Download presentation

Presentation is loading. Please wait.

Published byJesse Henry Modified over 3 years ago

1
Simple linear models Straight line is simplest case, but key is that parameters appear linearly in the model Needs estimates of the model parameters (slope and intercept)- usually by least squares Makes a number of assumptions, usually checked graphically using residuals

2
Examples for linear regression How is LOI related to moisture? How should we estimate merchantable volume of wood from the height of a living tree? How is pest infestation late in the season affected by the concentration of insecticide applied early in the season?

3
Scatterplot of tree volume vs height

4
Minitab commands

5
Regression Output

6
Interpreting the output Goodness of fit (R-squared) and ANOVA table p-value? Confidence intervals and tests for the parameters Assessing assumptions (outliers and influential observations Residual plots

7
t = distance between estimate and hypothesised value, in units of standard error vs Confidence intervals and t-tests

10
Regression output

11
Outliers

12
Residual plots

13
Confidence and prediction intervals

14
Low R-sq High R-sq Low p-value: significant High p-value: non-significant Four possible outcomes

15
Not because relationships are linear Transformations can often help linearise Good simple starting point – results are well understood Approximation to a smoothly varying curve Why linear?

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google