Math Problem Statement

The coefficient of determination is:

2.786

0.701

0.679

Report the value of the coefficient of determination.

Solution

The coefficient of determination, denoted as R2R^2, is a measure of the proportion of the variance in the dependent variable (here, "grade") that is predictable from the independent variables.

From the provided output, the value of R2R^2 is given as 70.1%.

To report it as a decimal, the value is:

R2=0.701R^2 = 0.701

Thus, the correct value of the coefficient of determination is 0.701.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

  1. What does the adjusted R2R^2 indicate?
  2. How is the degrees of freedom calculated in this context?
  3. What is the difference between R2R^2 and adjusted R2R^2?
  4. What does the value of s=2.786s = 2.786 represent in the output?
  5. Why is the coefficient of determination important in regression analysis?

Tip: Always compare R2R^2 and adjusted R2R^2 to understand the impact of additional predictors on the model's performance.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Coefficient of Determination

Formulas

R² = SSR / SST

Theorems

Linear Regression

Suitable Grade Level

Undergraduate Level