NOTE: the specific content of the following is not really important BUT, it
just struck me how much we take for granted ... the "ability" to use cut
and paste methods with software and, couple it with our email ... to make
for easy to do and (i think quite effective) short instructional modules
that can be sent to a class, etc.
here is one example
we have been talking about basic linear regression in a course ... focusing
on partitioning Y variance into the predictable and error parts ... so, i
did another example (different from our regular class example) and ...
using minitab ... got output and copied to the email message with added
comments
seems like we just take this capability too much for granted ... but, it is
mighty powerful
--------------------
here is another example related to a regression problem ... and finding the
COD and COA values
i put some data in c16 and c17 ... and did a regression analysis ... NOTE:
MTB CAN STORE THE PREDICTED VALUES (fits) AND THE ERROR VALUES (residuals)
... USING SUBCOMMANDS (or dialog boxes)
MTB > regr c17 1 c16; <<< basic regr equation command
SUBC> fits c30; <<< asked mtb to store the predicted values in c30
SUBC> resi c31. <<< asked mtb to store the errors in c31
Regression Analysis: Y versus X
The regression equation is
Y = 339 - 2.79 X
Predictor Coef SE Coef T P
Constant 338.93 34.39 9.86 0.000
X -2.7923 0.6765 -4.13 0.001
S = 29.41 R-Sq = 48.6% R-Sq(adj) = 45.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 14734 14734 17.04 0.001
Residual Error 18 15567 865
Total 19 30301
Unusual Observations
Obs X Y Fit SE Fit Residual St Resid
3 74.0 116.00 132.31 17.58 -16.31 -0.69 X
X denotes an observation whose X value gives it large influence.
here is the plot between c16 and c17 ... note the NEGATIVE relationship
MTB > plot c17 c16
Plot
-
Y - *
- *
- * *
240+
- *
- *
- * * *
- * * * *
180+ * *
- * *
- * *
-
-
120+ *
-
-
--+---------+---------+---------+---------+---------+----X
32.0 40.0 48.0 56.0 64.0 72.0
MTB > corr c16 c17
Correlations: X, Y
Pearson correlation of X and Y = -0.697 <<< negative r
P-Value = 0.001
MTB > prin c16 c17 c30 c31
here are the columns of X, Y, Y' and errors
Data Display
Row X Y PredY ErrY
1 31 248 252.374 -4.3736
2 40 280 227.243 52.7567
3 74 116 132.307 -16.3067
4 42 208 221.659 -13.6588
5 49 228 202.113 25.8870
6 44 168 216.074 -48.0743
7 47 220 207.698 12.3025
8 51 152 196.529 -44.5285
9 51 172 196.529 -24.5285 <<< note that Y = Y' + error
10 62 184 165.814 18.1863
11 62 192 165.814 26.1863
12 39 260 230.036 29.9644
13 58 152 176.983 -24.9827
14 51 248 196.529 51.4715
15 46 192 210.490 -18.4898
16 55 180 185.360 -5.3595
17 60 188 171.398 16.6018
18 49 204 202.113 1.8870
19 48 196 204.905 -8.9053
20 39 204 230.036 -26.0356
MTB > let k1=stdev(c17)**2 <<< variance of Y
MTB > let k2=stdev(c30)**2 <<<< variance of Y'
MTB > let k3=stdev(c31)**2 <<< variance of errors
MTB > prin k1-k3
Data Display
K1 1594.78 <<< Y variance
K2 775.482 <<< Y' variance
K3 819.297 < error variance
MTB > let k4=k2/k1
MTB > prin k4
Data Display
K4 0.486263 <<< proportion of Y variance that is Y' variance
MTB > let k5=k3/k1
MTB > prin k5
Data Display
K5 0.513737 <<< proportion of Y variance that is error variance
MTB > corr c16 c17
Correlations: X, Y
Pearson correlation of X and Y = -0.697 <<< again, the r value
P-Value = 0.001
MTB > let k6=(.697)**2
MTB > prin k6
Data Display
K6 0.485809 <<< r SQUARED ... r squared = COD or 49% ... 1 - r squared
= COA or 51%
Y variance = Y' variance + error variance
100% = 49% + 51%
_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
.
.
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