If SSR = 54 and SST = 72, compute the coefficient of determination, r, and interpret its meaning. *= (Type an integer or a decimal. Do not round.)
If SSR = 54 and SST = 72, compute the coefficient of determination, r, and interpret its meaning. *= (Type an integer or a decimal. Do not round.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Problem Statement:**
"If SSR = 54 and SST = 72, compute the coefficient of determination, \( r^2 \), and interpret its meaning."
**Solution:**
\[ r^2 = \boxed{\text{(Type an integer or a decimal. Do not round.)}} \]
---
**Explanation:**
- **SSR (Sum of Squares for Regression):** This is the sum of the squares of the differences between the predicted values and the mean of the observed data.
- **SST (Total Sum of Squares):** This is the sum of the squares of the differences between the observed values and the mean of the observed data.
**Coefficient of determination, \( r^2 \):**
The formula to compute the coefficient of determination is:
\[ r^2 = \frac{\text{SSR}}{\text{SST}} \]
This value represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It provides an indication of how well the independent variables explain the variability of the dependent variable. A value closer to 1 indicates a better fit of the model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35965c83-49a0-4a61-abb5-b01d5b731ec3%2F9284d5dd-0b4f-4ba0-b336-c1427d6a17cc%2F65fd6ha_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
"If SSR = 54 and SST = 72, compute the coefficient of determination, \( r^2 \), and interpret its meaning."
**Solution:**
\[ r^2 = \boxed{\text{(Type an integer or a decimal. Do not round.)}} \]
---
**Explanation:**
- **SSR (Sum of Squares for Regression):** This is the sum of the squares of the differences between the predicted values and the mean of the observed data.
- **SST (Total Sum of Squares):** This is the sum of the squares of the differences between the observed values and the mean of the observed data.
**Coefficient of determination, \( r^2 \):**
The formula to compute the coefficient of determination is:
\[ r^2 = \frac{\text{SSR}}{\text{SST}} \]
This value represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It provides an indication of how well the independent variables explain the variability of the dependent variable. A value closer to 1 indicates a better fit of the model.
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