the number of initial public offerings of stock issued in a 10-year period and the total...

the number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in million) are shown in the table. Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 576. The equation of the regression line is ý = 32.688x + 17,464.523.

Issues, x 412 458 700 483 483 392 52 75 176 170

proceeds 17,976 29,418 43,736 30,522 36,578 35,848 20,092, 11,034 31,749 28,865

construct and interpret a 95% prediction interval for the proceeds when the number of issues is 576.

select the correct choice below and fill in the answer boxes to complete your choice.
(round to the nearest million dollars as needed. type your answer in standard form where "3.12 million" means 3,120,000)

A. we can be 95% confident that when there are 576 issues, the proceeds will be between $____ and $_____

or
B. There is a 95% chance that the predicted proceeds given 576 issues is between $___ and $____

Solutions

Expert Solution

	X	Y	X * Y	X2	Ŷ	Sxx =Σ (Xi - X̅ )2	Syy = Σ( Yi - Y̅ )2	Sxy = Σ (Xi - X̅ ) * (Yi - Y̅)
	412	17976	7406112	169744	30932.0859	5169.6100	112482993.6400	-762557.0200
	458	29418	13473444	209764	32435.7458	13900.4100	699230.4400	98587.9800
	700	43736	30615200	490000	40346.3047	129528.0100	229649777.6400	5453996.5800
	483	30522	14742126	233289	33252.9523	20420.4100	3764376.0400	277254.5800
	483	36578	17667174	233289	33252.9523	20420.4100	63939214.4400	1142656.9800
	392	35848	14052416	153664	30278.3207	2693.6100	52797662.4400	377115.7800
	52	20092	1044784	2704	19164.3123	83001.6100	72076704.0400	2445911.3800
	75	11034	827550	5625	19916.1423	70278.0100	307925284.8400	4651921.7800
	176	31749	5587824	30976	23217.6566	26928.8100	10031155.8400	-519737.5200
	170	28865	4907050	28900	23021.5270	28934.0100	80202.2400	-48172.3200
Total	3401	285818	110323680	1557955	283446.3735	401274.9000	853446601.6000	13116978.2000

X̅ = Σ (Xi / n ) = 3401/10 = 340.1
Y̅ = Σ (Yi / n ) = 285818/10 = 28581.8

Estimated Error Variance (σ̂2) =
S2 = ( 853446601.6 - 32.6883 * 13116978.2 ) / 10 - 2
S2 = 53084360.3881
S = 7285.9015

Predictive Confidence Interval of
Ŷ = 17464.5228 + 32.6883X
Ŷ = 36292.9836

t(α/2) = t(0.05/2) = 2.306
X̅ = (Xi / n ) = 3401/10 = 340.1
= 36292.9836

95% Predictive confidence interval is (17593.8208 < < 5 4992.1464)

A. we can be 95% confident that when there are 576 issues, the proceeds will be between $____ and $_____

orchestra answered 1 year ago

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