Liñas de tendencia

Pódense engadir liñas de tendencia a todos os tipos de gráficas en 2D, excepto as de sector e de cotizacións

1. To insert a trend line for a data series, first double-click the chart to enter edit mode and select the data series in the chart to which a trend line is to be created.

2. Choose Insert - Trend Line, or right-click the data series to open the context menu, and choose Insert Trend Line.

3. Mean Value Lines are special trend lines that show the mean value. Use Insert - Mean Value Lines to insert mean value lines for data series.

4. To delete a trend line or mean value line, click the line, then press the Del key.

The trend line has the same color as the corresponding data series. To change the line properties, select the trend line and choose Format - Format Selection - Line.

Trend Line Equation and Coefficient of Determination

When the chart is in edit mode, LibreOffice gives you the equation of the trend line and the coefficient of determination R², even if they are not shown: click on the trend line to see the information in the status bar.

To show the trend line equation, select the trend line in the chart, right-click to open the context menu, and choose Insert Trend Line Equation.

To change format of values (use less significant digits or scientific notation), select the equation in the chart, right-click to open the context menu, and choose Format Trend Line Equation - Numbers.

Default equation uses x for abscissa variable, and f(x) for ordinate variable. To change these names, select the trend line, choose Format - Format Selection – Type and enter names in X Variable Name and Y Variable Name edit boxes.

To show the coefficient of determination R², select the equation in the chart, right-click to open the context menu, and choose Insert R².

Trend Lines Curve Types

Están dispoñíbeis os tipos de regresión seguintes:

• Linear trend line: regression through equation y=a∙x+b. Intercept b can be forced.

• Polynomial trend line: regression through equation y=Σ_i(a_i∙xⁱ). Intercept a₀ can be forced. Degree of polynomial must be given (at least 2).

• Logarithmic trend line: regression through equation y=a∙ln(x)+b.

• Exponential trend line: regression through equation y=b∙exp(a∙x).This equation is equivalent to y=b∙m^x with m=exp(a). Intercept b can be forced.

• Power trend line: regression through equation y=b∙x^a.

• Moving average trend line: simple moving average is calculated with the n previous y-values, n being the period. No equation is available for this trend line.

Restricións

O cálculo da liña de tendencia considera só pares de datos cos valores seguintes:

• Liña de tendencia logarítmica: só se consideran valores positivos de x.

• Liña de tendencia exponencial: só se consideran valores de y positivos, excepto se todos os valores de y foren negativos: neste caso a regresión sigue a ecuación seguinte y=-b∙exp(a∙x).

• Power trend line: only positive x-values are considered; only positive y-values are considered, except if all y-values are negative: regression will then follow equation y=-b∙x^a.

Ten que transformar os seus datos de acordo con isto; é mellor traballar cunha copia dos datos orixinais e transformar os datos copiados.

Calcular parámetros no Calc

Tamén pode calcular os parámetros empregando as funcións do Calc como segue.

A ecuación de regresión lineal

A regresión lineal segue a ecuación y=m*x+b.

m = SLOPE(Data_Y;Data_X)

b = INTERCEPT(Data_Y ;Data_X)

Calculate the coefficient of determination by

r² = RSQ(Data_Y;Data_X)

Besides m, b and r² the array function LINEST provides additional statistics for a regression analysis.

The logarithmic regression equation

The logarithmic regression follows the equation y=a*ln(x)+b.

a = SLOPE(Data_Y;LN(Data_X))

b = INTERCEPT(Data_Y ;LN(Data_X))

r² = RSQ(Data_Y;LN(Data_X))

A ecuación de regresión exponencial

For exponential trend lines a transformation to a linear model takes place. The optimal curve fitting is related to the linear model and the results are interpreted accordingly.

The exponential regression follows the equation y=b*exp(a*x) or y=b*m^x, which is transformed to ln(y)=ln(b)+a*x or ln(y)=ln(b)+ln(m)*x respectively.

a = SLOPE(LN(Data_Y);Data_X)

The variables for the second variation are calculated as follows:

m = EXP(SLOPE(LN(Data_Y);Data_X))

b = EXP(INTERCEPT(LN(Data_Y);Data_X))

Calculate the coefficient of determination by

r² = RSQ(LN(Data_Y);Data_X)

Besides m, b and r² the array function LOGEST provides additional statistics for a regression analysis.

The power regression equation

For power regression curves a transformation to a linear model takes place. The power regression follows the equation y=b*x^a, which is transformed to ln(y)=ln(b)+a*ln(x).

a = SLOPE(LN(Data_Y);LN(Data_X))

b = EXP(INTERCEPT(LN(Data_Y);LN(Data_X))

r² = RSQ(LN(Data_Y);LN(Data_X))

A ecuación de regresión polinomial

Para curvas de regresión polinomial realízase unha transformación a un modelo lineal.

Crear unha táboa coas columnas x, x², x³, … , xⁿ, y até o grao desexado n.

Use the formula =LINEST(Data_Y,Data_X) with the complete range x to xⁿ (without headings) as Data_X.

The first row of the LINEST output contains the coefficients of the regression polynomial, with the coefficient of xⁿ at the leftmost position.

The first element of the third row of the LINEST output is the value of r². See the LINEST function for details on proper use and an explanation of the other output parameters.