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# 近似曲線

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

このコマンドの見つけ方

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.

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

トレンド線は対応するデータ系列と同じ色で表示されます。線の属性を変更するには、トレンド線を選択して、書式 → 書式選択 → 線 を選択します。

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, 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.

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.

## 制約

トレンド線(回帰曲線)の計算は、次の値のデータペアのみを対象に行われます。

- 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.

このようにして、データを変換します。元のデータはそのまま残しておき、コピーしたデータを使って作業することをお勧めします。

## Calculate Parameters in Calc

また、次の Calc 関数を使用してパラメーターを計算することもできます。

### 直線回帰式

直線回帰は、式 y=m*x+b に従ったものになります。

m = SLOPE(Data_Y;Data_X)

b = INTERCEPT(Data_Y ;Data_X)

決定係数を次の式で計算します:

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))

### 指数回帰式

指数回帰曲線は直線モデルへ変換されます。曲線適合法は線形モデルに関係しているので、その結果も線形モデルに従って解釈されます。

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)

第２変動の変数は次の式で計算されます。:

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

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

決定係数を次の式で計算します:

r2 = RSQ(LN(Data_Y);Data_X)

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

### 乗冪 (両対数) 回帰式

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))

### 多項回帰式

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.

関連項目

X/Y Error Bars

LINEST function

LOGEST function

SLOPE function

INTERCEPT function

RSQ function