Polyval returning different values than when manually making an equation with polyfit.

If I have this set of data:

 year = [1928 1932 1936 1948 1952 1956 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000];
 finish = [12.2 11.9 11.5 11.9 11.5 11.5 11.4 11.08 11.07 11.08 11.06 10.97 10.54 10.82 10.94 10.75];

and find the line of best fit using polyfit:

 Fit1=polyfit(year,finish,1)

This returns an array of:

 [-0.0185 47.6837]

If I use polyval to get the y-values of the line of best fit:

 mypoly = polyval(Fit1, year)

I get these values:

 11.9852   11.9112   11.8371   11.6149   11.5409   11.4668   11.3187   11.2446   11.1705   11.0965   11.0224   10.9484   10.8743   10.8002   10.7262   10.6521

However, if I make an equation myself using the values from Fit1:

 myequ = -0.0185*year + 47.6837

I get:

 12.0157   11.9417   11.8677   11.6457   11.5717   11.4977   11.3497   11.2757   11.2017   11.1277   11.0537   10.9797   10.9057   10.8317   10.7577   10.6837

Why are the values different? Aren't polyval and my equation supposed to do the same thing?

The thing that's even more strange is when I make an array the has the same values of Fit1 and compare them using isequal, it returns 0(not equal)

 Fit1Copy = [-0.0185 47.6837];
 comparefit = isequal(Fit1,Fit1Copy)

Returns

 0

What's going on!!!??

Answer 1

[John D'Errico]

What is going in is you don't understand that MATLAB does not print out every digit of a number that is stored. If it did, you would quickly ask how to display only a few digits. (And, yes, that is a common question asked by people, those who have the format setting at a longer value.)

Fit1=polyfit(year,finish,1)
Fit1 =
    -0.018516       47.684

format long g
Fit1=polyfit(year,finish,1)
Fit1 =
       -0.0185157815631264          47.6836673346697

In the second case, I told MATLAB to use a longer display format. There is a difference. So when you used the APPROXIMATE values displayed in the command window, you got different numbers. Why should you be remotely surprised? If you use different numbers you WILL get different prediction.

Note that in fact, even the numbers displayed with "format long g" are STILL only approximate.