Final answer:
The student's mathematics question deals with the calculation of the Sum of Squares for Error (SSE) in a multiple regression model using the provided SST and SSR values. Subtracting SSR from SST yields an SSE of 1,124.3, which is essential for further statistical calculations like R^2 and MSE.
Step-by-step explanation:
The student's question pertains to the domain of statistics within mathematics, specifically the analysis of variance in a multiple regression model. In regression analysis, we are often interested in assessing the goodness of fit of the model, which involves the calculation of certain sums of squares.
Total Sum of Squares (SST) measures the total variation present in the dependent variable, while Sum of Squares due to Regression (SSR), also known as the explained variation, measures how much of the total variation is explained by the model. The remaining variation, which is not explained by the model, is found by subtracting SSR from SST and is known as the Sum of Squares for Error (SSE).
Using the data provided, SST = 15,144.1 and SSR = 14,019.8. To find the SSE, we subtract SSR from SST, which gives us:
\[SSE = SST - SSR\]
\[SSE = 15,144.1 - 14,019.8\]
\[SSE = 1,124.3\]
This value of SSE can further be used to calculate the coefficient of determination (R2) and Mean Square Error (MSE), among other metrics. The R2 statistic indicates the proportion of variance in the dependent variable that is predictable from the independent variables, while MSE is an average of the squares of the errors, which indicates the average squared difference between the estimated values and the actual value.