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Can i use simple linear regression when there is unequal sample sizes for the dependent and independent variable? Will this be a problem?

That is; y=a+bx+epsilon, where y and x have unequal sample sizes.

Jenny
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  • How can it happen, that an $x_i$ does not have a corresponding $y_i$ ? – callculus42 Aug 18 '15 at 01:19
  • due to missing observations.. y is actually a cross sectional list of returns, and x is also a cross sectional list of returns...x and y represent the returns of managers, just that x is the first fund of the manager while y is the same manager subsequent funds... i want to see if y depends on x. – Jenny Aug 18 '15 at 01:23
  • I don´t think, that I have the understood whole situation. Obviously molarmass have it understood better. Good luck. – callculus42 Aug 18 '15 at 01:39

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If you have a data point that lacks either a value for the dependent or the independent variable, the data point does not carry any meaningful information and hence it is pretty much useless.

For example, assume you are investigating the influence of education on income and in your sample you have a person who earns $100,000 per year, but you don’t know his education level. Such information does not tell you anything about the relation between education and income, simply because you have no idea what his education level is.

Therefore you can only meaningfully use observations for which both the dependent and independent values are known.

molarmass
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  • @Jenny It depends a little bit on the context of the regression, but in many cases it is best to leave “incomplete” observations out of the sample altogether, such that you have the same number of observations for each variable. – molarmass Aug 18 '15 at 01:14
  • great answer! thanks. since i have a cross sectional list of x and y that are unequal in sample size, do you think i can regress as follows, y = a + dummyvariable + episilon...that is, according to your cited example, the dummy would be 1 for with education and 0 for without? – Jenny Aug 18 '15 at 01:15