Question at position 4 The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.constant termresidualerror termmodel parameterClear my selection

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Question at position 4 The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.constant termresidualerror termmodel parameterClear my selection

BlackTom AI · Accepted Answer

The prompt asks about the quantity that measures how far off an observed value is from what the regression equation predicts. 
Option: constant term. This refers to the intercept in the regression equation, not the deviation between observed and predicted values. It is a parameter that shifts the line up or down, not an error measure.
Option: residual. This is the term for the difference between the observed dependent variable value and the value predicted by the estimated regression equation for a given observation. It directly captures the discrepancy we are discussing.
Option: error term. In regression contexts, the error term often represents unobserved factors or random noise affecting the dependent variable; while related, it is a broader concept and not the specific sample-by-sample difference between observed and predicted values.
Option: model parameter. Model parameters include quantities like coefficients and the intercept that define the regression equation; they are not the per-observation deviations but fixed characteristics estimated from the data.
In summary, the quantity described—the difference between what we observe and what our model predicts for each case—is best identified as the residual for that observation.

Question at position 4 The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.constant termresidualerror termmodel parameterClear my selection

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