## 12.1 Introduction to Simple Linear Regression

An introduction to simple linear regression. The pain-empathy data is estimated from a figure given in: Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157–1162. The Janka hardness-density data is found in: Hand, D.J., Daly, F. , Lunn, A.D., McConway, K., and Ostrowski, E., editors (1994). … Read more

## 12.2 Simple Linear Regression: The Least Squares Regression Line

An introduction to the least squares regression line in simple linear regression. The pain-empathy data is estimated from a figure given in: Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157-1162. The Janka hardness-density data is found in: Hand, D.J., Daly, F. , Lunn, A.D., McConway, … Read more

## 12.3 Simple Linear Regression: Interpreting Model Parameters

A look at the interpretation of the parameters (β 0, β 1, σ2), and their corresponding estimates in simple linear regression.

## 12.4 Simple Linear Regression: Assumptions

A look at the assumptions on the epsilon term in our simple linear regression model.

## 12.5 Checking assumptions with residual plots

An investigation of the normality, constant variance, and linearity assumptions of the simple linear regression model through residual plots. The pain-empathy data is estimated from a figure given in: Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157–1162. The Janka hardness-density data is found in: Hand, … Read more

## 12.6 Inference on the slope (the formulas)

I show the formulas (and work through some of the underlying logic) for confidence intervals and hypothesis tests on the slope parameter in simple linear regression.

## 12.7 Inference on the Slope (An Example)

I work through an example, finding a confidence interval and carrying out a hypothesis test on the slope parameter. The data used is estimated from a figure in: Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157–1162.

## 12.8 The Correlation Coefficient and Coefficient of Determination

A look at the Pearson correlation coefficient (r), the coefficient of determination (r 2), some of their properties and a few examples. (This is discussed in the context of measuring the strength of the linear relationship between 2 variables.) One of the data sets used is estimated from a figure given in: Singer et al. … Read more

## 12.9 Simple Linear Regression: An Example

I work through an example relating eggshell thickness to DDT concentration, fitting the least squares line, using the line for prediction, interpreting the coefficient of determination, checking the residual plots and carrying out a test on the slope.

## 12.10 Simple Linear Regression: Always Plot Your Data!

A quick look at a few cautions about simple linear regression. Anscombe’s quartet can be found in: Anscombe, F. (1973). Graphs in statistical analysis. American Statistician, 27:17–21. The fuel use vs speed data is found in: West, B.H., McGill,R.N., Hodgson, J.W., Sluder, S.S. , and Smith D.E., Development and Verification of Light-Duty Modal Emissions and … Read more