Question

Consider the following set of ordered pairs.

x	5	1	2	4	4
y	6	1	0	6	5

Calculate the coefficient of determination and test its significance using α=0.05.

A. Calculate the coefficient of determination.

R^2equals=

B. Determine the null and alternative hypotheses.

Determine the critical​ F-score, Fα.

Fα=

​(Round to three decimal places as​ needed.)

Calculate the​ F-score for this test.

F=

​(Round to three decimal places as​ needed.)

Reject or Do not reject?

Answer 1

ΣX = 16
ΣY = 18
ΣX * Y = 75
ΣX2 = 62
ΣY2 = 98

Part a)

r = 0.919

Coefficient of Determination
= 0.844

SSE =Σ(Y - Ŷ)2 =    5.167
SST = Σ(Yi - Y̅ )2 =    33.200
SSR = Σ( Ŷ - Y̅ )2 =    28.033

Part b)

Critical value f(0.05 , 1 , 3 ) = 10.128 ( from f table )

Part c)

Test Statistic :-
f = SSR / ( SSE / ( n - 2 ) )
f = 16.277

Test Criteria :-
Reject null hypothesis if f > f(α,1,n-2)
f(0.05 , 1 , 3 ) = 10.128
f > f(0.05,1 , n-2 ) = 16.27729 > 10.128 , hence we reject the null hypothesis

We reject H0.