#### Linear Trendline #2

```Excel has created a linear trendline with its equations from the following
points:
X	Y
1	4
3	12
6	15

the equations are:
y = 2.1053x + 3.3158
R2 = 0.8681

I wonder if you can tell me how excel create this linear trendline from the
points shown.

Maperalia

```
 0
maperalia (28)
5/4/2006 2:03:01 AM
excel.charting 18370 articles. 0 followers.

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```Maperalia  -

Excel uses "ordinary least squares," i.e., matrix operations that yield
coefficients that minimize the sum of squared deviations.

For the simple linear case, the results are equivalent to the formulas in
Excel's Help for the INTERCEPT and SLOPE worksheet functions.

See Excel's Help for the LINEST function for more details.

For more discussion of numerical accuracy, see
"Description of the LINEST function in Excel 2003 and in Excel 2004 for Mac"
at
support.microsoft.com/kb/828533
and
"Description of improvements in the statistical functions in Excel 2003 and
in Excel 2004 for Mac" at
support.microsoft.com/default.aspx?kbid=828888&product=xl2003

-  Mike
www.mikemiddleton.com

"maperalia" <maperalia@discussions.microsoft.com> wrote in message
> Excel has created a linear trendline with its equations from the following
> points:
> X Y
> 1 4
> 3 12
> 6 15
>
> the equations are:
> y = 2.1053x + 3.3158
> R2 = 0.8681
>
> I wonder if you can tell me how excel create this linear trendline from
> the
> points shown.
>
> Maperalia
>

```
 0
mike5208 (300)
5/4/2006 2:44:15 AM
```Mike;
I have read the information you adviced me. This information shows how the
formulas to create a linear trend from this points
However, what I am looking is the formulas where excel takes these point and
adjust them to make a linear trendline.

Wher do you think I can get this information?

Maperalia

"Mike Middleton" wrote:

> Maperalia  -
>
> Excel uses "ordinary least squares," i.e., matrix operations that yield
> coefficients that minimize the sum of squared deviations.
>
> For the simple linear case, the results are equivalent to the formulas in
> Excel's Help for the INTERCEPT and SLOPE worksheet functions.
>
> See Excel's Help for the LINEST function for more details.
>
> For more discussion of numerical accuracy, see
> "Description of the LINEST function in Excel 2003 and in Excel 2004 for Mac"
> at
> support.microsoft.com/kb/828533
> and
> "Description of improvements in the statistical functions in Excel 2003 and
> in Excel 2004 for Mac" at
> support.microsoft.com/default.aspx?kbid=828888&product=xl2003
>
> -  Mike
> www.mikemiddleton.com
>
> "maperalia" <maperalia@discussions.microsoft.com> wrote in message
> > Excel has created a linear trendline with its equations from the following
> > points:
> > X Y
> > 1 4
> > 3 12
> > 6 15
> >
> > the equations are:
> > y = 2.1053x + 3.3158
> > R2 = 0.8681
> >
> > I wonder if you can tell me how excel create this linear trendline from
> > the
> > points shown.
> >
> > Maperalia
> >
>
>
>
```
 0
maperalia (28)
5/4/2006 5:23:01 PM
```Maperalia  -

I don't understand what other "formulas" you are looking for.

For example, the XY data is used by the INTERCEPT and SLOPE functions (or by
the chart trendline feature), and the fitted Y values for the line are
determined using =INTERCEPT+SLOPE *X.

What more do you want?

-  Mike

"maperalia" <maperalia@discussions.microsoft.com> wrote in message
> Mike;
> Thanks for your quick reponse.
> I have read the information you adviced me. This information shows how the
> formulas to create a linear trend from this points
> However, what I am looking is the formulas where excel takes these point
> and
> adjust them to make a linear trendline.
>
> Wher do you think I can get this information?
>
> Maperalia
>
> "Mike Middleton" wrote:
>
>> Maperalia  -
>>
>> Excel uses "ordinary least squares," i.e., matrix operations that yield
>> coefficients that minimize the sum of squared deviations.
>>
>> For the simple linear case, the results are equivalent to the formulas in
>> Excel's Help for the INTERCEPT and SLOPE worksheet functions.
>>
>> See Excel's Help for the LINEST function for more details.
>>
>> For more discussion of numerical accuracy, see
>> "Description of the LINEST function in Excel 2003 and in Excel 2004 for
>> Mac"
>> at
>> support.microsoft.com/kb/828533
>> and
>> "Description of improvements in the statistical functions in Excel 2003
>> and
>> in Excel 2004 for Mac" at
>> support.microsoft.com/default.aspx?kbid=828888&product=xl2003
>>
>> -  Mike
>> www.mikemiddleton.com
>>
>> "maperalia" <maperalia@discussions.microsoft.com> wrote in message
>> > Excel has created a linear trendline with its equations from the
>> > following
>> > points:
>> > X Y
>> > 1 4
>> > 3 12
>> > 6 15
>> >
>> > the equations are:
>> > y = 2.1053x + 3.3158
>> > R2 = 0.8681
>> >
>> > I wonder if you can tell me how excel create this linear trendline from
>> > the
>> > points shown.
>> >
>> > Maperalia
>> >
>>
>>
>>

```
 0
mike5208 (300)
5/4/2006 5:40:00 PM
```Mike wrote  on Thu, 4 May 2006 10:40:00 -0700:

MM> I don't understand what other "formulas" you are looking
MM> for.

MM> For example, the XY data is used by the INTERCEPT and SLOPE
MM> functions (or by the chart trendline feature), and the
MM> fitted Y values for the line are determined using
MM> =INTERCEPT+SLOPE *X.

MM> What more do you want?

MM> -  Mike

MM> "maperalia" <maperalia@discussions.microsoft.com> wrote in
MM> message
??>> Mike;
??>> Thanks for your quick reponse.
??>> information shows how the formulas to create a linear
??>> trend from this points However, what I am looking is the
??>> formulas where excel takes these point and adjust them to
??>> make a linear trendline.
??>>  ??>> Wher do you think I can get this information?

I woder if the OP wants the actual details of calculating the
slope and intercept? The equations are given in HELP, AFAIK.

James Silverton.

```
 0
5/4/2006 6:33:31 PM
```Mike;
Thanks you very much. I really appreciatte your supporting in this matter.

Kind regards.
Maperalia

"Mike Middleton" wrote:

> Maperalia  -
>
> I don't understand what other "formulas" you are looking for.
>
> For example, the XY data is used by the INTERCEPT and SLOPE functions (or by
> the chart trendline feature), and the fitted Y values for the line are
> determined using =INTERCEPT+SLOPE *X.
>
> What more do you want?
>
> -  Mike
>
> "maperalia" <maperalia@discussions.microsoft.com> wrote in message
> > Mike;
> > Thanks for your quick reponse.
> > I have read the information you adviced me. This information shows how the
> > formulas to create a linear trend from this points
> > However, what I am looking is the formulas where excel takes these point
> > and
> > adjust them to make a linear trendline.
> >
> > Wher do you think I can get this information?
> >
> > Maperalia
> >
> > "Mike Middleton" wrote:
> >
> >> Maperalia  -
> >>
> >> Excel uses "ordinary least squares," i.e., matrix operations that yield
> >> coefficients that minimize the sum of squared deviations.
> >>
> >> For the simple linear case, the results are equivalent to the formulas in
> >> Excel's Help for the INTERCEPT and SLOPE worksheet functions.
> >>
> >> See Excel's Help for the LINEST function for more details.
> >>
> >> For more discussion of numerical accuracy, see
> >> "Description of the LINEST function in Excel 2003 and in Excel 2004 for
> >> Mac"
> >> at
> >> support.microsoft.com/kb/828533
> >> and
> >> "Description of improvements in the statistical functions in Excel 2003
> >> and
> >> in Excel 2004 for Mac" at
> >> support.microsoft.com/default.aspx?kbid=828888&product=xl2003
> >>
> >> -  Mike
> >> www.mikemiddleton.com
> >>
> >> "maperalia" <maperalia@discussions.microsoft.com> wrote in message
> >> > Excel has created a linear trendline with its equations from the
> >> > following
> >> > points:
> >> > X Y
> >> > 1 4
> >> > 3 12
> >> > 6 15
> >> >
> >> > the equations are:
> >> > y = 2.1053x + 3.3158
> >> > R2 = 0.8681
> >> >
> >> > I wonder if you can tell me how excel create this linear trendline from
> >> > the
> >> > points shown.
> >> >
> >> > Thanks in advance.
> >> > Maperalia
> >> >
> >>
> >>
> >>
>
>
>
```
 0
maperalia (28)
5/4/2006 10:23:02 PM

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