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An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3, 6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residuals y – ŷ and plot the residuals against their corresponding value of x.

An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3, 6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residuals y – ŷ and plot the residuals against their corresponding value of x.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.4: Mathematical Models And Least Squares Analysis
Problem 39E
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An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3, 6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residuals y – ŷ and plot the residuals against their corresponding value of x. An obvious megaphone pattern is apparent in the residuals y – ŷ. Calculate the line of best fit between a and y – ŷ|. (y – ŷ = mx + b. The value of the residual for a given value of x predicted by this linear relationship is an estimate of o(x), the standard deviation of the y variable (which increases with x). Compute 0,1, 2, 3, 4, 5 and use them for x o(x)? as weights in a matrix W to run a weighted regression on the original x, y data. 6.
Transcribed Image Text:An ordinary least squares regression on the points (0, 1), (1, 1.2), (2, 1.7), (3, 6.2), (4, 7.7), (5, 3.2) yields the equation y = 1+ x. Calculate the residuals y – ŷ and plot the residuals against their corresponding value of x. An obvious megaphone pattern is apparent in the residuals y – ŷ. Calculate the line of best fit between a and y – ŷ|. (y – ŷ = mx + b. The value of the residual for a given value of x predicted by this linear relationship is an estimate of o(x), the standard deviation of the y variable (which increases with x). Compute 0,1, 2, 3, 4, 5 and use them for x o(x)? as weights in a matrix W to run a weighted regression on the original x, y data. 6.
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