(Requires Appendix Material)In Deriving the OLS Estimator,you Minimize the Sum

question 35

Essay

(Requires Appendix material)In deriving the OLS estimator,you minimize the sum of squared residuals with respect to the two parameters 0 and 1.The resulting two equations imply two restrictions that OLS places on the data,namely that and .Show that you get the same formula for the regression slope and the intercept if you impose these two conditions on the sample regression function.

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Definitions:

Photosynthetic Bacteria

Bacteria capable of photosynthesis, a process that converts light energy into chemical energy, thereby producing oxygen as a by-product, crucial for earth's oxygen supply.

Chemosynthetic Bacteria

Microorganisms that obtain energy by converting inorganic molecules to organic matter, independent of sunlight.

Autotrophs

Organisms that produce their own food from inorganic substances, like carbon dioxide and water, typically through photosynthesis.

Heterotrophs

Organisms that obtain energy by consuming other living things, unable to synthesize their own food.