model)

-381.860 + 11.808*170
confint()