It's denoted by r and its always between -1 and 1.Īnd in order to calculate the correlation coefficient we can use this formula:Īnd then 100-43.56 = 56. The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". SolveUpperTriangular(subMatrix(dc.r,1,n,1,n),transpose(dc.Now we can calculate the determination coeffcient:Īnd then we can conclude that 43.56% of the variation in y can be explained by the explanatory variableĪnd then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variableįor this case we need to calculate the slope with the following formula:Īnd we can find the intercept using this: ScalarMatrix(m,1) - beta*transpose(outerProduct(v,v))įor i in 1.(if m=n then n-1 else n) repeat U := a + length(a)*signValue(a(1))*unitVector(m) R has (sign: R -> Integer) => coerce(sign(r)$R)$R V:Vector(R) ^ n:NonNegativeInteger = map((vi:R):R +-> vi^n, v)$Vector(R)
software to solve the case study on page 146 of the Heizer and. Use the forecasting module that you opened in the POM-QM for Windows. Next, select File, New, and Least Squares - Simple and Multiple regression.
V:Vector(R) / a:R = map((vi:R):R +-> vi/a, v)$Vector(R) Launch the POM-QM for Windows software and from the main menu select Module, and then Forecasting. The integrated solution to these equations constitutes the spacecrafts trajectory. Polyfit: (Vector(R),Vector(R),NonNegativeInteger) -> Vector(R) Least Squares With A Priori or Bayesian Weighted Least Squares. Qr: Matrix(R) -> Record(q:Matrix(R),r:Matrix(R)) SolveUpperTriangular: (Matrix(R),Vector(R)) -> Vector(R) "^": (Vector(R),NonNegativeInteger) -> Vector(R) Since the original design problem is essentially nonconvex, it is first. UnitVector: NonNegativeInteger -> Vector(R) In this paper, we propose an iterative method for designing IIR digital filters in the weighted least squares (WLS) sense. TestPackage(R:Join(Field,RadicalCategory)): with The following provides a generic QR decomposition for arbitrary precision floats, double floats and exact calculations: Q := Transpose (Q1 ) * Transpose (Q2 ) * TransPose (Q3 ) Hall (n - 1 + row, n - 1 + col ) := H (row, col ) Ī : constant Real_Matrix ( 1. Hall : Real_Matrix := Identity (inmat'Length ( 1 ) ) Ĭol := col - Mag (col ) * eVect (col, n ) H : Real_Matrix := Identity (mat'Length ( 1 ) ) mat'Length ( 2 ) ) įunction H_n (inmat : Real_Matrix n : Integer )ĬolT : Real_Matrix ( 1. n loop mat (i, i ) := 1.0 end loop įunction Chop (mat : Real_Matrix n : Integer ) return Real_Matrix is n => ( others => 0.0 ) ) įor i in Integer range 1. 1 ) įunction Identity (n : Integer ) return Real_Matrix is Generic_Elementary_Functionsįunction eVect (col : Real_Matrix n : Integer ) return Real_Matrix is
Sum : Real_Matrix := Transpose (mat ) * mat 1 ) įunction Mag (mat : Real_Matrix ) return Float is Put (mat (row, col ), Exp => 0, Aft => 4, Fore => 5 ) įunction GetCol (mat : Real_Matrix n : Integer ) return Real_Matrix isĬolumn : Real_Matrix (mat' Range ( 1 ), 1. Output matches that of Matlab solution, not tested with other matrices.