Question

You are given the following information concerning a bivariate analysis: N = 12; SEest = 10; SSt = 1100. What is the obtained F score for the analysis? Must have a final F score value, not just the associated equations.

Answer 1

Solution:

Given:

N= 12

SE_est = 10

SST = 1100

We have to find F score

F = MSR / MSE

where

MSR = SSR / df_regression

SSR = SST - SSE

MSE = ( SE_est ) ²

MSE = ( 10 ) ²

MSE = 100

Data is bi-variate, that is one dependent and one independent variable.

df = degrees of freedom

df for Regression = k = Number of independent variables = 1

df for total = N - 1 = 12 - 1 = 11

thus df for error = df Total - df regression = 11 - 1 = 10

Thus we can find SSE = sum of squares due to Error

Since

MSE = SSE / df_error

100 = SSE / 10

Thus SSE = 100 X 10

SSE = 1000

Thus

SSR = SST - SSE

SSR = 1100 - 1000

SSR = 100

Thus

MSR = SSR / df_regression

MSR = 100 / 1

MSR = 100

Thus

F = MSR / MSE

F = 100 /100

F = 1.00

Thus F score = 1.00