Math Problem Statement

The coefficient of determination = ____.

0.671

0.71

0.654

The coefficient of determination = ____. Options: 0.671 0.71 0.654

Solution

From the image, the coefficient of determination (denoted as R2R^2) is clearly provided as:

R2=67.1%R^2 = 67.1\%

This percentage can be converted into a decimal form by dividing by 100, giving:

R2=0.671R^2 = 0.671

Therefore, the correct value for the coefficient of determination is 0.671.

Would you like a detailed explanation of how this value is interpreted or calculated?

Here are 5 related questions that can deepen your understanding:

  1. What does the R2R^2 value represent in linear regression?
  2. How does the adjusted R2R^2 differ from R2R^2, and why is it important?
  3. What does the T-statistic indicate in regression analysis?
  4. Why is the coefficient of determination important in evaluating a model's performance?
  5. How do you interpret the regression equation y=5.22x13.11y = 5.22x - 13.11 in the context of this output?

Tip: R2R^2 indicates the proportion of variance in the dependent variable explained by the independent variable(s) in the model.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Coefficient of Determination

Formulas

R^2 = 1 - (SS_res / SS_tot)

Theorems

Coefficient of Determination (R^2)

Suitable Grade Level

Grades 10-12