Exploring Correlation Coefficients and Their Significance

What is the range of values for the correlation coefficient?

• -2 to 2

• -1 to 1

• 0 to 1

• 0 to 2

If the correlation coefficient (R) is 0, what does it indicate about the relationship between two numerical variables?

• Strong correlation

• Perfect positive correlation

• Perfect negative correlation

• No correlation

Which of the following R values indicates the strongest negative correlation?

• 0.7

• -0.3

• -0.9

• 0.1

What does a positive R value signify in terms of the slope of the linear regression model?

• Negative slope

• No slope

• Positive slope

• Undefined slope

What is the coefficient of determination commonly denoted as?

• R

• R squared

• R cubed

• R to the power of 4

How is the coefficient of determination (R squared) calculated?

• By taking the square root of R

• By doubling the R value

• By halving the R value

• By squaring the R value

What does an R squared value of 1 indicate?

• No correlation

• Perfect correlation

• Weak correlation

• Moderate correlation

What does the coefficient of determination measure?

• The average of the X and Y values

• How predictable the variance of the Y value is given the X variable

• The direction of the correlation

• The strength of the correlation

What is the arbitrary R squared value chosen by the instructor to indicate a good linear model?

• 0.95

• 0.5

• 0.75

• 1.0

Why does the instructor prefer using the R squared value over the correlation coefficient?

• It is easier to calculate

• It provides a better measure of predictability

• It is always higher

• It is less prone to errors