1<?xml version="1.0" encoding="UTF-8"?> 2 3<!--*********************************************************** 4 * 5 * Licensed to the Apache Software Foundation (ASF) under one 6 * or more contributor license agreements. See the NOTICE file 7 * distributed with this work for additional information 8 * regarding copyright ownership. The ASF licenses this file 9 * to you under the Apache License, Version 2.0 (the 10 * "License"); you may not use this file except in compliance 11 * with the License. You may obtain a copy of the License at 12 * 13 * http://www.apache.org/licenses/LICENSE-2.0 14 * 15 * Unless required by applicable law or agreed to in writing, 16 * software distributed under the License is distributed on an 17 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 18 * KIND, either express or implied. See the License for the 19 * specific language governing permissions and limitations 20 * under the License. 21 * 22 ***********************************************************--> 23 24<helpdocument version="1.0"> 25<meta> 26<topic id="textschart0104050100xml" indexer="include" status="PUBLISH"> 27<title xml-lang="en-US" id="tit">Trend Lines</title> 28<filename>/text/schart/01/04050100.xhp</filename> 29</topic> 30</meta> 31<body> 32<bookmark xml-lang="en-US" branch="index" id="bm_id1744743"> 33<bookmark_value>calculating;regression curves</bookmark_value> 34<bookmark_value>regression curves in charts</bookmark_value> 35<bookmark_value>trend lines in charts</bookmark_value> 36<bookmark_value>mean value lines in charts</bookmark_value> 37</bookmark> 38<comment>only use trend line, not regression curve: i89823</comment> 39<bookmark xml-lang="en-US" branch="hid/.uno:InsertMenuTrendlines" id="bm_id2001709" localize="false"/> 40<paragraph xml-lang="en-US" id="hd_id5409405" role="heading" level="1" l10n="CHG"><variable id="regression"><link href="text/schart/01/04050100.xhp">Trend Lines</link> 41</variable></paragraph> 42<paragraph xml-lang="en-US" id="par_id7272255" role="paragraph" l10n="CHG"><variable id="trendlinestext"><ahelp hid=".">Trend lines can be added to all 2D chart types except for Pie and Stock charts.</ahelp> 43</variable></paragraph> 44<embed href="text/schart/01/04030000.xhp#context"/> 45<section id="howtoget"> 46<embed href="text/schart/00/00000004.xhp#trendlines"/> 47</section><comment>None</comment> 48<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_NONE" id="bm_id2659077" localize="false"/> 49<paragraph xml-lang="en-US" id="par_id143436" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">No trend line is shown.</ahelp></paragraph><comment>Linear</comment> 50<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_LINEAR" id="bm_id6944181" localize="false"/> 51<paragraph xml-lang="en-US" id="par_id5716727" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">A linear trend line is shown.</ahelp></paragraph><comment>Logarithmic</comment> 52<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_LOGARITHMIC" id="bm_id886257" localize="false"/> 53<paragraph xml-lang="en-US" id="par_id5840021" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">A logarithmic trend line is shown.</ahelp></paragraph><comment>Exponential</comment> 54<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_EXPONENTIAL" id="bm_id8892483" localize="false"/> 55<paragraph xml-lang="en-US" id="par_id9417096" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">An exponential trend line is shown.</ahelp></paragraph><comment>Power</comment> 56<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_POWER" id="bm_id7198400" localize="false"/> 57<paragraph xml-lang="en-US" id="par_id8482924" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">A power trend line is shown.</ahelp></paragraph><comment>Show equation</comment> 58<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_SHOW_EQUATION" id="bm_id4724875" localize="false"/> 59<paragraph xml-lang="en-US" id="par_id8962370" role="paragraph" l10n="NEW"><ahelp hid="." visibility="hidden">Shows the trend line equation next to the trend line.</ahelp></paragraph><comment>Show correlation coefficient (R2)</comment> 60<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_SHOW_R_SQUARED" id="bm_id9068880" localize="false"/> 61<paragraph xml-lang="en-US" id="par_id6889858" role="paragraph" l10n="CHG"><ahelp hid="." visibility="hidden">Shows the coefficient of determination next to the trend line.</ahelp></paragraph> 62<paragraph xml-lang="en-US" id="par_id8398998" role="note" l10n="CHG">If you insert a trend line to a chart type that uses categories, like <emph>Line</emph> or <emph>Column</emph>, then the numbers 1, 2, 3, <emph>…</emph> are used as x-values to calculate the trend line.</paragraph> 63<list type="ordered"> 64<listitem> 65<paragraph xml-lang="en-US" id="par_id5676747" role="paragraph" l10n="CHG">To insert trend lines for all data series, double-click the chart to enter edit mode. Choose <item type="menuitem">Insert - Trend Lines</item>, then select the type of trend line from None, Linear, Logarithmic, Exponential, or Power trend line.</paragraph> 66</listitem> 67<listitem> 68<paragraph xml-lang="en-US" id="par_id4349192" role="paragraph" l10n="CHG">To insert a trend line for a single data series, select the data series in the chart, right-click to open the context menu, and choose <item type="menuitem">Insert - Trend Line</item>.</paragraph> 69</listitem> 70<listitem> 71<paragraph xml-lang="en-US" id="par_id9337443" role="paragraph" l10n="NEW">To delete a single trend line or mean value line, click the line, then press the Del key.</paragraph> 72</listitem> 73<listitem> 74<paragraph xml-lang="en-US" id="par_id4529251" role="paragraph" l10n="NEW">To delete all trend lines, choose <item type="menuitem">Insert - Trend Lines</item>, then select <emph>None</emph>.</paragraph> 75</listitem> 76</list> 77<paragraph xml-lang="en-US" id="par_id296334" role="note" l10n="CHG">A trend line is shown in the legend automatically.</paragraph> 78<bookmark xml-lang="en-US" branch="hid/.uno:InsertMenuMeanValues" id="bm_id7854243" localize="false"/> 79<paragraph xml-lang="en-US" id="par_id4072084" role="paragraph" l10n="NEW"><ahelp hid=".">Mean Value Lines are special trend lines that show the mean value. Use <item type="menuitem">Insert - Mean Value Lines</item> to insert mean value lines for data series.</ahelp></paragraph> 80<embed href="text/schart/01/04030000.xhp#context"/> 81<paragraph xml-lang="en-US" id="par_id9569689" role="paragraph" l10n="NEW">The trend line has the same color as the corresponding data series. To change the line properties, select the trend line and choose <item type="menuitem">Format - Format Selection - Line</item>.</paragraph> 82<bookmark xml-lang="en-US" branch="hid/.uno:InsertTrendlineEquation" id="bm_id2754600" localize="false"/> 83<paragraph xml-lang="en-US" id="par_id846888" role="paragraph" l10n="NEW"><ahelp hid=".">To show the trend line equation, select the trend line in the chart, right-click to open the context menu, and choose <emph>Insert Trend Line Equation</emph>.</ahelp></paragraph> 84<paragraph xml-lang="en-US" id="par_id8962065" role="paragraph" l10n="CHG">When the chart is in edit mode, %PRODUCTNAME gives you the equation of the trend line and the coefficient of determination R². Click on the trend line to see the information in the status bar.</paragraph> 85<paragraph xml-lang="en-US" id="par_id1328470" role="note" l10n="CHG">For a category chart (for example a line chart), the trend line information is calculated using numbers 1, 2, 3, … as x-values. This is also true if your data series uses other numbers as names for the x-values. For such charts the XY chart type might be more suitable.</paragraph> 86<paragraph xml-lang="en-US" id="par_id8092593" role="paragraph" l10n="CHG">To show the equation and the coefficient of determination, select the trend line and choose <item type="menuitem">Format - Format Selection - Equation</item>.</paragraph> 87<paragraph xml-lang="en-US" id="par_id7971434" role="paragraph" l10n="CHG"><ahelp hid="." visibility="hidden">Enable Show equation to see the equation of the trend line.</ahelp></paragraph><comment>hid</comment> 88<paragraph xml-lang="en-US" id="par_id558793" role="paragraph" l10n="CHG"><ahelp hid="." visibility="hidden">Enable Show Coefficient of Determination to see the determination coefficient of the trend line.</ahelp></paragraph> 89<paragraph xml-lang="en-US" id="par_id7735221" role="paragraph" l10n="NEW">You can also calculate the parameters using Calc functions as follows.</paragraph> 90<paragraph xml-lang="en-US" id="hd_id5744193" role="heading" level="2" l10n="NEW">The linear regression equation</paragraph> 91<paragraph xml-lang="en-US" id="par_id9251991" role="paragraph" l10n="NEW">The <emph>linear regression</emph> follows the equation <item type="literal">y=m*x+b</item>.</paragraph> 92<paragraph xml-lang="en-US" id="par_id7951902" role="code" l10n="NEW">m = SLOPE(Data_Y;Data_X)</paragraph> 93<paragraph xml-lang="en-US" id="par_id6637165" role="code" l10n="NEW">b = INTERCEPT(Data_Y ;Data_X)</paragraph> 94<paragraph xml-lang="en-US" id="par_id7879268" role="paragraph" l10n="NEW">Calculate the coefficient of determination by</paragraph> 95<paragraph xml-lang="en-US" id="par_id9244361" role="code" l10n="NEW">r² = RSQ(Data_Y;Data_X)</paragraph> 96<paragraph xml-lang="en-US" id="par_id2083498" role="paragraph" l10n="NEW">Besides m, b and r² the array function <emph>LINEST</emph> provides additional statistics for a regression analysis.</paragraph> 97<paragraph xml-lang="en-US" id="hd_id2538834" role="heading" level="2" l10n="NEW">The logarithm regression equation</paragraph> 98<paragraph xml-lang="en-US" id="par_id394299" role="paragraph" l10n="NEW">The <emph>logarithm regression</emph> follows the equation <item type="literal">y=a*ln(x)+b</item>.</paragraph> 99<paragraph xml-lang="en-US" id="par_id2134159" role="code" l10n="NEW">a = SLOPE(Data_Y;LN(Data_X))</paragraph> 100<paragraph xml-lang="en-US" id="par_id5946531" role="code" l10n="NEW">b = INTERCEPT(Data_Y ;LN(Data_X))</paragraph> 101<paragraph xml-lang="en-US" id="par_id5649281" role="code" l10n="NEW">r² = RSQ(Data_Y;LN(Data_X))</paragraph> 102<paragraph xml-lang="en-US" id="hd_id7874080" role="heading" level="2" l10n="NEW">The exponential regression equation</paragraph> 103<paragraph xml-lang="en-US" id="par_id4679097" role="paragraph" l10n="CHG"> 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.</paragraph> 104<paragraph xml-lang="en-US" id="par_id9112216" role="paragraph" l10n="NEW">The exponential regression follows the equation <item type="literal">y=b*exp(a*x)</item> or <item type="literal">y=b*m^x</item>, which is transformed to <item type="literal">ln(y)=ln(b)+a*x</item> or <item type="literal">ln(y)=ln(b)+ln(m)*x</item> respectively.</paragraph> 105<paragraph xml-lang="en-US" id="par_id4416638" role="code" l10n="NEW">a = SLOPE(LN(Data_Y);Data_X)</paragraph> 106<paragraph xml-lang="en-US" id="par_id1039155" role="paragraph" l10n="CHG">The variables for the second variation are calculated as follows:</paragraph> 107<paragraph xml-lang="en-US" id="par_id7184057" role="code" l10n="NEW">m = EXP(SLOPE(LN(Data_Y);Data_X))</paragraph> 108<paragraph xml-lang="en-US" id="par_id786767" role="code" l10n="NEW">b = EXP(INTERCEPT(LN(Data_Y);Data_X))</paragraph> 109<paragraph xml-lang="en-US" id="par_id7127292" role="paragraph" l10n="NEW">Calculate the coefficient of determination by</paragraph> 110<paragraph xml-lang="en-US" id="par_id5437177" role="code" l10n="NEW">r² = RSQ(LN(Data_Y);Data_X)</paragraph> 111<paragraph xml-lang="en-US" id="par_id6946317" role="paragraph" l10n="NEW">Besides m, b and r² the array function LOGEST provides additional statistics for a regression analysis.</paragraph> 112<paragraph xml-lang="en-US" id="hd_id6349375" role="heading" level="2" l10n="NEW">The power regression equation</paragraph> 113<paragraph xml-lang="en-US" id="par_id1857661" role="paragraph" l10n="NEW"> For <emph>power regression</emph> curves a transformation to a linear model takes place. The power regression follows the equation <item type="literal">y=b*x^a</item> , which is transformed to <item type="literal">ln(y)=ln(b)+a*ln(x)</item>.</paragraph> 114<paragraph xml-lang="en-US" id="par_id8517105" role="code" l10n="NEW">a = SLOPE(LN(Data_Y);LN(Data_X))</paragraph> 115<paragraph xml-lang="en-US" id="par_id9827265" role="code" l10n="NEW">b = EXP(INTERCEPT(LN(Data_Y);LN(Data_X))</paragraph> 116<paragraph xml-lang="en-US" id="par_id2357249" role="code" l10n="NEW">r² = RSQ(LN(Data_Y);LN(Data_X))</paragraph> 117<paragraph xml-lang="en-US" id="hd_id9204077" role="heading" level="2" l10n="NEW">Constraints<comment>UFI: is this still so?</comment></paragraph> 118<paragraph xml-lang="en-US" id="par_id7393719" role="paragraph" l10n="CHG"> The calculation of the trend line considers only data pairs with the following values:</paragraph> 119<list type="ordered"> 120<listitem> 121<paragraph xml-lang="en-US" id="par_id7212744" role="paragraph" l10n="NEW">logarithm regression: only positive x-values are considered,</paragraph> 122</listitem> 123<listitem> 124<paragraph xml-lang="en-US" id="par_id1664479" role="paragraph" l10n="NEW">exponential regression: only positive y-values are considered,</paragraph> 125</listitem> 126<listitem> 127<paragraph xml-lang="en-US" id="par_id8734702" role="paragraph" l10n="NEW">power regression: only positive x-values and positive y-values are considered.</paragraph> 128</listitem> 129</list> 130<paragraph xml-lang="en-US" id="par_id181279" role="paragraph" l10n="NEW">You should transform your data accordingly; it is best to work on a copy of the original data and transform the copied data.</paragraph> 131<paragraph xml-lang="en-US" id="hd_id7907040" role="heading" level="2" l10n="NEW">The polynomial regression equation</paragraph> 132<paragraph xml-lang="en-US" id="par_id8918729" role="paragraph" l10n="NEW">A <emph>polynomial regression</emph> curve cannot be added automatically. You must calculate this curve manually.</paragraph> 133<paragraph xml-lang="en-US" id="par_id33875" role="paragraph" l10n="NEW">Create a table with the columns x, x², x³, … , xⁿ, y up to the desired degree n.</paragraph> 134<paragraph xml-lang="en-US" id="par_id8720053" role="paragraph" l10n="NEW">Use the formula <item type="literal">=LINEST(Data_Y,Data_X)</item> with the complete range x to xⁿ (without headings) as Data_X.</paragraph> 135<paragraph xml-lang="en-US" id="par_id5068514" role="paragraph" l10n="NEW">The first row of the LINEST output contains the coefficients of the regression polynomial, with the coefficient of xⁿ at the leftmost position.</paragraph> 136<paragraph xml-lang="en-US" id="par_id8202154" role="paragraph" l10n="NEW">The first element of the third row of the LINEST output is the value of r². See the <link href="text/scalc/01/04060107.xhp#Section8">LINEST</link> function for details on proper use and an explanation of the other output parameters.</paragraph> 137<section id="relatedtopics"> 138<paragraph xml-lang="en-US" id="par_id4562211" role="paragraph" l10n="CHG"><link href="text/schart/01/04050000.xhp">Y Error Bars tab page</link></paragraph> 139</section> 140</body> 141</helpdocument> 142