For an experiment we have the following data set: n = 4, ∑x = a, ∑y = 10, ∑xy = 21, ∑x² = 30, ∑y² = 30. If the correlation coefficient is -0.8 then the value of a is:

The correct answer is 10.

Key Points

• The correlation coefficient only measures linear relationships, so it does not necessarily indicate causality.
• The value of a in this data set only represents the sum of the x values and does not necessarily have a specific meaning in the context of the experiment.
•  The value of a in the data set is 10.
• The correlation coefficient of -0.8 indicates a strong negative linear relationship between the two variables, x and y.
• This information along with the other statistics provided can be used to calculate a using statistical formulas.

Additional Information 

• The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables.
• A correlation of -1 indicates a perfect negative linear relationship, while a correlation of 1 indicates a perfect positive linear relationship.
• The formula to calculate the correlation coefficient is: r = (n∑xy - ∑x∑y) / (√(n∑x2 - (∑x)^2) * √(n∑y2 - (∑y)^2))
• In this case, we know the value of r (-0.8), so we can rearrange the formula and solve for a.