Regression Analysis
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| What is regression analysis? | Regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.
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| What is the usual form of simple (single variable) regression? | I = a + bE + e
a = a constant amount (what one earns with zero education);
b = the effect in rands of an additional year of schooling on income,
hypothesized to be positive; and
e = the "noise" term reflecting other factors that influence earnings.
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| In the simple regression equation -- I = a + bE + e -- what does the E and I stand for? | -I is termed the "dependent" or "endogenous" variable;
-E is termed the "independent," "explanatory," or "exogenous" variable;
-a is the "constant term" and b the "coefficient" of the variable E.
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| In the simple regression equation -- I = a + bE + e -- what factors are observable and what are not observable? | -The data set contains observations for I and E.
-The noise component e is comprised of factors that are unobservable. The parameters a and b are also unobservable.
-The task of regression analysis is to produce an estimate of these two parameters.
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| What assumption does regressional analysis make about the noise term? | Regression analysis assumes that the noise term has no systematic property, but is on average equal to zero.
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| How does regression analysis choose a line to fit the data? | Regression analysis chooses among all possible lines by selecting the one for which the sum of the squares of the estimated errors is at a minimum.
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| What is an estimate error? | The "estimated error" for each observation as the vertical distance between the value of I along the estimated line I = a + bE (generated by plugging the actual value of E into this equation) and the true value of I for the same observation.
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