MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made p…
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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**Title: Interpreting the Y-intercept in Linear Regression** **Introduction:** When fitting a straight line to a set of data, the resulting prediction model can help us understand the relationship between two variables. In this context, we examine the linear equation: \[ \hat{Y}_i = 2 + 4X_i \] **Objective:** Interpret the meaning of the Y-intercept (\(b_0\)) in this linear equation. **Question:** Choose the correct interpretation of the Y-intercept, \(b_0\), from the options below. - **A.** The Y-intercept, \(b_0 = 2\), implies that the average value of Y is 2. - **B.** The Y-intercept, \(b_0 = 2\), implies that for each increase of 1 unit in X, the value of Y is expected to increase by 2 units. - **C.** The Y-intercept, \(b_0 = 2\), implies that when the value of X is 0, the mean value of Y is 2. - **D.** The Y-intercept, \(b_0 = 4\), implies that when the value of X is 0, the mean value of Y is 4. **Explanation:** In a linear equation of the form \(\hat{Y} = b_0 + b_1X\), the Y-intercept \(b_0\) is the value of \(\hat{Y}\) when \(X = 0\). It represents the predicted value of the dependent variable (Y) when the independent variable (X) is zero. **Answer:** The correct interpretation is **C.** The Y-intercept, \(b_0 = 2\), implies that when the value of X is 0, the mean value of Y is 2. Understanding the Y-intercept is crucial for data analysis as it provides insight into the starting point of the relationship represented by the linear model.
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Transcribed Image Text:**Title: Interpreting the Y-intercept in Linear Regression** **Introduction:** When fitting a straight line to a set of data, the resulting prediction model can help us understand the relationship between two variables. In this context, we examine the linear equation: \[ \hat{Y}_i = 2 + 4X_i \] **Objective:** Interpret the meaning of the Y-intercept (\(b_0\)) in this linear equation. **Question:** Choose the correct interpretation of the Y-intercept, \(b_0\), from the options below. - **A.** The Y-intercept, \(b_0 = 2\), implies that the average value of Y is 2. - **B.** The Y-intercept, \(b_0 = 2\), implies that for each increase of 1 unit in X, the value of Y is expected to increase by 2 units. - **C.** The Y-intercept, \(b_0 = 2\), implies that when the value of X is 0, the mean value of Y is 2. - **D.** The Y-intercept, \(b_0 = 4\), implies that when the value of X is 0, the mean value of Y is 4. **Explanation:** In a linear equation of the form \(\hat{Y} = b_0 + b_1X\), the Y-intercept \(b_0\) is the value of \(\hat{Y}\) when \(X = 0\). It represents the predicted value of the dependent variable (Y) when the independent variable (X) is zero. **Answer:** The correct interpretation is **C.** The Y-intercept, \(b_0 = 2\), implies that when the value of X is 0, the mean value of Y is 2. Understanding the Y-intercept is crucial for data analysis as it provides insight into the starting point of the relationship represented by the linear model.
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