Trend Lines

Trend lines can be added to all 2-D chart types except for Pie and Stock charts.

To access this command...

Choose Insert - Trend Line (Charts)

If you insert a trend line to a chart type that uses categories, like Line or Column, then the numbers 1, 2, 3, … are used as x-values to calculate the trend line. For such charts the XY chart type might be more suitable.

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.
Choose Insert - Trend Line, or right-click the data series to open the context menu, and choose Insert Trend Line.
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.
To delete a trend line or mean value line, click the line, then press the Del key.

The menu item Insert - Trend Line is only available when the chart is in edit mode. It will appear greyed out if the chart is in edit mode but no data series is selected.

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

A trend line is shown in the legend automatically. Its name can be defined in options of the trend line.

Trend Line Equation and Coefficient of Determination

When the chart is in edit mode, Office 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 R 2.

If intercept is forced, coefficient of determination R2 is not calculated in the same way as with free intercept. R2 values can not be compared with forced or free intercept.

Trend Lines Curve Types

The following regression types are available:

Linear trend line: regression through equation y=a∙x+b. Intercept b can be forced.
Polynomial trend line: regression through equation y=Σi(ai∙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∙mx with m=exp(a). Intercept b can be forced.
Power trend line: regression through equation y=b∙xa.
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.

Constraints

The calculation of the trend line considers only data pairs with the following values:

Logarithmic trend line: only positive x-values are considered.
Exponential trend line: only positive y-values are considered, except if all y-values are negative: regression will then follow equation 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∙xa.

You should transform your data accordingly; it is best to work on a copy of the original data and transform the copied data.

Calculate Parameters in Calc

You can also calculate the parameters using Calc functions as follows.

The linear regression equation

The linear regression follows the equation 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))

The exponential regression equation

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*mx, 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*xa, 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))

The polynomial regression equation

For polynomial regression curves a transformation to a linear model takes place.

Create a table with the columns x, x2, x3, … , xn, y up to the desired degree 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.