O Ý = Bo + B,X1 + B2X2 + …·+ BnX,n O Ý = Bo + B,X1 %3D B,X1 = Ỹ + Bo + B2X2 + …·+ BnXn B,X1 = ŷ
O Ý = Bo + B,X1 + B2X2 + …·+ BnX,n O Ý = Bo + B,X1 %3D B,X1 = Ỹ + Bo + B2X2 + …·+ BnXn B,X1 = ŷ
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Which of the following correctly shows the general form of a multiple regression model? Select one.
![This image appears to be a multiple-choice question related to linear regression models. It contains four options, each representing a different equation involving regression coefficients and predictors.
1. **Option 1:**
\[
\hat{Y} = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_n X_n
\]
This represents a multiple linear regression equation where \(\hat{Y}\) is the predicted value, \(\beta_0\) is the intercept, and \(\beta_1, \beta_2, \ldots, \beta_n\) are the coefficients for the predictors \(X_1, X_2, \ldots, X_n\).
2. **Option 2:**
\[
\hat{Y} = \beta_0 + \beta_1 X_1
\]
This represents a simple linear regression equation with one predictor \(X_1\).
3. **Option 3:**
\[
\beta_1 X_1 = \hat{Y} + \beta_0 + \beta_2 X_2 + \cdots + \beta_n X_n
\]
This equation appears to incorrectly rearrange the terms of a regression equation.
4. **Option 4 (Selected):**
\[
\beta_1 X_1 = \hat{Y}
\]
This represents a scenario where the predicted value \(\hat{Y}\) is equal to the product of a single coefficient \(\beta_1\) and its predictor \(X_1\). This equation is selected.
The image primarily focuses on understanding the structuring of linear regression equations in different forms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7c098e8-a055-46a5-964b-ab0cc684192c%2Fb870b67f-6ca7-4a19-8668-09b2fab13858%2F9b0razm_processed.png&w=3840&q=75)
Transcribed Image Text:This image appears to be a multiple-choice question related to linear regression models. It contains four options, each representing a different equation involving regression coefficients and predictors.
1. **Option 1:**
\[
\hat{Y} = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_n X_n
\]
This represents a multiple linear regression equation where \(\hat{Y}\) is the predicted value, \(\beta_0\) is the intercept, and \(\beta_1, \beta_2, \ldots, \beta_n\) are the coefficients for the predictors \(X_1, X_2, \ldots, X_n\).
2. **Option 2:**
\[
\hat{Y} = \beta_0 + \beta_1 X_1
\]
This represents a simple linear regression equation with one predictor \(X_1\).
3. **Option 3:**
\[
\beta_1 X_1 = \hat{Y} + \beta_0 + \beta_2 X_2 + \cdots + \beta_n X_n
\]
This equation appears to incorrectly rearrange the terms of a regression equation.
4. **Option 4 (Selected):**
\[
\beta_1 X_1 = \hat{Y}
\]
This represents a scenario where the predicted value \(\hat{Y}\) is equal to the product of a single coefficient \(\beta_1\) and its predictor \(X_1\). This equation is selected.
The image primarily focuses on understanding the structuring of linear regression equations in different forms.
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