Question

The number of initial public offerings of stock issued in a​ 10-year period and the total proceeds of these offerings​ (in millions) are shown in the table. Construct and interpret a​ 95% prediction interval for the proceeds when the number of issues is

585.

The equation of the regression line is

ModifyingAbove y with caret equals 33.634 x plus 17 comma 224.539y=33.634x+17,224.539.

​Issues, x	404	453	679	483	479	394	50	73	175	175
​Proceeds, y	19,308	29,108	43,643	31,033	35,712	35,665	21,501	10,090	31,384	27,981

Construct and interpret a​ 95% prediction interval for the proceeds when the number of issues is

585.

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 585 issues, the proceeds will be between $____ and ​$____.

B.There is a​ 95% chance that the predicted proceeds given 585 issues is between ​$____ and ​$____.

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
404	19,308	4556.25	85275990	-623329
453	29,108	13572.25	319790.3	65880.75
679	43,643	117306.25	2.28E+08	5171921
483	31,033	21462.25	6202590	364858.3
479	35,712	20306.25	51401730	1021654
394	35,665	3306.25	50730006	409543.8
50	21,501	82082.25	49582722	2017390
73	10,090	69432.25	3.4E+08	4862234
175	31,384	26082.25	8074122	-458902
175	27,981	26082.25	315282.3	90682.25

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	3365	285425	384188.5	8.2E+08	12921933
mean	336.5	28542.5	SSxx	SSyy	SSxy

sample size ,   n =   10          
here, x̅ =   336.5       ȳ =   28542.5  
                  
SSxx =    Σ(x-x̅)² =    384188.5          
SSxy=   Σ(x-x̅)(y-ȳ) =   12921932.5          
                  
slope ,    ß1 = SSxy/SSxx =   33.63435527          
                  
intercept,   ß0 = y̅-ß1* x̄ =   17224.53945          
                  
so, regression line is   Ŷ =   17224.5395   +   33.6344   *x
                  
SSE=   (Sx*Sy - S²xy)/Sx =    385801222.01          
                  
std error ,Se =    √(SSE/(n-2)) =    6944.4332          

----------------

X Value=   585
Confidence Level=   95%
  
  
Sample Size , n=   10
Degrees of Freedom,df=n-2 =   8
critical t Value=tα/2 =   2.306 [using t table]
X̅ =    336.500
Σ(x-x̅)² =Sxx = 384188.500
Standard Error of the Estimate,Se=   6944.433
h Statistic = (1/n+(X-X̅)²/Sxx) =    0.261
Predicted Y (YHat) at x=585 is 36900.637

standard error, S(ŷ)=Se*√(1+h stat) =    7797.3779

margin of error,E=t*std error=t/S(ŷ)=    17980.7856
Prediction Interval Lower Limit=Ŷ -E =   18919.8517 million
Prediction Interval Upper Limit=Ŷ +E =   54881.4229 million

B.There is a​ 95% chance that the predicted proceeds given 585 issues is between ​$_18920million___ and ​$__54881million__.