Question

You wish to estimate as precisely as possible the slope β1 in the simple linear regression model yi = β0 + β1xi + ei , i = 1, . . . , 4.

Each pair of observations (xi , yi) costs $1.00 and your budget is $4.00. A data analyst proposes that you consider one of the following two options:

(a) Make two y-observations at x = 1 and a further two at x = 4;

(b) Make one y-observation at each of the points x = 1; 2; 3 and 4.

Which of the two options would give you the most bang for your bucks? Show the relevant calculation to justify your choice.

Answer 1

Which of the two options would give you the most bang for your bucks?

(b) Make one y-observation at each of the points x = 1; 2; 3 and 4.

There are no calculations involved in the explanation -

It is always better to have the variety of sample points rather having one or two sample points. On the basis of only 2 X's, the output results are not very accurate hence it will create X selection bias in the Regression. Instead the selection of four X's will give you randomaly selected sample and regression will be meanigfull.