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 variablesGiven bivariate data make a scatterplot of data and predict the pattern and strength of the relationship between the variablesLinear relationshipDefine correlation, study its properties and use themFind correlation for a bivariate data and interpret the resultsInterpret the square of the correlationTest for the significance of correlation – set up hypothesis and interpret the p-value of the testLinear relationship – Estimate the linear relationship between the two variables.Interpret slope and intercept.Interpret the square of the correlationStudy residuals and residual plots,Distinguish between the terms correlation and causationTest 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
Statistics and Probability
Community College / Lower Division, Graduate / Professional, College Credit Plus
Ohio Transfer Module Mathematics, Statistics, and Logic (TMM) Standards
Core TMM010 Outcome: Core skill demonstrated by students who successfully complete an Introductory Statistics Course
Standard: Summarize univariate and bivariate data by employing appropriate graphical, tabular, and numerical methods and describe the attributes of or relationships between the data. These may include (but are not limited to): frequency distributions; box plots; scatter plots; correlation coefficients; regression analysis; and measures of center, variation, and relative position.