Sum of Squares Criterion In addition to the value of another m...

Question

Sum of Squares Criterion In addition to the value of another measurement used to assess the quality of a model is the sum of squares of the residuals. Recall from Section 10-2 that a residual is (the difference between an observed y value and the value predicted from the model). Better models have smaller sums of squares. Refer to the U.S. population data in Table 10-7.
a. Find the sum of squares of the residuals resulting from the linear model.

a. Find the sum of squares of the residuals resulting from the linear model.

Accepted Answer

Hello everyone. Let's take a look at this question together. A measurement used to assess the quality of a model is the sum of squares of the residuals or the SSR. Recall that a residual is the difference between an observed Y value and the value predicted by the model. Models with smaller SSR provide a better fit. Refer to the following data set, which represents the annual revenue in million dollars of a company at 5-year intervals and using a linear regression model, compute the sum of squares of the residuals or the SSR. Is it answer choice A 66.86? Answer choice B 102.58, answer choice C 324.51, or answer choice D 642.88. So in order to solve this question, we have to use a linear regression model and compute the sum of squares of the residuals, which we know that the equation of the regression line follows the form of Y is equal to M. X plus B, as the slope is represented as M, which can be calculated using the following formula. The Y intercept is represented as B, which can be calculated using the following formula, and in that formula, the variable N refers to the number of samples. So using the provided data, we can compute the following values to calculate M and B. Which we know that N is equal to 11, the slope M can be calculated, giving us the value of 7.1136, which can be rounded to 7.11, and the value of B can be calculated as 14111.699, which can be rounded to 14111.7, giving us the equation of the line of regression, Y equals 7.1. 1 X minus 14111.7 and using our equation of the line of regression, we can tabulate the values for Y actual and Y predicted where Y predicted is calculated for each year using the equation of line of regression formula, giving us the following data. And since we are computing the sum of squares of the residuals, we have the square of the Residual and the sum of the squares of residual. So the correct answer is 642.884. So the final answer is 642.884, which looking at our answer choices, we can identify is answer choice D, so answer choice D is correct, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Residuals

Sum of Squares of Residuals (SSR)

Model Quality Assessment

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