Question

In: Statistics and Probability

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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