Is there any simplest way to define both sample regression and population regression
A regression analysis always is the attemp to find (estimate) the regression coefficients so that the likelihood of the observed data is maximized.
If this observed data is from the complete population, then the regression is a population regression. The determined values of the coefficients are exactly those describing the regression model for the given population.
If the data is "just" a sample (from a real or a "statistical" population), then it's a sample regression. The determined values of the regression coefficients describe a regression model that is more or less "representative" for the population (how much depends on the sampling) is thus provides just a more or less uncertain estimate.
You can compare R square with Adjusted R square .
R² attempts to measure the explained variance of the dependent variable relative to its total variance for the Sample regression . Adjusted R square attempts to measure the explained variance of the dependent variable relative to its total variance for the population.
A regression analysis always is the attemp to find (estimate) the regression coefficients so that the likelihood of the observed data is maximized.
If this observed data is from the complete population, then the regression is a population regression. The determined values of the coefficients are exactly those describing the regression model for the given population.
If the data is "just" a sample (from a real or a "statistical" population), then it's a sample regression. The determined values of the regression coefficients describe a regression model that is more or less "representative" for the population (how much depends on the sampling) is thus provides just a more or less uncertain estimate.
This may or may not help|!
For me the sample is the observed data that you have to hand and the relationship derived from that information; the population is the true but unknown and indeed unknowable relationship ; you try to go from one to the other and there are lots of procedures and advice to help you, but you can never be absolutely sure that you have achieved it- you are reasoning under uncertainty.
You may want to look at my lengthy response here - in short I argue that even with a 'census' you have to make inferences under conditions of uncertainty; ie a census does not equate to a population- you will see from the many other replies that my views are not generally shared!
https://www.researchgate.net/post/Are_p-values_and_significance_tests_still_meaningful_in_census_data_analysis
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