Show necessary calculation/justification for each answer. a) In regression analysis, the residuals represent the: a. difference between the actual y values and their predicted values. b. difference between the actual x values and their predicted values. c. square root of the slope of the regression line. d. change in y per unit change in x.

Show necessary calculation/justification for each answer. a) In regression analysis, the residuals represent the: a. difference between the actual y values and their predicted values. b. difference between the actual x values and their predicted values. c. square root of the slope of the regression line. d. change in y per unit change in x.

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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Question

Show necessary calculation/justification for each answer.

a) In regression analysis, the residuals represent the:
a. difference between the actual y values and their predicted values.
b. difference between the actual x values and their predicted values.
c. square root of the slope of the regression line.
d. change in y per unit change in x.

b) The least squares method for determining the best fit minimizes:
a. total variation in the dependent variable
b. sum of squares for error
c. sum of squares for regression
d. All of these choices are true.

c) The regression line has been fitted to the data points (4, 8), (2, 5), and (1, 2).
The sum of the squared residuals will be:
a. 7
b. 15
c. 8
d. 22

Definition Definition Statistical method that estimates the relationship between a dependent variable and one or more independent variables. In regression analysis, dependent variables are called outcome variables and independent variables are called predictors.

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