You are running a regression for an outcome Y, with the main intervention variable X₁and 5 additional control variables (call them X₂- X₆). You have a sample of 800 observations. Describe how the size of the standard error of the coefficient estimate (call it SE(₁)) of X_1,will be affected byeachof the following (if in a particular case you are not sure of the direction of the effect, explain why that's the case). Each situation is what in economics is called'ceteris paribus' (i.e. nothing else except theone thing describedchanges).

(a) Ceteris paribus, the overall sample size increases from 800 tp 1000.

(b) Ceteris paribus, the number of other X-variables that are controlled for in the model is increased by adding 4 more control variables.

(c) Ceteris paribus, one control variable is introduced in the model which is highly correlated with X₁.