Question

A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table.

LEFT:Watts (x) RIGHT: Minutes (y)

5	8
10	17
20	30
40	33

Compute an analysis of regression for this hypothetical study. (Round your answers to two decimal places.)

Source of Variation	SS	df	MS	Fobt
Regression
Residual (error)
Total

(Answer the blank table slots).

Answer 1

X	Y	XY	X²	Y²
5	8	40	25	64
10	17	170	100	289
20	30	600	400	900
40	33	1320	1600	1089
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
75	88	2130	2125	2342

Sample size, n =	4
x̅ = Ʃx/n =	18.75
y̅ = Ʃy/n =	22
SSxx = Ʃx² - (Ʃx)²/n =	718.75
SSyy = Ʃy² - (Ʃy)²/n =	406
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	480

SSR = SSxy²/SSxx = 480²/718.75 = 320.56

SSE = SSyy - SSxy²/SSxx = 406 - 480²/718.75 = 85.44

SST = SSyy = 406

df_r = 1, df_e = 4-2 = 2

MSR = 320.56/1 = 320.56

MSE = SSR/df_e = 85.44/2 = 42.72

F = MSR/MSE = 320.56/42.72 = 7.50

	SS	df	MS	F
Regression	320.56	1	320.56	7.50
Residual	85.44	2	42.72
Total	406	3