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a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? OA. A residual is the amount that one variable changes when the other variable changes by exactly one unit. B. A residual is a value of y-y, which is the difference between an observed value of y and a predicted value of y. OC. A residual is a value that is determined exactly, without any error.. OD. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the of the residuals is the possible sum.

a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? OA. A residual is the amount that one variable changes when the other variable changes by exactly one unit. B. A residual is a value of y-y, which is the difference between an observed value of y and a predicted value of y. OC. A residual is a value that is determined exactly, without any error.. OD. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the of the residuals is the possible sum.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Residuals and Regression Lines in Statistics** --- **a. What is a residual?** 1. **Question:** - What is a residual? 2. **Answer Options:** - **A.** A residual is the amount that one variable changes when the other variable changes by exactly one unit. - **B.** A residual is a value of \( y - \hat{y} \), which is the difference between an observed value of \( y \) and a predicted value of \( y \). - **C.** A residual is a value that is determined exactly, without any error. - **D.** A residual is a point that has a strong effect on the regression equation. **b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?** 1. **Question:** - In what sense is the regression line the straight line that "best" fits the points in a scatterplot? 2. **Answer Fill-in:** - The regression line has the property that the [Select Answer] of the residuals is the [Select Answer] possible sum. --- **Explanation:** - **Residuals:** The difference between the observed values of the dependent variable and the values predicted by the regression line. It helps in identifying the accuracy of the prediction. - **Regression Line:** This line minimizes the sum of the squared residuals, making it the "best fit" line to represent the data points on a scatterplot. This section helps in understanding the concepts related to residuals and how the regression line effectively fits the data points in statistical analysis.
Transcribed Image Text:**Understanding Residuals and Regression Lines in Statistics** --- **a. What is a residual?** 1. **Question:** - What is a residual? 2. **Answer Options:** - **A.** A residual is the amount that one variable changes when the other variable changes by exactly one unit. - **B.** A residual is a value of \( y - \hat{y} \), which is the difference between an observed value of \( y \) and a predicted value of \( y \). - **C.** A residual is a value that is determined exactly, without any error. - **D.** A residual is a point that has a strong effect on the regression equation. **b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?** 1. **Question:** - In what sense is the regression line the straight line that "best" fits the points in a scatterplot? 2. **Answer Fill-in:** - The regression line has the property that the [Select Answer] of the residuals is the [Select Answer] possible sum. --- **Explanation:** - **Residuals:** The difference between the observed values of the dependent variable and the values predicted by the regression line. It helps in identifying the accuracy of the prediction. - **Regression Line:** This line minimizes the sum of the squared residuals, making it the "best fit" line to represent the data points on a scatterplot. This section helps in understanding the concepts related to residuals and how the regression line effectively fits the data points in statistical analysis.
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