For insight on the construction of this matrix, consider the typical least squares regression formulation. Here, the response (Y) is a linear function of predictors (x’s) plus error (ε):
Each row of the data table contains a response value and values for the p predictors. For each observation, the predictor values are considered fixed. However, the response value is considered to be a realization of a random variable.
Considering the values of the predictors fixed, for any set of Y values, the coefficients, , can be estimated. In general, different sets of Y values lead to different estimates of the coefficients. The Correlation of Estimates option calculates the theoretical correlation of these parameter estimates. (For technical details, see Details of Custom Test Example.)
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Select Analyze > Fit Model.
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Select Total Population, Median School Years, Total Employment, and Professional Services and click Add.
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Click Run.
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From the Response red triangle menu, select Estimates > Correlation of Estimates.
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The report (Correlation of Estimates Report) shows high negative correlations between the parameter estimates for the Intercept and Median School Years (–0.9818). High negative correlations also exist between Total Population and Total Employment (–0.9746).