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Analysis of Data from Designed Experiments |
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Correlation and Regression |
Example:
The
following data was collected through a pilot sample survey
on Hybrid Jowar crop on yield and biometrical characters.
The biometrical characters were average Plant Population
(PP), average Plant Height (PH), average Number of Green
Leaves (NGL) and Yield (kg/plot).
|
S.No. |
PP |
PH |
NGL |
Yield |
|
S.No. |
PP |
PH |
NGL |
Yield |
|
1 |
142.00 |
0.525 |
8.2 |
2.470 |
24 |
55.55 |
0.265 |
5.0 |
0.430 |
|
|
2 |
143.00 |
0.640 |
9.5 |
4.760 |
25 |
88.44 |
0.980 |
5.0 |
4.080 |
|
|
3 |
107.00 |
0.660 |
9.3 |
3.310 |
26 |
99.55 |
0.645 |
9.6 |
2.830 |
|
|
4 |
78.00 |
0.660 |
7.5 |
1.970 |
27 |
63.99 |
0.635 |
5.6 |
2.570 |
|
|
5 |
100.00 |
0.460 |
5.9 |
1.340 |
28 |
101.77 |
0.290 |
8.2 |
7.420 |
|
|
6 |
86.50 |
0.345 |
6.4 |
1.140 |
29 |
138.66 |
0.720 |
9.9 |
2.620 |
|
|
7 |
103.50 |
0.860 |
6.4 |
1.500 |
30 |
90.22 |
0.630 |
8.4 |
2.000 |
|
|
8 |
155.99 |
0.330 |
7.5 |
2.030 |
31 |
76.92 |
1.250 |
7.3 |
1.990 |
|
|
9 |
80.88 |
0.285 |
8.4 |
2.540 |
32 |
126.22 |
0.580 |
6.9 |
1.360 |
|
|
10 |
109.77 |
0.590 |
10.6 |
4.900 |
33 |
80.36 |
0.605 |
6.8 |
0.680 |
|
|
11 |
61.77 |
0.265 |
8.3 |
2.910 |
34 |
150.23 |
1.190 |
8.8 |
5.360 |
|
|
12 |
79.11 |
0.660 |
11.6 |
2.760 |
35 |
56.50 |
0.355 |
9.7 |
2.120 |
|
|
13 |
155.99 |
0.420 |
8.1 |
0.590 |
36 |
136.00 |
0.590 |
10.2 |
4.160 |
|
|
14 |
61.81 |
0.340 |
9.4 |
0.840 |
37 |
144.50 |
0.610 |
9.8 |
3.120 |
|
|
15 |
74.50 |
0.630 |
8.4 |
3.870 |
38 |
157.33 |
0.605 |
8.8 |
2.070 |
|
|
16 |
97.00 |
0.705 |
7.2 |
4.470 |
39 |
91.99 |
0.380 |
7.7 |
1.170 |
|
|
17 |
93.14 |
0.680 |
6.4 |
3.310 |
40 |
121.50 |
0.550 |
7.7 |
3.620 |
|
|
18 |
37.43 |
0.665 |
8.4 |
1.570 |
41 |
64.50 |
0.320 |
5.7 |
0.670 |
|
|
19 |
36.44 |
0.275 |
7.4 |
0.530 |
42 |
116.00 |
0.455 |
6.8 |
3.050 |
|
|
20 |
51.00 |
0.280 |
7.4 |
1.150 |
43 |
77.50 |
0.720 |
11.8 |
1.700 |
|
|
21 |
104.00 |
0.280 |
9.8 |
1.080 |
44 |
70.43 |
0.625 |
10.0 |
1.550 |
|
|
22 |
49.00 |
0.490 |
4.8 |
1.830 |
45 |
133.77 |
0.535 |
9.3 |
3.280 |
|
|
23 |
54.66 |
0.385 |
5.5 |
0.760 |
46 |
89.99 |
0.490 |
9.8 |
2.690 |
1.
Obtain
correlation coefficient between each pair of the variables
PP, PH, NGL and yield.
2.
Obtain
partial correlation between NGL and yield after removing the
linear effect of PP and PH.
3.
Give
a scatter plot of the variable PP.
4.
Fit
a multiple linear regression equation by taking yield as
dependent variable and biometrical characters as explanatory
variables. Print the matrices used in the regression
computations.
5.
Test
the significance of the regression coefficients and also
equality of regression coefficients of (a) PP and PH (b) PH
and NGL
6.
Obtain
the predicted values corresponding to each observation in
the data set.
7.
Check
for the linear relationship among the biometrical
characters, i.e., multi-colinearity in the data.
8.
Fit
the multiple linear regression model without intercept.
Analysis Using SAS Analysis Using SPSS
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For
exposure on SAS, SPSS,
MINITAB, SYSTAT and
MS-EXCEL
for analysis of data from designed experiments:
Please see Module I of Electronic Book II: Advances in Data Analytical Techniques
available at Design Resources Server (www.iasri.res.in/design)