Wikipedia:Reference desk/Archives/Mathematics/2014 May 19

= May 19 =

predicting results from a trend
I have this graph (http://dota2.cyborgmatt.com/prizetracker/international2014) that I want to extend to see the predicted results at any day. I've been out of school too long to know how to do this. I would love an explanation of what to do with this set of data. I'm nearly sure it's quadratic in nature. Oh and the daily tracker is good enough, don't need to use the hourly tracker. Thanks  Bluefist  talk  05:37, 19 May 2014 (UTC)
 * Do you have a set of data or do you only have the graph? The graph looks like $$y_i \approx \sqrt{a(x_i-b)}$$, so if you have $$(x_i,y_i)$$ you should compute $$(x_i,y_i^2)$$ and make a regression analysis to find reasonable values for a and b. Bo Jacoby (talk) 17:58, 19 May 2014 (UTC).
 * If you hover over the points it tells you the data in a popup. Also I don't know how to do any of that.  Bluefist  talk  16:19, 20 May 2014 (UTC)

The data are these: x    y  0 1600000 1 2682056 2 3412386  3 3887103  4 4359369  5 4751090  6 5032238  7 5293739  8 5556659  9 5757481 10 5920247 Subtract y0 from the y-column. 0      0  1 1082056  2 1812386  3 2287103  4 2759369  5 3151090  6 3432238  7 3693739  8 3956659  9 4157481 10 4320247 Then divide by y10−y0 0 0.000000 1 0.250462  2 0.419510  3 0.529392  4 0.638706  5 0.729377  6 0.794454  7 0.854983  8 0.915841  9 0.962325 10 1.000000 Square the y-values, and multiply by 10 0 0.00000  1  0.62731  2  1.75988  3  2.80256  4  4.07946  5  5.31991  6  6.31157  7  7.30996  8  8.38765  9  9.26069 10 10.00000 The two columns are now reasonably equal. $$x\approx 10\left(\frac{y-y_0}{y_{10}-y_0}\right)^2$$ and so $$y\approx y_0+(y_{10}-y_0)\sqrt{\frac{x}{10}}$$. This formula does what you requested: the predicted results (y) at any day (x). Note that y0 = 1600000 and y10 = 5920247. Bo Jacoby (talk) 22:30, 20 May 2014 (UTC).

Logarithmic operation
Is there any logarithmic operation of adding 1?? We know that (defining the logarithmic operation of an operation as the operation that relates the binary logarithms of the numbers the way the original operation relates the original numbers):


 * The logarithmic operation of doubling is adding 1.
 * The logarithmic operation of squaring is doubling.
 * The logarithmic operation of raising a number to the power of its binary logarithm is squaring.

But what operation is there that can be the logarithmic operation of adding 1?? Georgia guy (talk) 15:36, 19 May 2014 (UTC)


 * See List of logarithmic identities, especially the summation/subtraction section of that article. The formal answer to you question is "raising 2 to the power of the number, adding 1 to the result, taking the base-2 logarithm of the result", but the identities for the logarithm of a sum aren't as pretty as the identities for products, quotients or powers. Icek (talk) 18:34, 19 May 2014 (UTC)


 * $$\log(x+1)=\log(x)+\log(1+\frac 1 x)$$. "The logarithmic operation of adding 1 is adding the logarithm of 1+1/x". Bo Jacoby (talk) 19:29, 19 May 2014 (UTC).


 * But you have to add that x = 2y, if y is the number for which the logarithmic operation shall be performed. Icek (talk) 17:49, 20 May 2014 (UTC)