Question

What is the hypothesis that the ANOVA F-test is used for a multiple regression model Y = ?0 + ?1 X1+ ?2 X2+ ?3 X3 + A. H0: ?1 = ?2 = ?3 =0, H1: At least ?i ? 0 B. H0: At least ?i ? 0, H1: ?1 = ?1 = ?2 =0 C. H0: ?1 = ?2 = ?3, H1: At least ?i ? ?j D. H0: ?0 = ?1 = ?2 = ?3, H1: At least ?i ? ?j

Answer 1

Answer:

So the correct option for this case would be C:

H0:$\beta_1 =\beta_2 =\beta_3$

H1: At least one $\beta_i \neq \beta_j , i,j=1,2,3$

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

When we conduct an ANOVA test to test the coefficients for the regression, the correct system of hypothesis are:

The hypothesis for this case are:

Null hypothesis: $\beta_{1}=\beta_{2}=\beta_{3}$

Or on other words we want to check if each variable X1, X2 and X3 NOT have a significant effect on the regression.

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=1,2,3$

Or on other words we want to check if at least one of the variables( X1, X2 or X3), have a significant effect on the regression.

So the correct option for this case would be C:

H0:$\beta_1 =\beta_2 =\beta_3$

H1: At least one $\beta_i \neq \beta_j , i,j=1,2,3$