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| − | <div id="6SpaceContent" class="zcontent" align="left"> | + | <div style="font-size:30px">'''SLOPE(y,x)'''</div><br/> |
| | + | *<math> y </math> is the set of dependent values. |
| | + | *<math> x </math> is the set of independent values. |
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| − | <font face="Arial, sans-serif"><font size="2">'''SLOPE'''</font></font><font face="Arial, sans-serif"><font size="2">(</font></font><font face="Arial, sans-serif"><font size="2">'''ky's'''</font></font><font face="Arial, sans-serif"><font size="2">,</font></font><font face="Arial, sans-serif"><font size="2">'''kx's'''</font></font><font face="Arial, sans-serif"><font size="2">)</font></font>
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| − | <font face="Arial, sans-serif"><font size="2"></font></font><font face="Arial, sans-serif"><font size="2">'''Where ky's'''</font></font><font face="Arial, sans-serif"><font size="2"> is an array or cell range of numeric dependent data points and </font></font><font face="Arial, sans-serif"><font size="2">'''Kx's'''</font></font><font face="Arial, sans-serif"><font size="2"> is the set of independent data points.</font></font>
| + | ==Description== |
| | + | *This function gives the slope of the linear regression line through a set of given points. |
| | + | *The slope of a regression line (b) represents the rate of change in y as x changes. |
| | + | *To find a slope we can use the least squares method. |
| | + | *Slope is found by calculating b as the covariance of x and y, divided by the sum of squares (variance) of x. |
| | + | *In SLOPE(y,x), y is the array of the numeric dependent values and x is the array of the independent values. |
| | + | *The arguments can be be either numbers or names, array,constants or references that contain numbers. |
| | + | *Suppose the array contains text,logical values or empty cells, like that values are not considered. |
| | + | *The equation for the slope of the regression line is :<math>b = \frac {\sum (x-\bar{x})(y-\bar{y})} {\sum(x-\bar{x})^2</math>. where <math>\bar{x}</math> and <math>\bar{y}</math> are the sample mean x and y. |
| | + | *This function will return the result as error when |
| | + | 1. Any one of the argument is nonnumeric. |
| | + | 2. x and y are empty or that have a different number of data points. |
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| − | </div>
| + | ==Examples== |
| − | ----
| + | 1.y={4,9,2,6,7} |
| − | <div id="1SpaceContent" class="zcontent" align="left"> <font face="Arial, sans-serif"><font size="2">It calculates the slope of the linear regression line through data points in ky's and kx's. </font></font></div>
| + | x={1,5,10,3,4} |
| − | ---- | + | SLOPE(A1:A5,B1:B5)=-0.305309734513 |
| − | <div id="7SpaceContent" class="zcontent" align="left"><font size="2" color="#7f7f7f" face="Arial">The equation for the slope of the regression line is: </font>
| + | 2.y={2,9,3,8,10,17} |
| | + | x={4,5,11,7,15,12} |
| | + | SLOPE(B1:B6,C1:C6)=0.58510638297 |
| | + | 3.y={0,9,4} |
| | + | x={-1,5,7} |
| | + | SLOPE(C1:C3)=0.730769230769 |
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| − | <br /><br />
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| − | <font size="2" color="#7f7f7f" face="Arial">where x and y are the sample means AVERAGE(kx’s) and AVERAGE(ky’s).</font><br />
| + | ==See Also== |
| | + | *[[Manuals/calci/INTERCEPT | INTERCEPT]] |
| | + | *[[Manuals/calci/RSQ | RSQ ]] |
| | + | *[[Manuals/calci/PEARSON | PEARSON ]] |
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| − | </div>
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| − | ----
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| − | <div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
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| − | SLOPE
| + | ==References== |
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| − | </div></div>
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| − | ----
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| − | <div id="8SpaceContent" class="zcontent" align="left">
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| − | <font color="#000000"><font face="Arial, sans-serif"><font size="3"><nowiki>=SLOPE(B2:B8,C2:C8) is 0.3993</nowiki></font></font></font>
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| − | | |
| − | </div>
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| − | ----
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| − | <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
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| − | ----
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| − | <div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
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| − | ----
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| − | <div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
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| − | ----
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| − | <div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
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| − | ----
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| − | <div id="5SpaceContent" class="zcontent" align="left"><div>
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| − | {| id="TABLE1" class="SpreadSheet blue"
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| − | |- class="even"
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| − | | class=" " |
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| − | <div id="5Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | | class=" " | Column1
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| − | | class=" " | Column2
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| − | | class=" " | Column3
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| − | | class=" SelectTD" |
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| − | <div id="5Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="5Space_Copy" title="Click and Drag over to AutoFill other cells."></div>Column4
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| − | |- class="odd"
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| − | | class=" " | Row1
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| − | | class="sshl_f " | 5
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| − | | class="sshl_f " | 16
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| − | | class="sshl_f" | 0.3993
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| − | |- class="even"
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| − | | class=" " | Row2
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| − | | class="sshl_f" | 6
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| − | | class="sshl_f" | 10
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| − | | class="sshl_f" | 5
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| − | | class=" sshl_f " |
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| − | <div id="5Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | | class="sshl_f" |
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| − | |- class="odd"
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| − | | class=" " | Row5
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| − | | class="sshl_f" | 18
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| − | | class="sshl_f" | 17
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| − | | class="sshl_f " |
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| − | <div id="5Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | | class="sshl_f" |
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| − | |- class="even"
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| − | | class="sshl_f" | rOW6
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| − | | class="sshl_f" | 4
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| − | | class="sshl_f" | 9
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| − | | class="sshl_f " |
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| − | |- class="odd"
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| − | | class="sshl_f" | Row7
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| − | | class=" " | 3
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| − | | class="sshl_f " | 9
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| − | | class=" " |
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| − | <div id="5Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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| − | |}
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| − | <div align="left">[[Image:calci1.gif]]</div></div>
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| − | ----
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| − | </div>
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