Question

Please write the answer in standard form.

9.3.21 E Questio The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millins) are shown in the table. Cons nte pret a 95% prediction interval for the pr eeds when the number of issues is 630. The equation of the regression line is y:32 242x + 17,847 713. Issues, x Proceeds, y 424 462 688 476 491 380 50 71 191 158 19,12428,693 43,655 32.358 36,720 35,468 22,116 11.546 30,306 27823 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 630. 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 milion" means 3,120,000) We can be 95% confident that when there are 630 issues, the proceeds wil be between S There is a 95% chance that the predicted proceeds given 630 issues is between S and S OA and S 0 B.

Answer 1

X	Y	XY	X²	Y²
424	19124	8108576	179776	365727376
462	28693	13256166	213444	823288249
688	43655	30034640	473344	1905759025
476	32358	15402408	226576	1047040164
491	36720	18029520	241081	1348358400
380	35468	13477840	144400	1257979024
50	22116	1105800	2500	489117456
71	11546	819766	5041	133310116
191	30306	5788446	36481	918453636
158	27823	4396034	24964	774119329

Sample size, n =	10
Ʃ x =	3391
Ʃ y =	287809
Ʃ xy =	110419196
Ʃ x² =	1547607
Ʃ y² =	9063152775
x̅ =	339.1
y̅ =	28780.9
SSxx = Ʃx² - (Ʃx)²/n =	397718.9
SSyy = Ʃy² - (Ʃy)²/n =	779750726.9
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	12823164.1
Sum of Square error, SSE = SSyy -b*Ssxy =	366309129
Standard error, se = √(SSE/(n-2)) =	6766.73046

Regression equation :               

ŷ = 17847.713 + 32.242 x

Predicted value at X =   630          

ŷ = 17847.713 + 32.2418 * 630 = 38160.047

At α = 0.05 and df = n-2 = 8, critical value, tc = T.INV.2T(0.05, 8 ) =   2.306

95% prediction interval:

$\\ \\ \left( \hat y\pm t_c*se\sqrt{1+\frac{1}{n}+\frac{(x-\bar x)^2}{SS_{xx}}} \right ) \\ \\ \left ( 38160.047 \pm 2.306 * 6766.73046 \sqrt{1+\frac{1}{ 10 }+\frac{(630 -339.1 )^2}{ 397718.9 }}\right ) \\ \\ \textbf{ ( 20281.440 , 56038.626 )}$

Answer B:

There is a 95% chance that the predicted proceeds given 630 issues is between $ 20281440000 and $ 56038626000.