Applied Regression Modeling, 3rd Edition

Chapter 2Simple Linear Regression

In the preceding chapter, we considered univariate data, that is, datasets consisting of measurements of just a single variable on a sample of observations. In this chapter, we consider two variables measured on a sample of observations, that is, bivariate data. In particular, we will learn about simple linear regression, a technique for analyzing bivariate data which can help us to understand the linear association between the two variables, to see how a change in one of the variables is associated with a change in the other variable, and to estimate or predict the value of one of the variables knowing the value of the other variable. We will use the statistical thinking concepts from Chapter 1 to accomplish these goals.

After reading this chapter you should be able to:

• Define a simple linear regression model as a linear association between a quantitative response variable and a quantitative predictor variable.
• Express the value of an observed response variable as the sum of a deterministic linear function of the corresponding predictor value plus a random error.
• Use statistical software to apply the least squares criterion to estimate the sample simple linear regression equation by minimizing the residual sum of squares.
• Interpret the intercept and slope of an estimated simple linear regression equation.
• Calculate and interpret the regression standard error in simple linear regression.
• Calculate and interpret the coefficient of determination ...