Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 602. 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 andinterpret a 95% prediction interval for the proceeds when the number of issues is 602. The equation of the regression line is y = 33.481x + 17,073.355.Issues, xProceeds, y68774199169 e18,065 29,450 43,070 30,672 37,118 35,408 21,529| 10,249 30,894 28,983416 458490479 39856Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 602.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.)O A. There is a 95% chance that the predicted proceeds given 602 issues is between Sand $O B. We can be 95% confident that when there are 602 issues, the proceeds will be between $and $

Name: Construct and interpret a 95% prediction interval for the proceeds wh
Uploaded: 2024-03-20T06:46:03.000Z
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Description: Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 602. 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

1] n=10 2] The equation of the regression line is y^=33.481x+17073.355 x y 416 18065 458 29450 687 43070 490 30672 479 37118 398 35408 74 21529 56 10249 199 30894 169 28983The sum of squares obtained from the above table: SSxx=∑i=1nxi2-1n×∑i=1nxi2=1559508-110×34262SSxx=385760.4SSyy=∑i=1nyi2-1n×∑i=1nyi2=8983908964-110×2854382SSyy=836423780SSxy=∑i=1nxiyi-1n×∑i=1nxi×∑i=1nyi=110706539-110×3426×285438SSxy=12915480now we have to calculate slope and y intercept coefficentβ1^=SSxySSxx=12915480385760.4=33.480576β0^=Y^-β1^×X^Y^=28543810=28543.8X^=342610=342.6β0^=Y^-β1^×X^=28543.8-33.480576×342.6=17073.355therefore regression line is y^=33.481x+17073.355we can compute the predicted value for x=602y^=33.481×602+17073.355y^=37228.917Now we have to calculate SStotal,SSregression,SSerror as followsSStotal=SSyy=836423780SSregression=β1^×SSxy=33.481×12915480SSregression=432423193SSerror =SStotal-SSregression=836423780-432423193SSerror =404000587now to calculate mean squared errorMSE=SSerror n-2=4040005878MSE=50500073By taking square root of MSE we get Standard errorof estimatesσ^=50500073σ^=7106.3404Since we want compute 95% prediction interval for predicted value 37228.917 the level of significance α=0.05 the critical value for df=n-2=10-2=8tcrit=2.306now we calculate error of the prediction intervalE=tα2,n-2σ^21+1n+x-x^2SSxx=2.306×7106.340421+110+602-342.62385760.4=18499.68Hence, 95% prediction interval for predicted value y^=37228.917 is,PI=37228.917-E,37228.917+E=37228.917-18499.68,37228.917+18499.68=18729.24,55728.59 option (B) we can be 95% confident that when there are 602 issues the proceeds will be between $18729.24 and $55728.59.