Question

Part A

Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the slope coefficient Beta1. Provide your answer with three decimal places of precision, e.g. 0.001.

Part B

Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the intercept Beta0.  Provide your answer with three decimal places of precision, e.g. 0.001.

Answer 1

In a simple linear regression model , the equation of the straight line is of the form :

                                           y = a+bx

             where a and b are coeffecients to be calculated such the sum of squares due to error is minimum.

The coeffecients a and b are evaluated using :

                                    $a=\overline{y}-b\overline{x}$             (1)

           and,                 $b=Cov(X,Y)/Var(X)$         (2)

In Part A :

           Cov(X,Y) = 2.4 , Var(X)=1..2 , $\overline{x}$=9.6 and $\overline{y}$=23.4

   We are to find the slope coeffecient b which is found using equation (2) :

                            b = 2.4 /1.2

                              = 2    (Ans)

In Part B :

   We are to find the intecept which is found by using equation (1) :

                           a = 23.4 - (2*9.6)

                              = 4.2 (Ans)