Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 6 12 14

Question

Question

Given are five observations for two variables, x and y.

xi 1 2 3 4 5

yi 3 8 6 12 14

Given are five observations for two variables, x and y. 1 2 3 4 5 Xi 3 6 12 14 Уi The estimated regression equation is y = 0.

c. Compute the estimated standard deviation b 1 using the following equation (to 3 decimals) Sp d. Use the t test to test the

e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Complete the F table below. Calculate th

math Statistics-And-Probability

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Answer 1

Answer #1

S.No	X	Y	(x-x̅)²	(y-y̅)²	(x-x̅)(y-y̅)
1	1	3	4.0000	31.3600	11.2000
2	2	8	1.0000	0.3600	0.6000
3	3	6	0.0000	6.7600	0.0000
4	4	12	1.0000	11.5600	3.4000
5	5	14	4.0000	29.1600	10.8000
Total	15	43	10.0000	79.2000	26.0000
Mean	3.000	8.600	SSX	SSY	SXY

SSE =Syy-(Sxy)²/Sxx=

11.600

a)

error Variance σ² =

s² =SSE/(n-2)

=

3.867

b)

std error σ =

se =√s²

=

1.966

c)

estimated standard error of slope =se(β₁) =

s/√S_xx=

0.622

d)

test stat t =	β₁/se(β₁)=	=	4.18

p value:		=	0.0249

e)

Source	DF	SS	MS	F
regression	1	67.6	67.600	17.48
Residual error	3	11.6	3.867
Total	4	79.2

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Answer 2

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