Quad Regression: model to fit data on year, num of hospitals

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juliemariefort

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Apr 3, 2009
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Year Number of hospitals in the U.S. for various years
1950 1 6788
1975 25 7156
1990 40 6649
1995 45 6291
2000 50 5810
2005 55 ???

When I fit a quadratic function to the data to figure out what the number of hospitals will be in 2005, I get 5,362. Would someone mind checking this? It doesn’t seem right to me.

I get for y = ax^2 + bx + c:

- 1.45x^2 + 54.94x + 6726.64 =

- 1.45(55)^2 + 54.94(55) + 6726.64 =

= 5,362.09

= 5,362
 
juliemariefort said:
… It doesn’t seem right to me …
Click to expand...


You're very perceptive. It's off by 2. :wink:

You probably have the correct quadratic polynomial. The actual number of hospitals (per this model) when x = 55 is 5,364. The reason for your slightly-lower result is called "round-off error".

To get the more-precise number, round your coefficients A, B, and C to four decimal places, instead of two.

When we use regression to find an equation to model data like this, we often need to increase the number of decimals in our approximate values, in order to increase the precision of our result(s).

 
Re: Quad Regression

juliemariefort said:
Code: 
Year		Number of hospitals in the U.S. for various years
1950	0	6788 <--- the first year should be zero.
1975	25	7156
1990	40	6649
1995	45	6291
2000	50	5810
2005	55	???
When I fit a quadratic function to the data to figure out what the number of hospitals will be in 2005, I get 5,362. Would someone mind checking this? It doesn’t seem right to me.

I get for y = ax^2 + bx + c:

- 1.45x^2 + 54.94x + 6726.64 = <---- how did you get these numbers?

- 1.45(55)^2 + 54.94(55) + 6726.64 =

= 5,362.09

= 5,362
Click to expand...
 
Re: Quad Regression

I thought it should be "0" too, but my instructor said that it should be "1."

a = -1.4078
b = 51.8546
c = 6780.0498

y = ax^2 + bx + c

y = - 1.4078 (55)^2 + 51.8546 (55) + 6780.0498

y = 5373.4578

y = 5373

How about this?
 
Re: Quad Regression

Depending on which software/hardware you used find those coefficients - those look reasonable.
 
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