To use Excel to fit an equation by **Linear
Least Squares Regression**:

Have yourY = A + BX + CX^2 + DX^3 + ...

Below this block of numbers select a block just as wide
as that one and 2 to 4 rows high - so if you just have **Y**
and **X** values (linear equation)
the new highlighted block is 2 columns by 2 to 4 rows.

Type "**= linest(**" and
then drag down to hilite your column of **Y-values**
- this should now look like "**= linest(B2:B12**"
.

Type a comma, then drag across all of the **X,
X^2, X^3, ... ** values from upper left to lower right to
hilite the whole block - this is just one column if you have a linear
equation - and now the text should look like "**=
linest(B2:B12,C2:C12**" or "**= linest(B2:B12,C2:E12**"
if you have cubic terms.

Now type "**,1,1)**" and
**hold
down the open-apple key** (next to the space bar) while
you hit **Enter**. If you type "**0**"
in place of the first "**1**" it forces
A to be zero. "**0**" in place of
the second "**1**" cuts off uncertainties
in A, B, C, ... Dragging across the values to include them in the
formula is just a convenience, you can simply type the "linest" statement
if you wish.

The equation that you are fitting does not have to be
a power series.

You could be fitting **Y**
to any set of variables (**X,V,W**):

Just put yourY = A + BX + CV + DW.

In the new block, the top row is the coefficients
in reverse order - the one on the far right is A, then B to the left
of that, etc. Below each of these is an estimated **uncertainty
or standard deviation** in the value. The leftmost entry in the
third row is the correlation coefficient (**R^2**)
which should be close to 1.000. The second item is the **standard
deviation** (the scatter) of the Y values about the calculated
line.

The fourth line is other statistical things.

|___2 |___B____|___C___|____D____|__E___|___F___|

3 |___

4 |___

5 |___

6 |___

7 |___

8
|________|________|________|_______|__

9
|________|________|________|_______|__

10 |________|________|________|_______|__

11 |________|________|________|_______|__

Hilite this whole block by dragging the mouse from cell
**B8** to cell **E11**

Type "**= linest(B2:B7,C2:E7,1,1)**"
and "**open-apple**" **ENTER**

Gives **Y = A + BX + CX^2
+ DX^3**

8 **|____D___|____C___|____B___|___A___|**

9 **|___dD___|___dC___|___dB___|__dA___|**

10 **|__R^2___|___dY___|________|________|**

11 **|__?_____|___dF___|________|________|**

dF = degrees of Freedom = (# of Y-values) - (# of parameters)The # of Y-values should be at least the square of the number of parameters.

1. Select data to be graphed, usually in (a) column(s).
The name of the column for the Legend may be included as the topmost entry.
If only one column is selected , that is normally the Y-values, and the
X-values are equally spaced (1,2,3,...). If two are more columns are selected,
you will be able to designate one as the X-values - the other columns will
be graphed on different lines. It is best to have the X-column on the left
of the Y-column(s). It is OK if some Y-values are missing from some
of the columns.

2. Drag down under **INSERT**
on the menubar to **CHART**. Select whether
you want the chart to be on the same page as the data or on a different
page. You can Cut&Paste later, so this isn't critical.

3. Hold down the mousebutton and drag over the area where the chart will appear. You can reshape and relocate it later if you wish. A dialog box appears.

4. Check that the indicated range is the data that
you want to graph. Click on **NEXT**.

5. Choose a **SCATTER**
Plot or a LINE Plot (IF you haven't entered X-values). Click on **NEXT**.

6. Choose the format that you want for the graph.
Click on **NEXT**.

7. Check the entries that appear, then click on
**FINISH**.

Modifying:

1. Click on the graph to select it for moving or re-shaping. Double-click to produce a thick border in order to make internal changes.

2. Drag down under **FORMAT**
to **CHART TYPE** to change the basic type
of plot (as in 5 above). Drag to **AUTOFORMAT**
to change the Format (as in 6 above). Drag to **OBJECT**
to change fonts, colors, line types, etc.

3. Double-click on an **axis**
to edit it. You can set the **scale, tick
marks, font, **etc. This is
also where you choose **symbols, line colors, dashed
lines,** etc.

4. Click on the **CHART WIZARD**
icon on the ToolBar to change the data selection and other attributes.