set.seed(02119)

y<- round(runif(20, 2, 9), 3)

x1<- round(y*25*(1-runif(20, -0.7, 0.7)), 3)

x2<- c(rep("East", 5), rep("West", 5), rep("North", 5), rep("South", 5))

x3<- round(y*(1-runif(20, -0.5, 0.5)), 3)

For the purpose of the exam, the generated variables represent the following:

y - "selling price of a house in 2021" in 100,000 USD

x1 - "square footage" in sq. m.

x2 - "location within the city - East/West/North/South"

x3 - "selling price of a house in 2020" in 100,000 USD

Now perform the ANCOVA analysis using the following code:

summary(aov(y~x2+x3))

Copy the output from R in your report and answer the following questions:

- What are the null and alternative hypotheses behind this analysis of covariance? NB:

For the null and alternative hypotheses provide both the formula and explain the

hypotheses in words (using the information of what the variables represent)

- Have you got evidence to suggest that the variable x3 is an important covariate?

Justify your answer with as much details as possible