The number of initial public offeringe 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 646. The equation of the regression line is y 32.641x+ 17,627.405. Issues, x Proceeds, y 418 469 678 482 478 390 56 64 191 174 0 18,086 28.254 43.358 31,463 36,626 37,262 21,845 10,449) 30,157|29,753 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 646, 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.) OA There is a 95% chance that the predicted proceeds given 646 issues is between S and $ B. We can be 95% confident that when there are 646 issues, the proceeds will be between $ and $
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
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