Question

x:4,5,3,6,10

y:4,6,5,7,7

A.)Determine .95 confidence interval for the mean perdicted when x =7

b.) Determine the .95 perdection interval for an indvidual predicted when x =7

Answer 1

X	Y	XY	X²	Y²
4	4	16	16	16
5	6	30	25	36
3	5	15	9	25
6	7	42	36	49
10	7	70	100	49
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
28	29	173	186	175

Sample size, n =	5
x̅ = Ʃx/n = 28/5 =	5.6
y̅ = Ʃy/n = 29/5 =	5.8
SSxx = Ʃx² - (Ʃx)²/n = 186 - (28)²/5 =	29.2
SSyy = Ʃy² - (Ʃy)²/n = 175 - (29)²/5 =	6.8
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 173 - (28)(29)/5 =	10.6

Slope, b = SSxy/SSxx = 0.3630137

y-intercept, a = y̅ -b* x̅ = 3.76712329

Regression equation :

ŷ = 3.7671 + (0.363) x

Predicted value of y at x = 7

ŷ = 3.7671 + (0.363) * 7 = 6.3082

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 6.8 - (10.6)²/29.2 = 2.95205

Standard error, se = √(SSE/(n-2)) = √(2.95205/(5-2)) = 0.992

Significance level, α = 0.05

Critical value, t_c = T.INV.2T(0.05, 3) = 3.1824

A) 95% confidence interval for the mean predicted when x =7

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B) 95% prediction interval for an individual predicted when x =7