Page 190 - Coincidences in the Bible and in Biblical Hebrew

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CHAPTER 12 THE COLORS
CHAPTER 12 THE COLORS 169
12.3.3 Linear Regression Analysis: Description and Results (Stage 3)
Analysis I: Based on the Extended Set (basic set plus interpolated and
extrapolated observations)

Implementing simple linear regression, with CNV as the regressor (the indepen-
dent variable) and WF as the response (the dependent variable), the following

equation is obtained:
WF = 475.95 + 0.20175*CNV
-6
(p<10 ) (p = 0.000197)

(Numbers in brackets indicate the significance levels of the model’s
coefficients.)
2
The associated linear correlation is R = 0.9754, with adjusted-R = 0.9745. A

normal probability plot shows the residuals to properly behave within the con-

fines of the normal scenario (the latter is needed for linear regression analysis to be

valid; refer to any basic text in statistics for definition of the normal scenario—for
example, Shore 2005).
For n = 7 (the sample size), the model’s F-ratio value is 97.85, which, with

1 and 5 degrees of freedom, has significance value of p = 0.00020. This implies

likelihood of less than 0.02% of obtaining an F value that high (or higher) by
chance alone. In other words, if the null hypothesis were true, this would be the
probability of getting that high F value.
A scatter plot of the observations, with the fitted linear regression equation

and 95% confidence limits, is given in Figure 12.1. To allow easy identification of

each observation, the WF value is marked for each point in the plot.

The reader is encouraged to find out whether similar results would have

obtained if one changed the CNV value of one of the observations in the basic set.
For example, for yellow, let CNV = 600 (instead of the current 97!). Note, that
for these further scenario analyses to be valid, the interpolated and extrapolated
values need also be recomputed.
Analysis II: Based on the Basic Set (Four Observations)

Applying simple linear regression, with CNV as the regressor (the independent
variable) and WF as the response (the dependent variable), the following equation

is obtained: