Question

A researcher who is evaluating the significance of a regression equation with one predictor variable obtains an F-ratio with df = 1, 16. How many pairs of scores, x and y values, are in the data? Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.

Answer 1

We find the total degree of freedom = Degrees of freedom for Regression + degrees of freedom for error

Total degrees of freedom = 1 + 16 = 17

We know formula for the total number of the degrees of freedom = n -1

Now we compare n-1 and 17

n-1 = 17

n = 17 + 1 = 18

n : means the number of x , y pairs of scores

SS : sum of square

Df: degress of freedom

p : number of regress variable

MS : mean sum of square

Source of variation	SS	df	MS	F
Regression	SSR	p = 1	MSR	F = MSR/MSE
Error	SSE	n-p - 1 = 16	MSE
Total		n - 1 = 17

So Final answer :

Pairs of scores x , y = 18

I hope this will help you :)