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# Calculus/Calculus

Question

Modeling with data

The following data gives the median age of women in the united states at first marriage from 1960 through 2000

Decade        1960    1970   1980   1990   2000
Median Age    20.1    21.0   22.0   24.0   25.1

a. Use Cubic Reg to find the third degree polynomial regression model for these data. Let t be measured in decades, with t=0 corresponding in 1960

b. Plot the graph of the polynomial function f found in part (a) using the viewing window [0,4] x [18,28]

c. Where is f increasing? What does this tells us?

d. Verify the results of part (c) analytically

Using regression, it can be seen that a cubic does not fit the data very well at all.
The curve is y = 21.00 + 0.07x³.  That gives

Actual  Approx  Err
20.1   21.00   -0.90
21.0   21.08   -0.08
22.0   21.15    0.85
24.0   21.22    2.78
25.1   21.29    3.81.

Viewing the graph in Excel, the approximation turns out to be an almost straight line when a cubic is used.  This tells me that a lower power should be used.  When using a quadratic, the error is way off.

Using a linear estimation, it fits a lot better.  The result is y = 19.84 + 1.30x.
This gives

Actual  Approx  Err
20.1   19.84    0.26
21   21.14   -0.14
22   22.44   -0.44
24   23.74    0.26
25.1   25.04    0.06.

Calculus

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