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 a value of y-y, which is the difference between an observed value of y and a predicted value of y. OB. A residual is the amount that one variable changes when the other variable changes by exactly one unit. OC. A residual is a point that has a strong effect on the regression equation. OD. A residual is a value that is determined exactly, without any error. 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 sum ... of the residuals is sum of squares 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 a value of y-y, which is the difference between an observed value of y and a predicted value of y. OB. A residual is the amount that one variable changes when the other variable changes by exactly one unit. OC. A residual is a point that has a strong effect on the regression equation. OD. A residual is a value that is determined exactly, without any error. 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 sum ... of the residuals is sum of squares possible sum.
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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Transcribed Image Text:### Understanding Residuals and Regression Lines
**a. What is a residual?**
1. **Definition:**
- A residual is defined as the value of \( y - \hat{y} \), which represents the difference between an observed value of \( y \) and a predicted value of \( y \).
2. **Options Explained:**
- **A.** Correct. A residual is a value of \( y - \hat{y} \), which is the difference between an observed value of \( y \) and a predicted value of \( y \).
- **B.** Incorrect. This option describes a change in variables, not specifically a residual.
- **C.** Incorrect. This option suggests residuals have a strong effect on the regression equation, which is not accurate.
- **D.** Incorrect. This option implies residuals are determined exactly without error, which is incorrect since residuals represent the error.
**b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?**
1. **Understanding the Regression Line:**
- The regression line is considered the "best" fit line for a scatterplot in the sense that it minimizes the differences (residuals) between the observed values and the predicted values.
2. **Property of the Regression Line:**
- The regression line has the property that the sum of the squared residuals is the smallest possible sum.
3. **Dropdown and Options:**
- The dropdown menu provides options such as "sum" and "sum of squares." The correct choice is "sum of squares."
**Complete Statement:**
- The regression line has the property that the **sum of squares** of the residuals is the **smallest** possible sum.
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