IStatistics.Trend

Syntax

Trend(KnownYs: Array; KnownXs: Array; NewXs: Array; HasConstant: Boolean): Array;

Parameters

KnownYs. The range of Y values that are already known in ratio y=mx+b. Values contained in data array must be greater than zero. If there is only one column in the KnownYs array, each column of the KnownXs array is regarded as a separate variable. If there is only one row in the KnownYs array, each row of the KnownXs array is regarded as a separate variable. The KnownXs array can contain one or more variable sets. If only one variable is used, KnownYs and KnownXs can have any form, provided that they have the same dimension. If several variables are used, KnownYs must be a vector (i.e. an interval with a row height or a column width).

KnownXs. The range of X values that are already known for the ratio y=mx+b.

NewXs. New X values for which the Trend method returns corresponding Y values. Like KnownXs, NewXs must have a column or a row for each independent variable. Thus, if KnownYs has a single column, KnownXs and NewXs should have the same number of columns. If KnownYs is represented by one row, KnownXs and NewXs must have the same number of rows.

HasConstant. Boolean value that indicates whether the constant b must be equal to zero:

True. b is computed in a standard way;
False. b is regarded as zero, and m values are selected to satisfy y=mx.

Description

The Trend method returns values for a linear trend. It approximates the KnownYs array and the KnownXs array using a straight line (the least-squares method). It returns Y values based on this straight line for the specified NewXs array.

Example

Sub Main;

Var

st: Statistics;

d0: Double;

x, y, nx: Array Of Double;

res: Array Of Double;

i: Integer;

Begin

y := New Double[12];

x := New Double[12];

nx := New Double[4];

x[00] := 1; y[00] := 33100;

x[01] := 2; y[01] := 47300;

x[02] := 3; y[02] := 69000;

x[03] := 4; y[03] := 102000;

x[04] := 5; y[04] := 150000;

x[05] := 6; y[05] := 220000;

x[06] := 7; y[06] := 220100;

x[07] := 8; y[07] := 247300;

x[08] := 9; y[08] := 269000;

x[09] := 10; y[09] := 270020;

x[10] := 11; y[10] := 275210;

x[11] := 12; y[11] := 276030;

nx[0] := 13;

nx[1] := 14;

nx[2] := 15;

nx[3] := 16;

st := New Statistics.Create;

res := st.Trend(y,x,x,True);

Debug.WriteLine("Calculated values corresponding to existing Y values");

For i := 0 To res.Length - 1 Do

d0 := res[i];

Debug.WriteLine(d0.ToString);

End For;

res := st.Trend(y,x,nx,True);

Debug.WriteLine("Predicted Y values for new X values (nx)" );

For i := 0 To 3 Do

d0 := res[i];

Debug.WriteLine(d0.ToString);

End For;

End Sub Main;

Executing this example shows the calculation results in the console window:

Module execution started

Calculated values for the existing Y values

42019.871794871789

67395.955710955706

92772.03962703963

118148.12354312354

143524.20745920745

168900.29137529139

194276.3752913753

219652.45920745921

245028.54312354312

270404.62703962706

295780.71095571097

321156.79487179487

Predicted Y values for the new X (nx) values

346532.87878787878

371908.96270396269

397285.0466200466

422661.13053613051

Module execution finished