1. Lecture 10 Regression Analysis
Research Methods and Statistics

2. 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.

3. 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

4. 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

5. 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).

6. 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)
= 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)

7. 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 = – 1.51(Adult Literacy Rate)

8. 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.

9. 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%)
= 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)

10. 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 = (Adult Literacy) – 2.62(Avg. Female Life Expectancy)

11. 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?