Fill in the blank: A perfect positive correlation is denoted by r = ___ and a perfect negative correlation by r = ___ .

R = +1; r = -1

True or False: The coefficient of correlation can exceed the range of –1 to +1.

False. The coefficient of correlation always lies between –1 and +1.

What is the purpose of the scatter diagram in correlation analysis?

Scatter diagrams show variable relationships.

• Visualizes data distribution.

• Identifies correlation strength.

• Aids in predicting trends.

Explain the difference between linear and non-linear correlation.

Linear vs Non-linear Correlation

• Linear shows constant change.

• Non-linear varies in relationship.

• Different applications in analysis.

What are the assumptions of Karl Pearson’s coefficient of correlation?

Assumptions of Pearson’s Coefficient

• Both variables must be random.

• Bivariate population is normally distributed.

• Relationship between variables is linear.

Fill in the blank: In multiple correlation, ___ or more variables are studied simultaneously.

Three

What is the significance of the regression coefficient in regression analysis?

The regression coefficient indicates the amount of change in the dependent variable for a unit increase in the independent variable.

True or False: The values of the regression coefficients can be interpreted independently of each other.

False. Regression coefficients must be interpreted in the context of the variables they relate to and their relationship.

What is the method used to estimate the parameters in simple linear regression?

Least squares estimate parameters.

• Minimizes prediction errors.

• Calculates slope and intercept.

• Widely used in statistics.

Explain the term 'spurious correlation'.

Spurious correlation misleads interpretations.

• Two variables seem related.

• Influenced by a third factor.

• Can lead to false conclusions.

What distinguishes correlation analysis from regression analysis in statistical studies?

Correlation analysis shows relationship strength.

• Focuses on relationship direction.

• Does not predict outcomes.

• Useful for exploratory analysis.