This example teaches you how to perform a regression analysis in Excel and how to interpret the Summary Output.
Below you can find our data. The big question is: is there a
relation between Quantity Sold (Output) and Price and Advertising (Input). In
other words: can we predict Quantity Sold if we know Price and Advertising?
1. On the Data tab, in the Analysis group, click Data
Analysis.
2.
Select Regression and click OK.
3. Select the Y Range (A1:A8). This is the predictor
variable (also called dependent variable).
4. Select the X Range(B1:C8). These are the explanatory
variables (also called independent variables). These columns must be adjacent
to each other.
5. Check Labels.
6. Click in the Output Range box and select cell A11.
7. Check Residuals.
8. Click OK.
Excel produces the following Summary Output (rounded to 3
decimal places).
R Square
R Square equals 0.962, which is a very good fit. 96% of the
variation in Quantity Sold is explained by the independent variables Price and
Advertising. The closer to 1, the better the regression line (read on) fits the
data.
Significance F and P-values
To check if your results are reliable (statistically
significant), look at Significance F (0.001). If this value is less than 0.05, you're
OK. If Significance F is greater than 0.05, it's probably better to stop using
this set of independent variables. Delete a variable with a high P-value
(greater than 0.05) and rerun the regression until Significance F drops below
0.05.
Most or all P-values should be below below 0.05. In our
example this is the case. (0.000,
0.001 and 0.005).
Coefficients
The regression line is: y = Quantity Sold = 8536.214 -835.722 * Price + 0.592 *
Advertising. In other words, for each unit increase in price, Quantity Sold
decreases with 835.722 units. For each unit increase in Advertising, Quantity
Sold increases with 0.592 units. This is valuable information.
You can also use these coefficients to do a forecast. For
example, if price equals $4 and Advertising equals $3000, you might be able to
achieve a Quantity Sold of 8536.214
-835.722 * 4 + 0.592 * 3000 = 6970.
Residuals:
The residuals show you how far away the actual data points
are fom the predicted data points (using the equation). For example, the first
data point equals 8500. Using the equation, the predicted data point equals 8536.214 -835.722 * 2 + 0.592 *
2800 = 8523.009, giving a residual of 8500 - 8523.009 = -23.009.
You can also create a scatter plot of these residuals.
Author : NAGARJUNA MAHANTI
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