Reference no: EM132583612

Questions -

Question 1 - Write a function in R to perform the linear regression. You are not allowed to use any linear regression specific functions or any package. Your function should take two inputs namely Y vector and the design matrix X. You need to apply your custom-built function on the following data:

n = 20

X1i = rnorm(n, 10, 2)

X2i = rbeta(n, 2, 3)

Y = -2 - 3*X1i + 4*X2i + rnorm(n)

Also, apply this function on the data data_for_problem_1.xlsx to predict PCB using THICKNESS. Perform the residual analysis to validate the working of your function.

Question 2 - Write a function from scratch which can perform the t-testing for any data (i.e. one-sample, two samples etc. ) in R. This function should mimic the base function t.test(). Use your function to perform t-testing on the following simulated data:

# simulate the data

xi1 = rnorm(20, 3, sqrt(9))

xi2 = 2*xi1

You are not allowed to use any R-package for these task.