Decomposition of Error in Simple Linear Regression-Armand\'s Pizza Conceptual Ov

Question

Decomposition of Error in Simple Linear Regression-Armand's Pizza Conceptual Overview: Explore the relationship between the three sum of squares measures in simple linear regression In the figure below you will see a scatter diagram and trend line for data comparing a university student population and quarterly sales for a nearby pizza place. When the line is horizontal at the mean of the y-axis data, the errors are represented as red lines. Squaring these lines and summing their areas yields the total sum of squares (SST Drag the trend line with your mouse. As the line moves, the distance between the line and the mean turns blue because part of the original error is now accounted for by the regression line. Squaring the blue lines and summing their areas yields the regression sum of squares (SSR). The remaining error is still red. Squaring the remaining red lines and summing their areas yields the error sum of squares (SSE) The total sum of squares is the sum of the regression and error sum of squares: SST = SSR + SSE. The coefficient of determination is the proportion total sum of squares that is accounted for by the regression sum of squares. It is shown above the meter and is calculated as such 2SSAR SST r-sq = 0.903

Explanation / Answer

(1) b. Sum of squares due to regression

r-squre (r-sq) is proportion of variation explained by the model and it ranges between 0 and 1. Since r-square=0.903 is mentioned and it is explained varation by the regression model. so right choice would be b. Sum of squares due to regression

(2) c. 15725

here r-sq=SSR/SST

so SST=SSR/r-sq=14200/0.903=15725 ( whole number approximation). right choice is c. 15725

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