![]() The MEDIAN function is used in case there are multiple instances of the same x ( Number) in your sample. SELECT ( Alpha + ( Beta * (SELECT MEDIAN( Number)))) We can now calculate our linear regression estimate using α, β, and the x value ( Number). Metric 10 - hi Linear Regression Estimate ![]() The two mean metrics are carried over from the topic Covariance and Correlation and R-Squared. SELECT ( Avg Claim Value (Mean Y ) - ( Beta * Avg Claim Number (Mean X))) BY ALL OTHER Then, we are able to calculate α using β from above, the mean of x, and the mean of y: The BY ALL OTHER clause is used to prevent the amount from being sliced by anything present in the report. SELECT ((SELECT Pearson Correlation (r))*(SELECT (SELECT STDEV( Value))/(SELECT STDEV( Number)))) BY ALL OTHER Metric 8 - Beta Regression Coefficientįirst, we calculate β using Pearson Correlation (r), the standard deviation of x ( Number) and the standard deviation of y ( Value): Let's assume the same scenario as the insurance company in the topic Covariance and Correlation and R-Squared.Īfter we have generated Metric 6: Pearson Correlation (r) defined in the above topic, you can immediately calculate metrics for β, α and our linear estimate hi. The above metrics enable us to solve for our linear regression equation h: Scenario The result yields the following two equalities for β and α:
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