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 r|r|, we first need to find the coefficient of determination R2R^2 from the given regression table, which is related to the correlation coefficient as r=R2r = \sqrt{R^2}.

Here are the steps:

Step 1: Calculate R2R^2

The coefficient of determination R2R^2 is the proportion of the total variation explained by the regression model. It is calculated as: R2=SSRegressionSSTotalR^2 = \frac{\text{SS}_{\text{Regression}}}{\text{SS}_{\text{Total}}}

From the table, we have:

  • SSRegression=33\text{SS}_{\text{Regression}} = 33
  • SSTotal=48\text{SS}_{\text{Total}} = 48

So, R2R^2 is: R2=3348=0.6875R^2 = \frac{33}{48} = 0.6875

Step 2: Calculate the correlation coefficient rr

Since r=R2r = \sqrt{R^2}, we can now calculate rr: r=0.68750.8292r = \sqrt{0.6875} \approx 0.8292

Step 3: Report the absolute value of the correlation coefficient

The absolute value of rr is: r=0.8292|r| = 0.8292

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:

  1. What is the significance of the correlation coefficient in a regression model?
  2. How is the FF-statistic related to the significance of the regression model?
  3. What does the residual sum of squares (SS) tell us about the model's fit?
  4. How do we interpret the coefficient of determination R2R^2 in practical terms?
  5. 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.

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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