Understanding Correlation Coefficients

The video tutorial explains the correlation coefficient (r), which measures the strength and direction of a linear relationship between two variables. It describes how r values range from -1 to 1, with 1 indicating a perfect positive correlation, -1 a perfect negative correlation, and 0 no correlation. The tutorial demonstrates how to sketch lines of best fit for scatter plots and analyze them to determine the strength of the correlation. It provides examples of scatter plots with strong positive and negative correlations, as well as those with weaker correlations, and explains how to select appropriate r values based on the data's behavior.

What is the range of values that the correlation coefficient can take?

• Between -0.5 and 0.5

• Between -2 and 2

• Between -1 and 1

• Between 0 and 1

If the correlation coefficient is 1, what does it indicate?

• No correlation

• Weak positive correlation

• Perfect negative correlation

• Perfect positive correlation

What does a correlation coefficient of -1 signify?

• No correlation

• Weak negative correlation

• Perfect negative correlation

• Perfect positive correlation

In a scatter plot with a strong negative correlation, what is the likely value of r?

• 0.9

• -0.6

• -0.9

• 0.6

What does it mean if the points in a scatter plot are very close to the line of best fit?

• The correlation is undefined

• There is no correlation

• There is a strong correlation

• There is a weak correlation

For a scatter plot with a strong positive correlation, what is the likely value of r?

• 0.6

• -0.9

• -0.6

• 0.9

What does a positive slope in the line of best fit indicate?

• There is no relationship between the variables

• As one variable increases, the other also increases

• As one variable increases, the other remains constant

• As one variable increases, the other decreases

In a scatter plot with a weaker positive correlation, what is the likely value of r?

• -0.6

• 0.9

• -0.9

• 0.6

What does a negative slope in the line of best fit suggest?

• There is no relationship between the variables

• As one variable increases, the other decreases

• As one variable increases, the other remains constant

• As one variable increases, the other also increases

In a scatter plot with a weaker negative correlation, what is the likely value of r?

• -0.6

• 0.6

• -0.9

• 0.9