Tip 1: How to calculate the correlation coefficient

correlation coefficient also called normalized correlation point, which is the ratio of the time correlation of two random variables (CER) and its maximum value.In turn, the correlation time is called mixed central moment of the second order (TCO X and Y).
Guide
1
It should be noted that the value of W (x, y) will be the joint probability density of CERs.In turn, the correlation will be a moment of mutual variation characteristic values ​​with respect to a certain point CERs average values ​​(mathematical expectations of my, and mx), the level of the linear relationship between the
values ​​of the free parameters X and Y.
2
Consider properties of the correlationmoment: Rxx = Dx (dispersion);R (xy) = 0 - for independent parameters X and Y. This is really the following equation: M {Yts, Xts} = 0, which in this case shows the lack of a linear relationship (here we have in mind not any communication, but, for example,quadratic).In addition, if there is a linear relationship between the rigid values ​​of X and Y, the following equation is really: Y = Xa + b - | R (xy) | = bybx = max.
3
Return to consider r (xy) - the coefficient of correlation , the meaning of which must be in a linear relationship between random variables.Its value may vary from -1 to units other than that it can not have a dimension.Accordingly, with this: R (yx) / bxby = R (xy).
4
Transfer the values ​​obtained on the chart.This will help you visualize the meaning of the normalized correlation moment empirically derived parameters X and Y, which in this case will be the coordinates of a point on a certain plane.In the presence of a linear rigid connection of these points must lie on a straight line exactly Y = Xa + b.
5
Take the positive values ​​of the correlation and connect them to the resulting chart.When the equation r (xy) = 0, all the points should be designated to be within the ellipse in the central region (mx, my).The value of the semi-axes cents will be determined by the values ​​of the variances of the random variables.
6
Note the values ​​obtained experimentally by CB can not 100% reflect the probability density.That is why it is best to use estimates of required quantities: mx * = (x1 + x2 + ... + xn) (1 / n).Then count similar to my *.

Tip 2: How to find the coefficient of friction

friction coefficient - a set of characteristics of the two bodies that are in contact with each other.There are several types of friction: static friction, sliding friction and rolling friction.Static friction is friction body which is at rest, and it was set in motion.Sliding friction occurs when the body moves, this friction is less than the static friction.A rolling friction occurs when the body to roll on the surface.Represented by friction depending on the type, as follows: μsk - sliding friction, static friction μo-, μkach - rolling friction.
How to find the coefficient of friction
Guide
1
rolling friction force is determined by the radius of the body of the subject.In most cases, the calculation of rolling friction of the vehicle when the radius of the wheel is constant, it is determined in the friction coefficient.
2
In determining the coefficient of friction during the experiment, the body is placed on an inclined plane and calculated angle.It should be borne in mind that the determination of the coefficient of friction given body begins to move, and the determination of the coefficient of sliding friction is moving at a speed that is constant.
3
friction coefficient can also be calculated during the experiment.You need to place an object on an inclined plane and calculate the angle.Thus, the coefficient of friction is determined by the formula: μ = tg (α), where μ - friction force, α - the angle of the plane.

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