Math Problem Statement
Calculate and report the absolute value of the "correlation coefficient" for the following Regression table:
df SS MS F
Regression 1 33 33 44 Residual 20 15 0.75 Total 21 48
Round to two decimal places For example, 45.67% is to be reported as 0.4567
Solution
To calculate the absolute value of the correlation coefficient , we first need to find the coefficient of determination from the given regression table, which is related to the correlation coefficient as .
Here are the steps:
Step 1: Calculate
The coefficient of determination is the proportion of the total variation explained by the regression model. It is calculated as:
From the table, we have:
So, is:
Step 2: Calculate the correlation coefficient
Since , we can now calculate :
Step 3: Report the absolute value of the correlation coefficient
The absolute value of is:
Thus, the absolute value of the correlation coefficient is 0.8292.
Would you like further details or have any questions?
Here are 5 related questions to explore further:
- What is the significance of the correlation coefficient in a regression model?
- How is the -statistic related to the significance of the regression model?
- What does the residual sum of squares (SS) tell us about the model's fit?
- How do we interpret the coefficient of determination in practical terms?
- What are some assumptions behind linear regression models?
Tip: Always check if your regression model satisfies key assumptions like linearity and homoscedasticity before interpreting the results.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Regression Analysis
Correlation Coefficient
Coefficient of Determination (R²)
Formulas
R² = (SS_Regression / SS_Total)
r = sqrt(R²)
Theorems
Coefficient of Determination
Linear Regression Correlation
Suitable Grade Level
College Level
Related Recommendation
Compute Coefficient of Determination from Correlation Coefficient
Calculating the Coefficient of Correlation, Determination, and Non-Determination
Calculating Correlation Coefficient and Determination (R²) from Bivariate Data
How to Report the Coefficient of Determination from a Regression Analysis
Find the Coefficient of Determination from a Correlation Coefficient of 0.908