It consists of two expressions.
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(y-y1)=m(x-x1) OR we can write it y=m(x-x1)+y1
y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
The formula: distance=sqrt(((x1-x2)*(x1-x2))+((y1-y2)*(y1-y2))+((z1-z2)*(z1-z2))) In DarkBASIC it's: function distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=sqrt((x*x)+(y*y)+(z*z)) endfunction result In classic BASIC I think it's: FUNCTION distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=SQRT((x*x)+(y*y)+(z*z)) RETURN result END FUNCTION
y=x2+3 x1=1 x2=2 y(x1) = 1*1+3 = 4 y(x2) = 2*2+3 = 7 x2/x1 = 2, While y2/y1 = 7/4 !=2, and thus the function is nonlinear.
Y-y1=m(x-x1)
Suppose that you have simple two variable model: Y=b0+b1X1+e The least squares estimator for the slope coefficient, b1 can be obtained with b1=cov(X1,Y)/var(X1) the intercept term can be calculated from the means of X1 and Y b0=mean(Y)-b1*mean(X1) In a larger model, Y=b0+b1X1+b2X2+e the estimator for b1 can be found with b1=(cov(X1,Y)var(X2)-cov(X2,Y)cov(X1,X2))/(var(X1)var(X2)-cov(X1,X2)2) to find b2, simply swap the X1 and X2 terms in the above to get b2=(cov(X2,Y)var(X1)-cov(X1,Y)cov(X1,X2))/(var(X1)var(X2)-cov(X1,X2)2) Find the intercept with b0=mean(Y)-b1*mean(X1)-b2*mean(X2) Beyond two regressors, it just gets ugly.
(y-y1)=m(x-x1) OR we can write it y=m(x-x1)+y1
y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
y-y1=m(x+x1)
Armstrong's Inference RulesSpecify rules for reasoning about dependency functions: Reflexive rule:{Y 1,...,Y n}⊆{X1,...,Xm}implies {X1,...,Xm}→{Y 1,...,Y n} {Name,Sex}→{Name}Augmentation Rule:{X1,...,Xm}→{Y 1,...,Y n}implies {X1,...,Xm,Z}→{Y 1,...,Y n,Z} {Name,Sex}→{Name}implies {Name,Sex,Age}→{Name,Age}Transitive rule:{X1,...,Xm}→{Y 1,...,Y n},{Y 1,...,Y n}→{Z1,...,Zs}imply {X1,...,Xm}→{Z1,...,Zs} {Number}→{Name}{Name}→{Sex}imply{Number}→{Sex}Armstrong inference rules are sound Produce only functional dependencies belonging to the closure complete Produce all the functional dependencies in the closure
(y-y1)=(y2-y1/x2-x1)(x-x1)
if we take the (x1,y1),(x2,y2) as coordinates the formula was (x-x1)/(x2-x1)=(y-y1)/(y2-y1)
(y - y1) = m*(x - x1) where (x1, y1) are the coordinates of a point on the line and , is the slope.
The formula: distance=sqrt(((x1-x2)*(x1-x2))+((y1-y2)*(y1-y2))+((z1-z2)*(z1-z2))) In DarkBASIC it's: function distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=sqrt((x*x)+(y*y)+(z*z)) endfunction result In classic BASIC I think it's: FUNCTION distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=SQRT((x*x)+(y*y)+(z*z)) RETURN result END FUNCTION
(y -y1)=(x -x1)(y2 -y1)/(x2 -x1) defines the line containing coordinates (x1,y1) and (x2.y2).
y=x2+3 x1=1 x2=2 y(x1) = 1*1+3 = 4 y(x2) = 2*2+3 = 7 x2/x1 = 2, While y2/y1 = 7/4 !=2, and thus the function is nonlinear.
Points: (x, y) and (x, y) Slope: y1-y2/x1-x2