1. What is the least-squares regression line? (A) A line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible, giving the smallest sum of the vertical distances between the observed values (y) and the predicted values (^y). (B) A line that gives the smallest total sum of squared residuals. (C) A line that makes the squares of r in the data as large as possible. (D) Both A and B. 2. What is the "squares" in a least-squares regression line equal to? (A) (observed - predicted)^2 (B) (observed - mean)^2 (C) (residuals)^2 (D) Both A and C. 3. If two variables (x and y), have a strong linear relationship and almost all of the data points fall on the least-squares regression line, then (A) x causes y to happen. (B) y causes x to happen. (C) the y-intercept should be positive. (D) there might or might not be any relationship between x and y.

1. What is the least-squares regression line? (A) A line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible, giving the smallest sum of the vertical distances between the observed values (y) and the predicted values (^y). (B) A line that gives the smallest total sum of squared residuals. (C) A line that makes the squares of r in the data as large as possible. (D) Both A and B. 2. What is the "squares" in a least-squares regression line equal to? (A) (observed - predicted)^2 (B) (observed - mean)^2 (C) (residuals)^2 (D) Both A and C. 3. If two variables (x and y), have a strong linear relationship and almost all of the data points fall on the least-squares regression line, then (A) x causes y to happen. (B) y causes x to happen. (C) the y-intercept should be positive. (D) there might or might not be any relationship between x and y.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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