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28<meta>
| 25<meta>
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29 <topic id="textschart0104050100xml" indexer="include" status="PUBLISH">
30 <title xml-lang="en-US" id="tit">Trend Lines </title>
31 <filename>/text/schart/01/04050100.xhp</filename>
32 </topic>
33 </meta>
34 <body>
35<bookmark xml-lang="en-US" branch="index" id="bm_id1744743"><bookmark_value>calculating;regression curves</bookmark_value>
36 <bookmark_value>regression curves in charts</bookmark_value>
37 <bookmark_value>trend lines in charts</bookmark_value>
38 <bookmark_value>mean value lines in charts</bookmark_value>
| 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>
|
39</bookmark>
40<comment>only use trend line, not regression curve: i89823</comment>
41<bookmark xml-lang="en-US" branch="hid/.uno:InsertMenuTrendlines" id="bm_id2001709" localize="false"/>
42<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>
43</variable></paragraph>
| 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>
|
44 <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>
| 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>
|
45</variable></paragraph>
| 43</variable></paragraph>
|
46 <embed href="text/schart/01/04030000.xhp#context"/>
47 <section id="howtoget">
48 <embed href="text/schart/00/00000004.xhp#trendlines"/>
49 </section><comment>None</comment>
| 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>
|
50<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_NONE" id="bm_id2659077" localize="false"/>
51<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>
52<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_LINEAR" id="bm_id6944181" localize="false"/>
53<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>
54<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_LOGARITHMIC" id="bm_id886257" localize="false"/>
55<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>
56<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_EXPONENTIAL" id="bm_id8892483" localize="false"/>
57<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>
58<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_RB_POWER" id="bm_id7198400" localize="false"/>
59<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>
60<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_SHOW_EQUATION" id="bm_id4724875" localize="false"/>
61<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>
62<bookmark xml-lang="en-US" branch="hid/CHART2_HID_SCH_TRENDLINE_SHOW_R_SQUARED" id="bm_id9068880" localize="false"/>
63<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>
| 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>
|
64 <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>
65 <list type="ordered">
66 <listitem>
67 <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>
68 </listitem>
69 <listitem>
70 <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>
71 </listitem>
72 <listitem>
73 <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>
74 </listitem>
75 <listitem>
76 <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>
77 </listitem>
78 </list>
79 <paragraph xml-lang="en-US" id="par_id296334" role="note" l10n="CHG">A trend line is shown in the legend automatically.</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>
|
80<bookmark xml-lang="en-US" branch="hid/.uno:InsertMenuMeanValues" id="bm_id7854243" localize="false"/>
81<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>
82<embed href="text/schart/01/04030000.xhp#context"/>
| 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"/>
|
83 <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>
| 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>
|
84<bookmark xml-lang="en-US" branch="hid/.uno:InsertTrendlineEquation" id="bm_id2754600" localize="false"/>
85<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>
| 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>
|
86 <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>
87 <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>
88 <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>
| 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>
|
89<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>
90<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>
| 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>
|
91 <paragraph xml-lang="en-US" id="par_id7735221" role="paragraph" l10n="NEW">You can also calculate the parameters using Calc functions as follows.</paragraph>
92 <paragraph xml-lang="en-US" id="hd_id5744193" role="heading" level="2" l10n="NEW">The linear regression equation</paragraph>
93 <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>
94 <paragraph xml-lang="en-US" id="par_id7951902" role="code" l10n="NEW">m = SLOPE(Data_Y;Data_X) </paragraph>
95 <paragraph xml-lang="en-US" id="par_id6637165" role="code" l10n="NEW">b = INTERCEPT(Data_Y ;Data_X) </paragraph>
96 <paragraph xml-lang="en-US" id="par_id7879268" role="paragraph" l10n="NEW">Calculate the coefficient of determination by</paragraph>
97 <paragraph xml-lang="en-US" id="par_id9244361" role="code" l10n="NEW">r² = RSQ(Data_Y;Data_X) </paragraph>
98 <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>
99 <paragraph xml-lang="en-US" id="hd_id2538834" role="heading" level="2" l10n="NEW">The logarithm regression equation</paragraph>
100 <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>
101 <paragraph xml-lang="en-US" id="par_id2134159" role="code" l10n="NEW">a = SLOPE(Data_Y;LN(Data_X)) </paragraph>
102 <paragraph xml-lang="en-US" id="par_id5946531" role="code" l10n="NEW">b = INTERCEPT(Data_Y ;LN(Data_X)) </paragraph>
103 <paragraph xml-lang="en-US" id="par_id5649281" role="code" l10n="NEW">r² = RSQ(Data_Y;LN(Data_X)) </paragraph>
104 <paragraph xml-lang="en-US" id="hd_id7874080" role="heading" level="2" l10n="NEW">The exponential regression equation</paragraph>
105 <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>
106 <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>
107 <paragraph xml-lang="en-US" id="par_id4416638" role="code" l10n="NEW">a = SLOPE(LN(Data_Y);Data_X) </paragraph>
108 <paragraph xml-lang="en-US" id="par_id1039155" role="paragraph" l10n="CHG">The variables for the second variation are calculated as follows:</paragraph>
109 <paragraph xml-lang="en-US" id="par_id7184057" role="code" l10n="NEW">m = EXP(SLOPE(LN(Data_Y);Data_X)) </paragraph>
110 <paragraph xml-lang="en-US" id="par_id786767" role="code" l10n="NEW">b = EXP(INTERCEPT(LN(Data_Y);Data_X)) </paragraph>
111 <paragraph xml-lang="en-US" id="par_id7127292" role="paragraph" l10n="NEW">Calculate the coefficient of determination by</paragraph>
112 <paragraph xml-lang="en-US" id="par_id5437177" role="code" l10n="NEW">r² = RSQ(LN(Data_Y);Data_X) </paragraph>
113 <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>
114 <paragraph xml-lang="en-US" id="hd_id6349375" role="heading" level="2" l10n="NEW">The power regression equation</paragraph>
115 <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>
116 <paragraph xml-lang="en-US" id="par_id8517105" role="code" l10n="NEW">a = SLOPE(LN(Data_Y);LN(Data_X)) </paragraph>
117 <paragraph xml-lang="en-US" id="par_id9827265" role="code" l10n="NEW">b = EXP(INTERCEPT(LN(Data_Y);LN(Data_X)) </paragraph>
118 <paragraph xml-lang="en-US" id="par_id2357249" role="code" l10n="NEW">r² = RSQ(LN(Data_Y);LN(Data_X)) </paragraph>
119 <paragraph xml-lang="en-US" id="hd_id9204077" role="heading" level="2" l10n="NEW">Constraints<comment>UFI: is this still so?</comment></paragraph>
120 <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>
121 <list type="ordered">
122 <listitem>
123 <paragraph xml-lang="en-US" id="par_id7212744" role="paragraph" l10n="NEW">logarithm regression: only positive x-values are considered,</paragraph>
124 </listitem>
125 <listitem>
126 <paragraph xml-lang="en-US" id="par_id1664479" role="paragraph" l10n="NEW">exponential regression: only positive y-values are considered,</paragraph>
127 </listitem>
128 <listitem>
129 <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>
130 </listitem>
131 </list>
132 <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>
133 <paragraph xml-lang="en-US" id="hd_id7907040" role="heading" level="2" l10n="NEW">The polynomial regression equation</paragraph>
134 <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>
135 <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>
136 <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>
137 <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>
138 <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>
139 <section id="relatedtopics">
140 <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>
141 </section>
142 </body>
| 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>
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