Understanding Coefficient of Determination

What is the range of possible values for the R value?

• 0 to 1

• -1 to 1

• 0 to 2

• -2 to 2

How is the coefficient of determination (R²) calculated from the R value?

• By halving the R value

• By squaring the R value

• By doubling the R value

• By taking the square root of the R value

What is the significance of a positive R² value?

• It indicates a negative correlation

• It indicates a positive correlation

• It indicates no correlation

• It indicates the proportion of variation explained

What does an R² value of 0.36 indicate in terms of variation?

• 64% of the variation in the dependent variable is explained by the independent variable

• 36% of the variation in the dependent variable is explained by the independent variable

• 36% of the variation in the independent variable is explained by the dependent variable

• The variables are not related

Why should the word 'cause' be avoided when interpreting R²?

• Because R² is not a reliable statistic

• Because R² values are always less than 0.5

• Because R² is always negative

• Because R² only measures correlation, not causation

What does an R² value of 0.65 suggest about the relationship between two variables?

• The relationship is weak

• The variables are not related

• 65% of the variation in the dependent variable is explained by the independent variable

• 65% of the variation in the independent variable is explained by the dependent variable

What is a potential issue when using calculators to find R²?

• Calculators require manual input of R²

• Calculators always give R² as zero

• Calculators may incorrectly display negative R² values

• Calculators cannot compute R²

What should be done if a calculator gives a negative R² value?

• Accept it as correct

• Ignore it, as R² should always be positive

• Recalculate using a different method

• Use a different calculator

How can you determine the sign of R when finding it from R²?

• By looking at the direction of the scatter plot

• By checking if R² is greater than 0.5

• By checking if R² is less than 0.5

• By using a different formula

If a scatter plot shows a downward trend, what can be inferred about the R value?

• R is positive

• R is negative

• R is zero

• R is greater than 1