Please anwer all the question, thanks!!! Suppose we begin with the following reg
ID: 3124828 • Letter: P
Question
Please anwer all the question, thanks!!!
Suppose we begin with the following regression model: Y_i = beta_0 + beta_1X_i + epsiloni answer the questions in parts (1) and (2). Using the formulae for estimating beta_1 and beta_0 under OLS, show what will happen to these estimated coefficients if we add a constant, say 1, to the dependent variable. Using the formulae for estimating beta_1 and beta_0 under OLS, show what will happen to these estimated coefficients if we add a constant, say 1, to the independent variable.Explanation / Answer
The regression coeff. are given by:
b0 = (y-mean) - b1 (x-mean)
b1 = Cov ( X,Y) / Var (X)
Adding a constant to either X or Y, would not change the value of b1 because it is expressed as a measure of dispersion.
However, b0 values will change.
When, +1 is added to dependent variable (Y), the mean value of Y increases by 1, and so b0 value will increase by 1.
Whereas, when +1 is added to the independent variable (X), the mean value of X increases by 1 and the since b0 = (y-mean) - b1 (x-mean), the value of bo will reduce by (b1)
Hope this helps.
P.S: (I am adding a numerical example to help and prove the statements.
X Y 2 3.2 4 4.5 7 7.9 9 10.1 10 11.2 15 16.5 16 17.9 20 22