Ratio and Regression Estimation

(sample sum of y / sample sum of x)*total sum of x = ratio estimator * total sum of x = Btx = total sum of y = ty

ratio estimator of total population y average is = sample y average * (total population x average/sample x average)

Ratio Estimator = R = sample covariance / (sample s.d. of x * sample s.d. of y)

Coefficient of Variation estimate = sample s.d. of x / mean of x

If R > CV(X)/CV(Y)*1/2 then ratio estimator is better

Confidence Interval = memorise the Var(total estimate of y ratio)

The fitted regression line can be calculated using ratio estimates

Intercept B0 = mean y - ratio estimator * mean of x

Coefficient = covariance(x,y) / variance(x)

Regression estimation applies in a similar setting to ratio estimation but can provide more precise estimation if y is linearly related to x, and the regression intercept is non-zero.

Ratio regression works well when there is high correlation between the two things and when the linear regression passes through the origin