Does each variable uniquely predict job choice beyond the other variable? Report

Question

Does each variable uniquely predict job choice beyond the other variable? Report the appropriate statistic(s) from the table. e) Assume that R2 drops to .172 when base pay is removed from the regression equation. How much variance in job choice did base pay predict by itself? . The regression equation generates a "best fitting" straight line for a set of data. What is the criterion for "best fitting"? Why is it not a good idea to just add every predictor variable you can think of into the regression equation to make it more precise?

Explanation / Answer

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The idea is that you want to develop a linear equation that will allow you to estimate the mean value of your response while taking into account the value x (referred to as independent variable, or predictor).

This is typically done by choosing the slope and intercept so that they minimize the sum of some "nice" function of the residuals (a residual is the difference between the data value and the estimate: in regression a residual is ei=yi(a+bxi)ei=yi(a+bxi))

That sum to be minimized is often called a dispersion function.

As others have pointed out, there are many choices for what qualifies as a "nice" function: least squares uses the squares of the residuals, least absolute residuals uses absolute value, robust methods use a variety of functions, etc.

The standard way of doing this in statistics, is to minimize the sum of the squared residuals, i.e., to minimze the summed differences between fitted (y) and their respective input values squared. It results in the estimation of the arithmetic mean of y, for a given x. This is handy, because it is in line with other wide-used statistical measures (like variance and standard-deviation), and makes sense whenever the effects of bigger residuals might be regarded to be disproportionately more important than those of smaller ones.

However, if your needs based on theoretical considerations, are arguably different, you are free to use other parameters for the minimization function, e.g., the absolute differences (resulting in the estimation of the median of y, given x), or even a non-linear function.

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