Question

1. Using the data Anscombe, included in the car package, perform a regression to examine whether the number of people living in an urban area have an effect on income. Remember to provide the code for everything. Hint: load data from the package with the following command A<-Anscombe you’re going to need the car package

install.packages(“car”)

library(car)

income = y

urban = x

obs: this is not code, it’s just identifying x and y for you.

1. Report the coefficients for urban.
2. Interpret the model’s R squared.
3. For the variance that is not explained by the model, what is the explanation?
4. Can we say that there is a linear relationship between income and urban?

Answer 1

Answer a. The estimated linear regression model is given as:

Income = a + b*Urban

Here, the regression coefficients are given as: Intercept, a = 1539.817 and Slope, b = 2.5364

So, estimated linear Regression Model is : Income = 1539.817 + 2.5364*Urban

Answer b.

Model R-squared is given in the Regression Summary Output as 0.4699 which means that 46.99% or 47% of the total variation in Income is explained by the variable Urban

Answer c.

The Unexplained Variation is the Sum of Squares due to Error which is given as 8313481 which expressed as sum of Total Variation is given as 1- Rsquared = 0.5301

This means that 53.01% of the total Variation in Income is not explained by the variable Urban

Answer d.

SInce p- value = 2.866e-08 < 0.05 say so we say that there is significant correlation between Income and Urban.

R-Output: