Question

2. You perform an analysis of variance to determine whether the slope of your best fit line is different from zero, and calculate an F-ratio of 12.6–you measured 24 randomly sampled individuals from your population of interest.

(a) What are the degrees of freedom for the regression?

(b) What are the degrees of freedom for the residuals?

(c) If the critical value is 4.3, is your P-value greater or less than alpha?

(d) Do you reject or fail to reject your null statistical hypothesis?

Please explain with equations/conceptually

Answer 1

a) The degrees of freedom for the regression is 1 because this is simple regression question and only one independent variable is there.

Degrees of freedom for the regression=1

b) The degrees of freedom for the residual :

Firstly Total degrees of freedom always equal to N-1 where N is sample size

So Total degrees of freedom = N-1=24-1=23

Now we have Total degrees of freedom and regression degrees of freedom

Residual degrees of freedom= Total D.f-Regression d.f

= 23-1=22

Residual degrees of freedom=22

c) F critical= 4.3

F statistic= 12.6

F statistic GREATER than F critical therefore SIGNIFICANT. Therefore in this case

P value SMALLER THAN ALPHA

d) P value smaller than alpha therefore we will REJECT NULL HYPOTHESIS H0.