   Chapter 2.4, Problem 34E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

College Basketball: Women The following table shows the number of NCAA women's college basketball teams in the United States for various years since 1990:55 t (years since 1990) 0 5 10 11 12 13 14 Teams 782 864 956 958 975 1,009 1,008 t (years since 1990) 15 16 17 18 19 20 Teams 1,036 1,018 1,003 1,013 1,032 1,036 a. What is the logistic regression model for the data? (Round all coefficients to three significant digits.) At what value does the model predict that the number of basketball teams will level off?b. According to the model, for what value of t is the regression curve steepest? Interpret the answer.c. Interpret the coefficient b in the context of the number of women’s basketball teams.

(a)

To determine

To calculate: A logistic regression model by using technology. At what value does the model predict that the number of basketball team will level off. Round coefficients to three significant figures, the data is given as follows:

 t (years since 1990) 0 5 10 11 12 13 14 Teams 782 864 956 958 975 1,009 1,008 t (years since 1990) 15 16 17 18 19 20 Teams 1,036 1,018 1,003 1,013 1,032 1,036
Explanation

Given Information:

The provided data is:

 t (years since 1990) 0 5 10 11 12 13 14 Teams 782 864 956 958 975 1,009 1,008 t (years since 1990) 15 16 17 18 19 20 Teams 1,036 1,018 1,003 1,013 1,032 1,036

Calculation:

The form of the logistic function is:

f(x)=N1+A(bx)

Where constants N,A

and b

are non-zero (A,bare positive and b1).

There are certain properties of the curve represented by the logistic curve,

1.

The graph of the function formed is S-shaped which is formed by sandwiching between the horizontal lines y=0 and y=N.

2.

If b>1, graph rises, if b<1, the graph falls.

A technological formula refers to the formula used when it is solved using technology that is programming. During programming certain instructions and symbols are already stored within the directory of the programming software. So, it has its own language in which the formula can be interpreted so that it would be comprehend by the software in operation.

Consider the provided data:

 t (years since 1990) 0 5 10 11 12 13 14 Teams 782 864 956 958 975 1,009 1,008 t (years since 1990) 15 16 17 18 19 20 Teams 1,036 1,018 1,003 1,013 1,032 1,036

Now to determine the logistic model y=N1+A(bt) use the Ti-83 calculator as follows:

Step 1: Use STAT EDIT to enter the table of values of the Ti-83 calculator as shown:

L1L2078258641095611</

(b)

To determine

To calculate: The value of t for which the logistic curve is steepest, according to the model.

(c)

To determine

The value of coefficient b

in terms of number of the women’s basketball team.

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