Power Regression as an Example of the Third Law of Hotels in Paris: Planets

All of the linear term regression model: Four ways too functional equation from the normal equations; obtaining normal equations from the functional equation by differentiation; variance analysis; extrapolation in Appell regression; improve the accuracy formula the isochronism; the number of Eulerian model; the statistical reliability, F-statistics; interpolation probabilities. All about power regression: four ways to display a functional equation of the normal equations; obtain the normal equations from the functional equation by differentiating; analysis of variance; extrapolation of the power of the regression flexicurity the accuracy with Juventus of the formula to My Short List's third law Euler number: statistical reliability: F-statistics; interpolation of probabilities, MATLAB, the standard normal probability calculators.


Introduction Use the regression in the physics celestial bodies
Sustainable related to statistics as to the stress hormones subject can overcome this article. In the minds of most statistics is fundamentally one of the parties-counting manufactured products, physical products, etc. But when such calculations may lead to the opening of world significance, statistics captures the spirit of the! (Figures 1 and 2). The author as a child lived in a garrison. The toys were on paper, paper plants strategic missiles and thin, like mannequins, anti-aircraft missiles... But childhood continues. So "Astrology and John ( Figure  1) was opened by the third act the motions of the planets, for which the current could get Nobel Peace prize , we can now for half an hour repeat his path, historically, as it was.
The author of the article "the laws isochronism" Mr. Chris Impey [1] noted: "The laws isochronism apply to any orbital movement, whether the planet around the Sun, the moon around the Earth, or stars around the center of the galaxy.
The second and third laws were not the result of isochronism attempts to find patterns in orbits planets. The second and third laws isochronism studying mathematical relationship between the distance the planet from the Sun and the speed it is moving around the sun. Both of these are consequences of the application of the law of gravity and Newton's law of conservation since the pulse object, moving on an elliptic trajectory, but "Astrology surprisingly was able to get them without any of these notions!" But the essence of and those quantitative steps in any items after math processing may result in an important opening and for you. No same any items? This is Sachs [2] produced calculations in healthbiological laboratory; you can take it in any other laboratory.
where x is the distance to the Sun, measured in millions of kilometers, T is the orbital period measured in days, and C is a constant. The observed data pairs (x, T) for the first four planets, Mercury, Venus, Earth and Mars, are (58; 88), (108; 225), (150; 365), (228; 687), and the coefficient C obtained from the method of least squares 1 is C = 0.199769. The curve 2 / 3 199769 , 0 x T = and the data points are shown in Figure 3".
The authors present a power adjustment: "Let us suppose that , ( Points with various abscissas.
Since we have only one variable as well -taking private derivatives is not required. In the case described is only a «A» factor, factor «M» is already known. It saves time, when a «A» -already known physical, a constant. But we are interested in, as well as received and the factor «M» and the factor «A». And here comes the assistance table ready normal equations (    19,18256a + 92,99381b = 108,5674. Equations system of the selection can be solved by Gaussian elimination, the decomposition of the triangular matrix or matrix, but saving a place, we will use the calculator equations: answer: Ответ: a = -64515504413/40046318464 = -1,611022109, b = 3753809803/2502894904 = 1,499787225, EXP(-1,611022109) = 0,199683412.
Using differentiation will show you how the system of equations is shown.
Homoscedasticity has not been identified.
The model will take a view:  The site "A large encyclopedia pupil" reports that the period of treatment in the orbit the planet Jupiter is 11.867 years!!!" Mr. Kepler and for today made a perfect calculation.
Dr. Mathews and Dr. Fink presented [3] (3, c.290) in exercises to the chapter "Building a curve on points", resulting in the modern data, which we, and offended in the processing.
The authors give an indication: "The following date give the distances of the nine planets from the sun and their side real period in days. Use it to find the power fit of the form  = − Next will be processing the same sample using the program Microsoft Office Excel, the creature some of its performance indicators we will look at below. The other indicators is well described in the 1 (Tables  7 and 8).   Upper Critical Value 4,30265273  Heteroscedasticity in Figure 5 and Table 11. Since 437091,8 ≥ 18,51282051 and 2,29E-06 ≤ 0,05, с 95% reliability zero hypothesis is rejected. And further, since 661,1292 ≥ 4,30265273, and 2,29E-06 ≤ 0,05, the zero hypothesis is rejected.
So, as expected, more than was possible Кеплеру exact formula: We will do the job "b" (Figure 6, Tables 12 and 13).
Since there is a definite гомоскедастичность, conclusions call for caution.
So, the most accurate formula, which we have been able to calculate: Pluto. 5909 90710 Source: John and Kurtis [3].

One-Tail F-Test
Critical Value 18,51282051 Two- Tail Test   Lower Critical Value  -4,30265273 Upper Critical Value 4,30265273 The balance Table 12: Summary regression depending on the completion of all 9 planets in orbit on the distance to the Sun (exponential model), with the use of modern data, created by using the program Microsoft Office Excel 2007.

One-Tail F-Test
Critical Value 5,591447848 Two- Tail Test   Lower Critical Value  -2,364624251 Upper Critical Value 2,364624251   around the Sun are, as well as Cuba large spindles orbits planets". It is true not only for planetary exploration, but also for their satellites.
Where T -Periods of planets around the Sun, as well as well -the length large spindles their orbits.
So, the formula the third act with increasing accuracy.  So, numerically error, not overwhelming. But, as pointed out Dr. Mathews and Dr. Fink [3]: "Error may spread in the follow-up calculations". Next, we can completely eliminate this error, by using formula (1), but for this we will need to pay a distortion factor «A»...

e-called Euler's number after the Swiss mathematician Leonhard
Euler, e is not to be confused with γ, the Euler-Mascheroni constant, sometimes called simply Euler's constant. The number e is also known as Napier's constant, but Euler's choice of the symbol e is said to have been retained in his honor. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest (8).
Natural logarithms (ln) as grounds have a constant This means that when throwing coins seventy threefold in a row the emblem is still permitted as likely, while seventy fourfold has already been considered as a "over random". By the theorem of probability for independent events the probability equal to: I.e. approximately 0,105879Е-20% and 0,529396Е-21%. So, the statistical reliability 99,99 999 999 999 999 999 999 104% means that accidental emergence circumstances equally incredible, as well as and the event, consisting of the landing emblem in a row 74 times. The likelihood that, when n-purchasable throwing coins each time will fall out emblem, is equal (1/2) n . And is listed in the following table. This is well stated in the 2" (Tables 14 and 15).    Dr. Lothar Sachs points out: "If we choose a factor in this, saying that the 95% is the correct and only in 5% wrong, we say: with the statistical reliability S in 95% confidence interval a custom statistics includes the parameter general population". In summary, you want to say: we have 5% -s chances to reject a valid factor equation and the 95 % -s -to take is also a valid factor [5-8].

Interpolation Probabilities
This method computational complexity (2, with. 152) The value of F-test for v 1 and v 2 . Degrees of Freedom offered. What is it for? In special cases, above all, when target is dangerous to human life, it is necessary to take smaller, than α=0,001 errors. Thus, for example, in the manufacture of vaccines required limit constant anti-serum. Not in fallible measurements must be detected and eliminated. Dr. Sachs notes that: "An unreasonable decision null-hypothesis "antiserum is correct" means a dangerous error" (2, C. 114). Null-hypothesis -the hypothesis that the two together, the issues from the point of view of one or more signs, are identical, i.e., the actual difference is equal to zero, and the found from experience unlike the zero is random in nature. The average of the µ. The general aggregate, evaluated on the basis random sampling, is not different from the desired values µ 0 . And further Sachs writes that science makes a cell network, all less than in order to continuously extend and check all the new hypotheses, the most accurate and the most credibly explaining this world. Gamma is the findings and conclusions will never be totally reliable, but they are engaged in the preliminary hypotheses go all the more general and strict theories, a thorough test, have led to a better understanding and peace paradigm (2, C. 112). A summary table value (F=106513, 2, (v 1 = 1 and v 2 = 2)). Arrange thus between two tabular values (F 1 , Offer cruises and the likelihood that this value will be exceeded. Observed F-value lies between the borders 0,000909091 and 0,000952381% (Table 16). We will determine the number of standard deviations for the S = 90%. So: P=0.1/2=0.05, z=1.56.
Since in the following table we have t=326.3635, then get confirmation: -331,66 > 326,3635 > 331,66 (Figure 9). Standard deviation: We will determine the arbitrary empirical F-test (2, P. 152), and in particular for values with a P>0.1, an attacker who successfully exploited this an approximation, the proposed [9,10], which is true for the number of degrees of freedom, not less than three (the greater number of degrees of freedom, the better approximation), and meaningful probability is defined as the area, the corresponding z-the limits on both ends of normal distribution. In Tables 7, 10 and                On the Figure 17 area under the curve normal distribution from z to ∞ probability that the variable Z will take the value ≥ z Р˂0,0 000 000 039. Since:  0,0 000 000 078 = 0,9 999 999 922 (Draw.18.). Confirmed waiting, that the condition above ( Figure 18).
Let's take a look at link F and 1 /F and v 1 uv 2 (2, C. 150): Excel provides the answer F = 0,005012531. A method of getting the data manually is still necessary because of the computer crashes, the lack of power sleep, as it was in Abkhazia.

Conclusion
In conclusion, it should be noted that the reliability S=99,999 061%, obtained for legacy Kepler equation even today sounds, because the default is used S=95%. Starting rocket to Mars, you will receive the error α=9,39E-04% -the missiles will not be different, but good will. Why is the same not excellent? Mathews is responsible (3, C. 49-50): "many real data contain uncertainty or error. This error type is treated as noise. It affects the accuracy for any numerical calculations, which are data. Improving the accuracy is not achieved when successful calculations, using noisy data". Submitted by Dr. Mathews source, as expected, in the job "a" have greatly reduced error; in the job "b" error on the merits has no