CJUS K300 1st Edition Final Exam Study Guide Lectures 20 23 Lecture 20 December 1 Bivariate Regression You read graphs as we read the English language from left to right So when we look at the graph if it starts low on the left side and rises to the right then there is a positive relationship between the variables If it looks like it is going down from left to right then the variables have a negative relationship Positive Relationship Non Linear Relationship No Relationship Line of Best Fit or Least Squares Regression Line Population y x Sample y a bx Slope x y x 2 2 x xy n b Lecture 21 December 3 Bivariate linear regression analysis is the simplest linear regression procedure simple leanera regression Explores the explanatory relationship for 2 variables Examines only linear relationships Simple linear regression focuses on explaining and predicting the dependent variables based on the information we know about he independent variable The regression model examines the changes in the dependent variable as a function of changes or differences in values of the independent variable This is what we would consider the interpretation of the answer Dependent variable DV variable that we are trying to explain or predict it is usually very easily identifiable we denote this as Y Independent variable IV used to predict systematic changes in the dependent variable we denote it as X The regression aims to determine how and to what extent the dependent variable Y varies as a function of changes in the independent variable X Best fitting straight line least squares regression line the extent to which the data points do not lie on the straight line indicate individual errors Intercept denoted as a this is the point where the regression line crosses the Y axis Slope denoted as b this tells you how much a 1 unit increase in X affects the value of Y Lecture 22 December 8 Pearson s correlation measures the strength of the linear relationship between the dependent variable and the independent variable For samples we use r to denote pearson s correlation for populations we use p for pearson s correlation It is always between 1 and 1 1 means there is a perfect negative relationship 1 means that there is a perfect positive relationship 0 means that there is a perfect absence of any relationship Rule of thumb for Pearson s r 70 or higher Strong positive relationship 40 to 69 Moderate positive relationship 20 to 39 Weak positive relationship 01 to 19 No or negligible relationship 01 to 19 No or negligible relationship 20 to 39 Weak negative relationship 40 to 69 Moderate negative relationship 70 or higher Strong negative relationship Interpretation of Pearson s r will also be used for the interpretation of hypothesis testing We are alpha value confident that there is negative or positive 1 between the dependent variable and independent variable o Negative relationship or positive relationship o You must write out the specific dependent and independent variables when doing the problem Lecture 23 December 10 R squared the coefficient of determination The amount of variance in the dependent variable which is associated with the independent variable How well data points fit a statistical 1 2 3 4 In bivariate regression R squared is the square of the sample correlation coefficient pearson s r In multivariate regression R squared is the square of the coefficient of multiple correlation In both cases R squared values range from 0 to 1 Generate Hypothesis Find the critical value Calculate obtained value Make a conclusion 5 Interpretation