Also when you do a least
squares curve fit using the normal equations (the usual method), there is an implicit weighting of the data points proportional to their distance from the center.
I have a least
squares curve fit program which allows you to weight each data point.
Least
squared curve fit to an N - th order polynomial?
Not exact matches
He used the Lomb - Scargle routine in IDL to determine the most significant periodicity in the data (= 3.2 days), and then used this as input into a least -
squares sine wave
fit to produce the
fitted curve shown.
Or you can try to find the best
fit by manually adjusting
fit parameters; Sample Learning Goals • Describe how correlation coefficient and chi
squared can be used to indicate how well a
curve describes the data relationship • Apply understanding of Curve Fitting to designing experi
curve describes the data relationship • Apply understanding of
Curve Fitting to designing experi
Curve Fitting to designing experiments
I used Excel's
curve fitting capability to
fit straight lines to the data and to report the equations (i.e., regression equations) and goodness of
fit (R -
squared).
I have listed all of the coefficients for the
curves along with the values of R
squared, which indicates the goodness of
fit.
R
squared tells us what fraction of the variance in the data is explained by the
curve fit.
Return0 = y and HSWR50 = x. Years R -
Squared Equation 1... 0.0908 y = 2.647 x - 10.053 2... 0.1704 y = 2.6542 x - 10.527 3... 0.2519 y = 2.506 x - 9.8705 4... 0.3386 y = 2.5412 x - 10.112 5... 0.4022 y = 2.4671 x - 9.7509 6... 0.4710 y = 2.6452 x - 9.7732 7... 0.5370 y = 2.4858 x - 9.8994 8... 0.6018 y = 2.4853 x - 9.9486 9... 0.6775 y = 2.4061 x - 9.5746 10... 0.7381 y = 2.341 x - 9.2439 11... 0.8002 y = 2.3113 x - 9.107 12... 0.8643 y = 2.33 x - 9.2065 13... 0.8949 y = 2.2709 x - 8.8728 14... 0.9027 y = 2.1245 x - 8.0652 15... 0.8964 y = 1.9819 x - 7.2668 16... 0.8773 y = 1.8006 x -6.2552 17... 0.8665 y = 1.6398 x - 5.3589 18... 0.8509 y = 1.5422 x - 4.7903 19... 0.8036 y = 1.412 x - 4.0325 20... 0.7286 y = 1.2552 x - 3.1208 21... 0.6626 y = 1.1094 x - 2.2726 22... 0.6045 y = 0.9825 x - 1.5285 23... 0.5293 y = 0.8381 x - 0.6976 24... 0.4287 y = 0.6779 x + 0.2077 25... 0.3156 y = 0.5041 x + 1.1781 26... 0.2079 y = 0.3336 x + 2.1127 27... 0.1100 y = 0.2031 x + 2.829 28... 0.0380 y = 0.1084 x + 3.3421 29... 0.0109 y = 0.0603 x + 3.583 30... 0.0004 y = 0.0116 x + 3.8169 Return0 = y and HSWR80 = x. Years R -
Squared Equation 1... 0.1258 y = 2.9412 x - 12.533 2... 0.2332 y = 2.9192 x - 13.189 3... 0.3294 y = 2.6717 x - 11.883 4... 0.4193 y = 2.616 x - 11.611 5... 0.4715 y = 2.4141 x - 10.377 6... 0.5241 y = 2.2778 x - 9.5372 7... 0.5778 y = 2.2064 x - 9.0847 8... 0.6309 y = 2.1431 x - 8.7466 9... 0.6951 y = 2.0267 x - 8.0839 10... 0.7478 y = 1.9526 x - 7.6448 11... 0.8085 y = 1.9398 x - 7.5947 12... 0.8703 y = 1.9776 x - 7.8088 13... 0.9001 y = 1.9485 x - 7.584 14... 0.9045 y = 1.8432 x - 6.8875 15... 0.8910 y = 1.7278 x - 6.112 16... 0.8566 y = 1.5774 x - 5.1143 17... 0.8395 y = 1.4588 x - 4.3331 18... 0.8151 y = 1.3856 x - 3.8072 19... 0.7602 y = 1.2813 x - 3.0685 20... 0.6819 y = 1.1517 x - 2.1588 21... 0.6170 y = 1.0346 x - 1.3363 22... 0.5699 y = 0.9358 x - 0.6359 23... 0.5099 y = 0.8232 x + 0.1334 24... 0.4265 y = 0.6936 x + 0.9921 25... 0.3218 y = 0.5417 x + 1.9799 26... 0.2284 y = 0.4031 x + 2.852 27... 0.1451 y = 0.2931 x + 3.542 28... 0.0826 y = 0.2118 x + 4.0356 29... 0.0551 y = 0.1774 x + 4.2041 30... 0.0318 y = 0.1399 x + 4.3784 Notice that the
curve fit is especially good from years 11 through 19 for HSWR50 (with 50 % stocks) and 11 through 18 for HSWR80 (with 80 % stocks).
I used Excel's
curve fitting capability to
fit straight lines to the data and report the equations (i.e., regression equations) and goodness of
fit (R -
squared).
An exponential
curve fit of the dividend amount has the equation: Dividend amount = 2E - 47 * exp (0.055 * Year) with R -
squared = 0.989.
Now here it comes: if you
fit a quadratic (by the standard least -
squares method) to this sea - level
curve, the quadratic term (i.e. the acceleration) is negative!
'' if you
fit a quadratic (by the standard least -
squares method) to this sea - level
curve, the quadratic term (i.e. the acceleration) is negative!»
As a case in point for (c), the least -
squares fit of SAW+AGW to HadCRUT3 implicitly entails a
fit to the Keeling
curve with an R2 of 99.56 % (which incidentally is better than Goodman's «triple - exponential»
fit which only achieves R2 = 98.98 %, which I'll comment on later this evening in a reply to Greg's long - neglected Jan. 2 comment).
Cumulative US crude - oil production from 1859, plotted from 1900 on, together with a normal
curve that is the least mean
square fit (ultimate 225Gb, 10 % year 1939, 90 % year 2011).
In the
curve fit you can minimize the absolute error, the
squared error or the maximum error and obtain different trends all depending on the norm you are minimizing.
Instead of the 1.6 - inch flat
square screen on the Gear 2, the Gear 3's would be slightly rectangular — not nearly so extreme as what we see on the Gear
Fit (right), but a bit taller than the Gear 2's display — with thin side bezels, and with a very pronounced
curve to it; look for it to be significantly more
curved than the Gear
Fit.