Question

A simple linear regression model based on 26 observations. The F-stat for the model is 6.45 and the standard error for the coefficient of X is 0.2. MSR = 54.75

Complete an ANOVA table.
Find the t-stat and the coefficient of X.
Find R2.

Answer 1

Solution:

Given:

F = 6.45

MSR= 54.75

Part a) Complete ANOVA table:

Source	SS	DF	MS	F
regression	SSR	dfregression	54.75	6.45
Error	SSE	dferror	MSE
Total	SST	dftotal

We have to find above blank entries.

Thus we use following steps:

We know

F = MSR / MSE

then

MSE = MSR / F

MSE = 54.75 / 6.45

MSE = 8.488372

Since this is simple linear regression, we have k = number of independent variables = 1

thus df_regression = k = 1

N = 26

then df_total = N - 1 = 26 - 1 = 25

and

df_error = N - k - 1 = 26 - 1 - 1 = 24

Now find SS

MSR = SSR /  df_regression  

then

SSR = MSR X df_regression  

SSR = 54.75 X 1

SSR = 54.75

MSE = SSE / df_error

then

SSE = MSE X df_error

SSE = 8.488372 X 24

SSE = 203.720930

and

SST = SSR + SSE

SST = 54.75 + 203.720930

SST = 258.470930

Thus we get ANOVA table:

Source	SS	DF	MS	F
regression	54.75	1	54.75	6.45
Error	203.720930	24	8.488372
Total	258.470930	25

Part b) Find the t-stat and the coefficient of X.

We know
F = t²

then

Coefficient of X is Slope = b₁

Part c) Find R²