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

Solution

IN A MULTIPLE REGRESSION ANOVA TABLE, THE DEGREES OF FREDOM FOR THE REGRESSION IS EQUAL TO

Answer : Total number of independent variables - 1

THE TEST TO CONFIRM WHETHER THE DEPENDENT VARIABLE CAN BE ESTIMATED WITHOUT RELYING ON THE INDEPENDENT VARIABLES IS REFERRED TO AS

Answer : ANOVA ( Analysis of variance)

WHAT STATISITIC WOULD WE USE FOR TESTING TO SEE IF AT LEAST ONE INDEPENDENT REGRESSION COEFFICIENTS IS SIGNIFICANT?

Answer : F -statistics

F -statistics = MSR/MSE

TO TEST INDEPENDENT VARIABLES INDIVIDUALLY TO DETERMINE WHETHER THE REGRESSION COEFFICIENTS DIFFER FROM ZERO WOULD BE

Answer : Significance of Regression Coefficients.

IF AN INDIVIDUAL COEFFICIENT HAS A P VALUE OF LESS THAT 0.05 (LEVEL OF SIGNIFICANCE) YOU WOULD KEEP THE COEFFICIENT IN THE MODEL.

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

COEFFICIENT OF MULTIPLE DETERMINATION = SSR/TSS

COEFFICIENT OF MULTIPLE DETERMINATION = 119 /166 = 0.7169

WHAT WOULD YOUR F CALCULATED BE

SSE = TSS- SSR

SSE = 166 -119 = 47

MSE = SSE / Degrees of freedom for Error

MSE = 47/ 20 = 2.35

MSR = SSR / Degrees of freedom for Regression

MSR = 119 /4 = 29.75

F = MSR/MSE

F = 2.35/29.75

F = 0.0790