5.6 Estimation of covariance

If we are interested in estimating the population variance and population covariance of the self-reported height and weight (\(\texttt{HWT_DHT_M_TRM}\) and \(\texttt{HWT_WGHT_KG_TRM}\)), the following codes can be used.

R

print(svyvar( ~ HWT_DHT_M_TRM + HWT_WGHT_KG_TRM, CLSA.design),
      covariance = TRUE)

Result

Statistics	Estimate	SE
Var(HWT_DHT_M_TRM)	5.266e-03	3.625e-04
Var(HWT_WGHT_KG_TRM)	2.757e+02	3.290e+01
Cov(HWT_DHT_M_TRM,HWT_WGHT_KG_TRM)	5.263e-01	6.703e-02

Note 1: There are no formal procedures for estimation of population variance and covariance in \(\texttt{SAS}\), \(\texttt{SPSS}\) or \(\texttt{Stata}\).

Note 2: The population covariance is a descriptive parameter on the relationship between the two target variables in the population. Estimation of a population covariance is a different task than regression analysis to be presented in the next chapter.