1. The World of Linear Regression

6. Scatterplot

8. Regression Equation The linear equation is specified as follows: Y = a + bX Where Y = dependent variable X = independent variable a = constant (value of Y when X = 0) b = is the slope of the regression line

12. Regression Equation The standard regression equation is the same as the linear equation with one exception: the error term. Y = α + βX + ε Where Y = dependent variable α = constant term β = slope or regression coefficient X = independent variable ε = error term

13. Regression Equation This regression procedure is known as ordinary least squares (OLS). α (the constant term) is interpreted the same as before β (the regression coefficient) tells how much Y changes if X changes by one unit. The regression coefficient indicates the direction and strength of the relationship between the two quantitative variables.

14. Regression Equation The error ( ε ) indicates that observed data do not follow a neat pattern that can be summarized with a straight line. A observation's score on Y can be broken into two parts: α + βX is due to the independent variable ε is due to error Observed value = Predicted value (α + βX) + error (ε)

15. Regression Equation The error is the difference between the predicted value of Y and the observed value of Y. This difference is known as the residual .

18. Regression Interpretation For the data on the scatterplot: Y (depvar) = telephone lines for 1,000 people X (indvar) = Infant mortality We can use regression analysis to examine the relationship between communication capacity (measured here as telephone lines per capita) and infant mortality.

19. Regression Interpretation In this analysis, the intercept and regression coefficient are as follows: α (or constant) = 121 Means that when X (infant deaths) is 0 deaths, there are 121 phone lines per 1,000 population. β = -1.25 Means that when X (deaths) increases by 1, there is a predicted or estimated decrease of 1.25 phone lines.

20. Regression Interpretation

22. Scatterplot