Question

1. DEFINE THE COMPONENTS OF A GENERAL MULTIPLE REGRESSION EQUATION.
2. IN A MULTIPLE REGRESSION ANOVA TABLE, THE DEGREES OF FREDOM FOR THE REGRESSION IS EQUAL TO:
3. THE TEST TO CONFIRM WHETHER THE DEPENDENT VARIABLE CAN BE ESTIMATED WITHOUT RELYING ON THE INDEPENDENT VARIABLES IS REFERRED TO AS:
4. WHAT STATISITIC WOULD WE USE FOR TESTING TO SEE IF AT LEAST ONE INDEPENDENT REGRESSION COEFFICIENTS IS SIGNIFICANT?
5. TO TEST INDEPENDENT VARIABLES INDIVIDUALLY TO DETERMINE WHETHER THE REGRESSION COEFFICIENTS DIFFER FROM ZERO WOULD BE:
6. WHAT ARE THE ASSUMPTIONS FOR MULTIPLE REGRESSION?
7. IF AN INDIVIDUAL COEFFICIENT HAS A P VALUE OF LESS THAT 0.05 (LEVEL OF SIGNIFICANCE) YOU WOULD (DISCARD / KEEP) THE COEFFICIENT IN THE MODEL. SELECT ONE.
8. YOUR SUM OF SQUARES FOR THE REGRESSION = 119 AND YOUR TOTAL SUM OF SQUARES = 166. YOU HAD 5 FACTORS AND 25 SAMPLES IN YOUR EVALUATION. WHAT IS YOUR COEFFICIENT OF MULTIPLE DETERMINATION?
9. FOR 8 – WHAT WOULD YOUR F CALCULATED BE?

Answer 1

Components of a general multiple linear regression model

Y = XB + U

Y is the vector of dependent variable of order n×1

X is the matrix of independent variable of order n×k

B is the vector of OLS cofficients of order k × 1

U is the vector of residuals of order n × 1

n is the number of observations, k is the total number of independent variables

DEGREE OF FREEDOM FOR REGRESSION

= k-1, in a model with k-1 explantory variables

TO TEST OVERALL SIGNIFICANCE OF REGRESSION

F test should be used, F = MSR/MSE, where MSR = mean regression sum of squares, MSE = mean error sum of square

TO TEST INDIVIDUAL SIGNIFICANCE OF INDEPENDENT VARIABLES

T - test, T = B^/s.e(B^), where B^ is the estimated cofficient and s.e is the standard error of the corresponding cofficient

ASSUMPTIONS OF A MULTIPLE LINEAR REGRESSION

1. Matrix of X should be non-stochastic

2. E(U/X) = 0, conditional expectation of U given X, is 0.

3. No perfect multicollinearity among covariates,i.e Rank(X) = k

3. No autocorrelation Cov(U,X) = 0

4. Hetroskadasticity, Variance(U) = constant

IF P VALUE IS LESS THAN 0.05

we should keep that variable, as it is statistically significant at 5% level of significance.

COFFICIENT OF DETERMINATION

R² =[ SSE/(n-k+1)] / [TSS/n-1]

and SSE = TSS - SSR = 166 - 119 = 47

R² = (47/25-5+1) /(166/25-1) = 0.32