# SSE

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```					Computing the Sum of Squares Error (SSE)
(Based on Example 1 in the text)

Note: Make sure macros are enabled; otherwise, the buttons will not work.

Here, we compute the value of SSE using the line y = 8t + 72 to approximate the given data.

t                y (Observed) y (Predicted) Residue^2       m            b
-4              50                                        8            72               Given values of m and b
-3              55
-2              57                                    SSE:              0
-1              60
0              68                                       1. To compute y (Predicted), use the formula
1              72                                                         =\$E\$15*A15+\$F\$15
2              80                                          representing     m*t + b
3              83                                          in cell C15 and copy it down to C22.

90                                  2. To compute the residue squared, use the formula
80                                                    =(B15-C15)^2
70                                     representing (y Obs - y Pred)^2
60                                     in cell D15 and copy it down to D22.
50
40
3. Now look at the formula for SSE in cell F17.
30
20
10
4. Now change the values of m and b in cells E15 and F15 to see its
0
effect on SSE. Now try to change m and b to make SSE as small a
-6      -4          -2           0      2           4              Notice the effect on the graph: a smaller SSE means a line that
y (Observed)                              is closer to the data points.
Given values of m and b

ared, use the formula

SE in cell F17.

and b in cells E15 and F15 to see its
ange m and b to make SSE as small as possible.
h: a smaller SSE means a line that
Using the Regression Formula                  (See sheet "Built-In" for use of the built-in regression features.)
(Based on Example 2 in the book.)             Note: Make sure macros are enabled; otherwise, the buttons will not work.

Example 2                                                                  Example 2*       (For you to complete)

Look at the chart below with columns labeled x and y.                        Below are a set of x- and y-coordinates.
The x- and y-columns contain the data from the example in the book.          You are to complete the regression by filling in the appropriate form
Look at the formulas in the xy- and x_squared columns, and compare
them with the formulas in the text.                                             Press here to see the correct equation:
We have placed the cells containing the results above the table
Results:           m=
Cells C28 and E28 contain the formulas for m and b.                             Equation: y = x + 0

Experiment by changing the calues of x and y in the table.                         n              Sums:

x- and y-values, and copy the remaining formulas in the                                           x               y
new row (xy and x_squared).                                                                           160             126
180             103
200              82
Results:            m= 0.5                           b= 0.8                                       220              75
Equation: y = 0.5x + 0.8                                                                           240              82
260              40
280              20
n              Sums:
4           10              8.2              23             30

x             y               xy         x_squared
1            1.5              1.5            1
2            1.6              3.2            4
3            2.1              6.3            9
4             3               12            16
e buttons will not work.

(For you to complete)

ession by filling in the appropriate formulas.

rect equation:

b=

xy         x_squared
Using the built-in linear regression functions
(Based on Example 3 in the book.)

x             y                     Using the built-in trendline feature
-4           50
-3           55               1. Highlight the table of x- and y-values (cells A7 through B15)
-2           57               2. Create an XY (Scatter) graph with points (no lines) and "series in columns."
-1           60               3. With the chart selected, select Chart -> Add Trendline… and choose the "linear"
0           68               trendline. Under "Options," choose "Display equation."
1           72
2           80
3           83
"series in columns."
… and choose the "linear"

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