Execution of the following 3 R commands will give us the data {(x(i), y(i), z(i), i = 1, 2, ...,100}.

x<-rpois(100, 50)

y<-rpois(100, 100)

z<-rpois(100, 150)

Using this data:

a. Fit the linear regression model of the form z = a +b.x + c.y using,

(i) R

(ii) By obtaining the three normal equations in a, b, and c. Solve these equations

using R and compare the model thus obtained with the model obtained in (i). The

compactness of R commands will be important for this part of the problem. For

example, a single line R command resulting into the formation and solution of the

3 equations shall attract the maximum marks.

Support your solution with appropriate tables involving the data, R commands, and

results obtained from R commands.

b. Fit the 3 models of the form y = a + b.x, y = a + b.x + c.x2

, and y = a.bx

to this data using,

(i) R

(ii) By obtaining two normal equations in a and b (or three normal equations in a, b,

and c). Solve these equations using R and compare the models thus obtained with

the models obtained in (i). The compactness of R commands will again be

important for this part of the problem. For example, a single line R command

resulting into the formation and solution of the 2 equations shall attract the

maximum marks.

(iii) Also, find the coefficient of determination, with the help of formula, for the three

models and decide for the best model.

Again, support your solution with appropriate tables involving the data, R commands,

and results obtained from R commands.