Fits and predictions for Orthogonal Regression

Fit for predictor (X)

The fitted value for the predictor variable accounts for the uncertainty in the value of the predictor.

Interpretation

Use the fitted value for the predictor to investigate any unusual residuals. If the fitted value of the predictor variable is much larger or much smaller than the observed value, investigate the cause.

Fit for response (Y)

The fitted value for the response variable accounts for the uncertainty in both the response and predictor variables.

Interpretation

Use the fitted value for the response variable to investigate any unusual residuals. If the fitted value of the response variable is much larger or smaller than the observed value, investigate the cause.

Residuals

The residual is the difference between the observed value and the fitted value.

Interpretation

Examine the residuals to determine how well the model fits the data. In general, the residuals should be randomly distributed with no obvious patterns and no unusual values. If a residual is unusual, you can determine whether the residual is unusual because of the fitted x-value, the fitted y-value, or both values.

St Resid

The standardized residual equals the value of a residual (ei) divided by an estimate of its standard deviation.

Interpretation

Use the standardized residuals to help you detect outliers. Standardized residuals that are greater than 2 and less than −2 are usually considered large enough to investigate.

Standardized residuals are useful because raw residuals might not be good indicators of outliers. The variance of each raw residual can differ by the x-values associated with it. This unequal scale causes it to be difficult to assess the sizes of the raw residuals. Standardizing the residuals solves this problem by converting the different variances to a common scale.

Predicted

The predicted value is the value of the response variable at a new setting of the predictor variable.

Interpretation

Use the predicted value to estimate the value of a new response value.

StDev

The standard deviation of the predicted value measures how precisely the model estimates new data. The standard deviations for all the predicted values are equal.

Interpretation

Use the standard deviation of the predicted value to measure the precision of the estimate of the prediction. The smaller the standard deviation, the more precise the prediction is. Standard deviations are always positive.

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