Lecture 10 Regression Analysis Research Methods and Statistics

Quantitative Data Analysis Types of Data Analysis - Descriptive Statistics: the use of statistics to summarize, describe or explain the essential characteristics of a data set. - Inferential Statistics: the use of statistics to make generalizations or inferences about the characteristics of a population using data from a sample. Also known as significance testing.

Quantitative Data Analysis Levels of Analysis - Univariate Analysis: conducted to describe individual variables - Bivariate Analysis: conducted to describe, explain or predict the relationship between two variables - Multivariate Analysis: conducted to describe, explain or predict the relationship between more than two variables

Regression Regression analysis is used examine the degree to which a quantitative independent variable(s) predicts a quantitative dependent variable Simple regression and multiple regression - Simple regression: the use of 1 quantitative independent variable to predict the values of 1 quantitative dependent variable - Multiple regression: the use of 2 or more quantitative independent variables to predict the values of 1 quantitative dependent variable

Bivariate Analysis: Simple Regression The goal of simple regression is to obtain a linear equation from which we can predict values of a DV using values of an IV. Basic Regression Equation Y = a + bX Y = predicted value of the DV X = value of the IV a = the Y intercept, or the value of Y when X is zero b = regression coefficient; or the value by which Y will change if X changes by 1 unit (slope of the line).

Bivariate Analysis: Simple Regression Example: Examining the extent to which we can use adult literacy rate (IV) to predict infant mortality rate (DV) R2 = how well your IV predicts the DV. How much of the variance in the DV is accounted for by the variance in the IV. Interpreting R2 < 0.1 = poor fit (10% or less) 0.11-0.3 = modest fit (11%-30%) 0.31 – 0.5 = moderate fit (31%- 50%) > 0.5 = strong fit (more than 50%) F-Test of Significance (tests the significance of your regression model)

Bivariate Analysis: Simple Regression B = regression coefficient; the value by which the DV is predicted to change if the IV changes by 1 unit. Beta = shows the effect size of the IV on the DV. Sig = p-value; shows the statistical significance of the relationship between each IV and the DV. Simple Regression Equation Y = a + bX Infant Mortality Rate = 160.7 – 1.51(Adult Literacy Rate)

Multivariate Analysis: Multiple Regression The goal of multiple regression is to obtain a linear equation from which we can predict values of a DV using values of multiple IVs. **Example: (1)Adult literacy rate and (2) Average female life expectancy (2 IVs) to predict Infant mortality (DV) Multiple Regression Equation Y = a + b1X1 + b2X2 Y = predicted value of the DV X1, X2 = value of each IV a = the intercept (value is meaningless for multiple regression) b1, b2, = regression coefficients for each IV; or the value by which Y is expected to change if each X changes by 1 unit.

Multivariate Analysis: Multiple Regression R2 = Tells you how well all IVs predict/explain the DV. How much of the variance in the DV is accounted for by the variance in the IVs. Interpreting R2 < 0.1 = poor fit (less than 10%) 0.11-0.3 = modest fit (11%-30%) 0.31 – 0.5 = moderate fit (31%- 50%) > 0.5 = strong fit (more than 50%) F-Test of Significance (tests the significance of your regression model)

Multiple Regression Equation B = regression coefficient; the value by which your DV is predicted to change if the IV changes by 1 unit. Beta = shows the effect size of each IV on the DV. Sig = p-value; shows the statistical significance of the relationship between each IV and the DV. Multiple Regression Equation Y = a + b1X1 + b2X2 Infant Mortality = 261.7 - 0.452(Adult Literacy) – 2.62(Avg. Female Life Expectancy)

Class Exercise Use the file employee_data.sav Form a scatterplot using the variable “current salary” as the y-variable and “education” as the x-variable. Include a best-fitting straight line in your scatterplot. Perform a regression analysis for the two variables (IV: education; DV: current salary). From the output, answer the following Qs. - Does the relation between the two variables appear to be linear? - What is the R-square value and what does it imply? - Is the relation between the two variables statistically significant? - What is the equation of the best-fitting straight line that predicts “current salary” from “education” ? - Do you think the finding from the sample will be significant in a population?