Regression uncertainty bands

Download: RegressionBands_init.xlsx

Download: Slides.pdf

Introduction

Up until now the regression screencasts have been mostly concerned with the prediction of the regression parameters: how to make those predictions using least-squares regression, and the statistical properties of those predictions or the related task of statistical inference on the basis of the parameter estimates. Now we turn our attention to two other types of prediction:

• prediction about the dependent variable $Y$ for a given value of independent variable $X$
• prediction about the independent variable $X$ for an observed value of dependent variable $Y$

The first type of prediction is the most common, and comes in two forms; these two types of predictions – which result in confidence bands and prediction bands around the regression fit – are the topic of this screencast.

Learning Goals

• Understand the nature and uses of confidence bands and prediction bands in regression analysis
• Learn how to calculate confidence intervals (or bands) and prediction intervals (or bands) in Excel

Tasks

• Manually calculate a 95% confidence interval for $\mu_y$ at 11.5 mM lactic acid
• Use the PolyConf function to calculate the same CI
• Calculate the confidence band and add it to the plot
• Manually calculate a 95% prediction interval for $y_u$ at 11.5 mM lactic acid
• Use PolyPred to calculate the same PI
• Calculate the prediction band and add it to the plot

When you are finished with the screencast your spreadsheet should look something like the image below. The wider band around the calibration curve is the prediction band.