Ŷ = 32.1 +66.8X, SER=15.1, R² = 0.81 (15.1) (12.2) searcher is interested in the same regression, but he makes an error when he enters the data ssion program: He enters each observation twice, so he has 200 observations. Using these tions, what results will be produced by his program? Write it in the following format: Ŷ (-. --X, SER= - -, R²
Ŷ = 32.1 +66.8X, SER=15.1, R² = 0.81 (15.1) (12.2) searcher is interested in the same regression, but he makes an error when he enters the data ssion program: He enters each observation twice, so he has 200 observations. Using these tions, what results will be produced by his program? Write it in the following format: Ŷ (-. --X, SER= - -, R²
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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![**Title: Understanding Regression Analysis with Incorrect Data Entry**
**Section 4: The Impact of Data Duplication on Regression Results**
**Scenario:**
Suppose we have a dataset with \( n = 100 \) independent and identically distributed (i.i.d) observations for \( (Y_i, X_i) \). The linear regression analysis of this dataset yields the following results:
\[ \hat{Y} = 32.1 + 66.8X, \quad SER = 15.1, \quad R^2 = 0.81 \]
Here:
- \(\hat{Y}\) represents the predicted value of the dependent variable \(Y\).
- The equation \( \hat{Y} = 32.1 + 66.8X \) indicates that for every one unit increase in \( X \), \( Y \) increases by 66.8 units.
- SER stands for Standard Error of the Regression, which measures the average distance that the observed values fall from the regression line. In this case, it is 15.1.
- \( R^2 \) (R-squared) is the coefficient of determination, indicating that 81% of the variability in \( Y \) can be explained by \( X \).
**Error Introduction:**
A separate researcher is investigating the same regression. However, this researcher mistakenly enters each observation twice, resulting in an apparent dataset of 200 observations instead of the original 100. This duplication affects the regression results.
**Objective:**
Using these 200 observations, determine the results produced by the researcher's program. The new results should be presented as follows:
\[ \hat{Y} = \_ \_ \_ + \_ \_ \_ X, \quad SER = \_ \_ \_, \quad R^2 = \_ \_ \_ \]
By understanding the theoretical framework of regression analysis and the impact of data duplication, students can better appreciate the importance of data integrity in statistical computations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F362a762f-914f-42d1-b0fa-542c2b1764ea%2Fee988aa9-9d58-4c7d-978f-ebd9ead3fb10%2Flbi4igh_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Regression Analysis with Incorrect Data Entry**
**Section 4: The Impact of Data Duplication on Regression Results**
**Scenario:**
Suppose we have a dataset with \( n = 100 \) independent and identically distributed (i.i.d) observations for \( (Y_i, X_i) \). The linear regression analysis of this dataset yields the following results:
\[ \hat{Y} = 32.1 + 66.8X, \quad SER = 15.1, \quad R^2 = 0.81 \]
Here:
- \(\hat{Y}\) represents the predicted value of the dependent variable \(Y\).
- The equation \( \hat{Y} = 32.1 + 66.8X \) indicates that for every one unit increase in \( X \), \( Y \) increases by 66.8 units.
- SER stands for Standard Error of the Regression, which measures the average distance that the observed values fall from the regression line. In this case, it is 15.1.
- \( R^2 \) (R-squared) is the coefficient of determination, indicating that 81% of the variability in \( Y \) can be explained by \( X \).
**Error Introduction:**
A separate researcher is investigating the same regression. However, this researcher mistakenly enters each observation twice, resulting in an apparent dataset of 200 observations instead of the original 100. This duplication affects the regression results.
**Objective:**
Using these 200 observations, determine the results produced by the researcher's program. The new results should be presented as follows:
\[ \hat{Y} = \_ \_ \_ + \_ \_ \_ X, \quad SER = \_ \_ \_, \quad R^2 = \_ \_ \_ \]
By understanding the theoretical framework of regression analysis and the impact of data duplication, students can better appreciate the importance of data integrity in statistical computations.
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