Solutions For An Introduction to Genetic Analysis Chapter 19 Problem 22P

Correlation coefficient (r) measures the strength and the direction of a linear relationship between two variables. The value of r lies between -1 and +1. If the two values have a strong positive linear correlation, r is close to +1. Positive correlation values indicate that if the values for x increases, values for y also increase.

If the r value is close to -1, it indicates that the x and y have a strong negative linear correlation. Negative correlation values indicate that if values for x increase, the values for y decrease.

If there is no correlation between x and y, then the value of r is either zero or close to zero.

For the given data, correlation coefficient is calculated as follows:

• The mean of all first coordinates (let them be x_i) is calculated

• The mean of all second coordinates (let them be y_i) is calculated

• Standard deviation of all the first coordinates x_i is calculated. Let it be s_x

•

Standard deviation of all the second coordinates y_i is calculated. Let it be s_y

• Standardized value for each x_i is calculated_. Let this standard value for each x_i variable be (z_x)_i

• Standardized value for each y_i is calculated_. Let this standard value for each y_i variable be (z_y)_i

• Corresponding standardized values for each pair are multiplied

• The sum of the value obtained from previous step is divided by n-1, where n is the total number of pairs of values

Standard deviation (s_x) for the x_i values = 7.7

Standard deviation (s_y) for the y_i values = 8.8

Twin 1(xi)	Twin 2 (yi)	Standardized values for xi (zx)i =	Standardized value for yi (zy)i =
158	163	-0.84	-0.056	0.05
156	150	-1.10	-1.75	1.92
172	173	0.97	1.07	1.04
156	154	-1.10	-1.07	1.18
160	163	-0.58	-0.05	0.03
159	153	-0.71	-1.19	0.85
170	174	0.71	1.19	0.85
177	174	1.62	1.19	1.92
165	168	0.06	0.511	0.03
172	165	0.97	0.170	0.16
	8.026

Correlation coefficient (r) =

Therefore, the two values are in strong positive correlation.