Regression
Analysis
Performs linear regression analysis by using the "least squares"
method to fit a line through a set of observations. By using this
tool to analyze how a single dependent variable is affected by the
values of one or more independent variables .
Example
The
following table gives for 25 progenies of cotton the data for mean
fiber length of each progeny , the corresponding parent plant value
and the mean value of the plot in which the parent was grown. It
is found that both the parental value as well as the plot mean bear
some relationship with the progeny mean. Express this relation in
the form of a partial regression equation with progeny mean as the
dependent variate.
Number of Progenies
|
Progeny Mean (mm)
Y
|
Parental Plant Value
X1
|
Parental Plot Mean
X2
|
1
|
24.3
|
26
|
25.5
|
2
|
24.48
|
28.8
|
25.5
|
3
|
23.41
|
25.2
|
25.5
|
4
|
21.6
|
23.4
|
25
|
5
|
22.49
|
26.6
|
25
|
6
|
23.62
|
25.4
|
24.6
|
7
|
22.75
|
23.4
|
24.6
|
8
|
24.4
|
27.6
|
23.6
|
9
|
22.6
|
24.4
|
23.6
|
10
|
25.36
|
24
|
24.42
|
11
|
23.21
|
24.2
|
24.42
|
12
|
24.76
|
26
|
24.42
|
13
|
21.53
|
22.8
|
22.56
|
14
|
21.32
|
20.8
|
22.56
|
15
|
22.81
|
24.8
|
22.56
|
16
|
25.41
|
26.2
|
24.9
|
17
|
24.3
|
27.2
|
24.9
|
18
|
23.65
|
26.6
|
24.91
|
19
|
24.31
|
25
|
24.91
|
20
|
21.88
|
23.4
|
24.05
|
21
|
24.1
|
25.6
|
24.05
|
22
|
21.91
|
23
|
24.05
|
23
|
22.24
|
25.4
|
24.57
|
24
|
23.45
|
23.4
|
24.57
|
25
|
22.1
|
24.2
|
24.57
|
Analysing
the Data
-
Enter
the above data in a separate worksheet of the same workbook as
did earlier.
-
On
the Main Menu Click the Tool menu to get various options in the
Tool menu.
-
Click
the Data Analysis Option to get the different options of Analysis
Tool Pack as shown in the previous exercise.
-
Click
the Regression option from the displayed Analysis Tool Pack Options.
-
Click
OK to get the Regression Analysis Tool Window as shown below

-
Input
Y Range :
Enter the range of dependent variable's data, that is, B2 :B26
The range must consist of a single column.
-
Input
X Range : Enter the range of independent variables data,
that is, C2:D26 The maximum number of input ranges is upto 16
variables.
-
Click
in the Labels check box to select the first row or column of input
range contains labels.
-
Click
in the Confidence Level check box to include an additional level
in the summary output table. In the box, enter the desired confidence
level in addition to the default 95% level.
-
Output
Range : Enter the range of cells or a cell that is A30
to keep the output on the worksheet. Allow at least seven columns
for the summary output table, which includes an anova table, coefficients,
standard error of y estimate, r2 values, number of observations,
and standard error of coefficients.
-
Click
in the Residuals check box to include residuals in the residuals
output table.
-
Click
in the Standardised Residuals check box to include standardised
residuals in the residuals output table.
-
Click
in the Residual Plots to generate a chart for each independent
variable versus the residual.
-
Click
in the Line Fit Plot to generate a chart for predicted values
versus the observed values.
-
Click
in the Normal Probability Plot to generate a chart plotting normal
probability.
|