Correlation Concepts

What is the formula for calculating Pearson's correlation coefficient?

• r = (Σ((X - X̄)(Y - Ȳ))) / (√(Σ(X - X̄)²) * √(Σ(Y - Ȳ)²))

• r = (Σ(X + Y)) / n

• r = (Σ(X - Y)) / (Σ(X) * Σ(Y))

• r = (Σ(X²) + Σ(Y²)) / n

If the Pearson correlation coefficient is 0.85, what does this indicate about the relationship between the two variables?

• There is a strong positive correlation between the two variables.

• There is no correlation between the two variables.

• The variables are independent of each other.

• There is a weak negative correlation between the two variables.

List two properties of Pearson's correlation coefficient.

• 1. Ranges from -1 to 1. 2. Indicates the strength and direction of a linear relationship.

• Only applicable to categorical data.

• Can only be used with normally distributed data.

• Measures the mean of a dataset.

How would you interpret a Pearson correlation coefficient of -0.5?

• There is a moderate negative correlation between the two variables.

• There is a weak negative correlation between the two variables.

• There is no correlation between the two variables.

• There is a strong positive correlation between the two variables.

What is the difference between Pearson's correlation and Spearman's rank correlation?

• Pearson's correlation measures monotonic relationships; Spearman's rank correlation measures linear relationships.

• Pearson's correlation is for linear relationships with continuous data; Spearman's rank correlation is for monotonic relationships with ordinal or non-normally distributed data.

• Pearson's correlation is non-parametric; Spearman's rank correlation is parametric.

• Pearson's correlation is used for categorical data; Spearman's rank correlation is for linear relationships.

In a dataset, if the correlation coefficient is close to 1, what can be inferred about the data?

• The data is randomly distributed without any pattern.

• The data shows a strong negative correlation.

• The data shows no correlation at all.

• The data shows a strong positive correlation.

Calculate the Pearson correlation coefficient for the following data points: (1,2), (2,3), (3,6), (4,8).

• 0.5

• -1.0

• 0.8

• 1.0

What type of correlation is indicated by a coefficient of 0?

• Perfect negative correlation

• Strong positive correlation

• No correlation

• Weak negative correlation

Explain why Pearson's correlation may not be suitable for non-linear relationships.

• Pearson's correlation is designed for categorical data analysis.

• Pearson's correlation can only be used with normally distributed data.

• Pearson's correlation measures the distance between data points.

• Pearson's correlation may not be suitable for non-linear relationships because it only captures linear associations and can misrepresent the strength of the relationship.

When would you prefer using Spearman's rank correlation over Pearson's correlation?

• Use Pearson's correlation for ordinal data.

• Use Spearman's rank correlation for normally distributed data.

• Use Spearman's rank correlation for non-normally distributed, ordinal, or non-linear data.

• Use Pearson's correlation for non-linear data.