For the simple linear regression model, the parameter values of the model are calculated by minimize the

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BlackTom AI · Accepted Answer

Question restatement: The prompt asks about the quantity that the simple linear regression model minimizes when estimating its parameters.
Option 1: 'the sum of all error terms' — In ordinary least squares (OLS) regression, the objective is not to minimize raw signed residuals, but to minimize the sum of squared residuals, since squaring eliminates cancellation and emphasizes larger errors. This makes this option incorrect as stated.
Option 2: 'SSR' — SSR stands for the sum of squares due to regression, which measures the explained variation in the dependent variable. While SSR is related to model fit, the parameter estimation process in OLS does not minimize SSR; it relates to maximizing explained variance given the constraint. This option misidentifies the target of the optimization.
Option 3: 'SST' — SST is the total sum of squares, representing the total variability in the dependent variable around its mean. The model does not minimize SST during parameter estimation; SST is a constant with respect to the model parameters and serves as a baseline for measuring explained versus unexplained variation. This option is incorrect.
Option 4: 'SSE' — SSE stands for the sum of squared errors (residual sum of squares). In simple linear regression, the OLS estimates of the intercept and slope are obtained by minimizing SSE, i.e., the sum of the squared differences between observed values and the fitted values. The minimization of SSE leads to the best linear unbiased estimates under standard assumptions. This option correctly identifies the optimization objective.
Additional context: While discussing these sums of squares, it can be helpful to recall the decomposition: SST = SSR + SSE, where SST is fixed for a given data set, so minimizing SSE is equivalent to maximizing SSR indirectly through the relationship above. This interplay explains why SSE is the focal quantity in the estimation process.
In summary, only SSE corresponds to the quantity that the OLS estimation routine minimizes to obtain the model parameters, whereas SSR and SST relate to model fit and total variability but are not the direct objective of the parameter minimization process.

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For the simple linear regression model, the parameter values of the model are calculated by minimize the

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