The least squares line ŷ =10 + 5x describes the following coordinates: (1, 15), (2, 20), (3, 25), and (4, 30). Using these data as a specific example, explain the meaning of "least squares." The line ŷ = 10 + 5x minimizes the sum of the squared horizontal distances from the points to the line. The line ŷ = 10 + 5x minimizes the sum of the squared difference between the x and y values. The line ŷ = 10 + 5x minimizes the sum of the vertical distances from the points to the line. The line ŷ = 10 + 5x minimizes the square of the standard deviation. The line ŷ = 10 + 5x minimizes the sum of the squared vertical distances from the points to the line.

The least squares line ŷ =10 + 5x describes the following coordinates: (1, 15), (2, 20), (3, 25), and (4, 30). Using these data as a specific example, explain the meaning of "least squares." The line ŷ = 10 + 5x minimizes the sum of the squared horizontal distances from the points to the line. The line ŷ = 10 + 5x minimizes the sum of the squared difference between the x and y values. The line ŷ = 10 + 5x minimizes the sum of the vertical distances from the points to the line. The line ŷ = 10 + 5x minimizes the square of the standard deviation. The line ŷ = 10 + 5x minimizes the sum of the squared vertical distances from the points to the line.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 75E

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	The line ŷ = 10 + 5x minimizes the sum of the squared horizontal distances from the points to the line.
	The line ŷ = 10 + 5x minimizes the sum of the squared difference between the x and y values.
	The line ŷ = 10 + 5x minimizes the sum of the vertical distances from the points to the line.
	The line ŷ = 10 + 5x minimizes the square of the standard deviation.
	The line ŷ = 10 + 5x minimizes the sum of the squared vertical distances from the points to the line.