Sometimes it is difficult to measure or find information on a variable of interest. The problem then is to use information from easily measurable variables to find the needed information. Naturally, the variables to use must be related to the variable of interest. In this module we will study about relationships between two quantitative variables. We will explore some standard mathematical (linear, quadratic, cubic, etc.) forms of relationships.

Learning Objectives:

• Identify response and explanatory variables
• Given bivariate data make a scatterplot of data and predict the pattern and strength of the relationship between the variables
• Linear relationship
• Define correlation, study its properties and use them
• Find correlation for a bivariate data and interpret the results
• Interpret the square of the correlation
• Test for the significance of correlation – set up hypothesis and interpret the p-value of the test

• Linear relationship – Estimate the linear relationship between the two variables.
• Interpret slope and intercept.
• Interpret the square of the correlation
• Study residuals and residual plots,
• Distinguish between the terms correlation and causation
• Test for the significance of the slope coefficient – set up hypothesis and interpret the p-value of the test.
• Study quadratic and other non-linear models.

Textbook Material - 

Chapter 12 – Correlation and Regression – Pages 673 - 699