In other words, we add up the squares of each of the residuals. One way of doing this is by minimising the sum of squares of the residuals (again, you have come across this concept a few times before). Because we want to fit a model that explains as much variation as possible, it is intuitive that we should wish to minimise this residual variation. These residuals represent the variation left after fitting the line (a linear model) through the data. These distances, measured parallel to the vertical axis, are called residuals (you have encountered them before in this course). When looking at data points on a graph, unless all of the data points are arranged perfectly along a straight line, there will be some distance between the points and the line. 24.8 Compare t-tests with randomisation testsįigure 16.2: The equation of straight lines.24.6 Sex differences in fine motor skills.24.5 Sexual selection in Hercules beetles.24.3 Temperature effects on egg laying dates.24.2 Wrangling the Amniote Life History Database.22.5 Extending the simulation (optional, advanced).22.3.2 Some questions for you to address:.22.3 An example of calculating statistical power.22.2 What determines statistical power?.22.1 Type I and II errors and statistical power.20.1.1 Example: Number of offspring in foxes.19.2 Akaike Information Criterion (AIC).18 n-way ANOVA: Linear models with >1 categorical explanatory variables.17.3 The summary of coefficients ( summary).17 ANCOVA: Linear models with categorical and continuous explanatory variables.16.4 Worked example: height-hand width relationship.16.2 Evaluating a hypothesis with a linear regression model.16 Linear regression: models with a single continuous explanatory variable.15.2.2 Tukey’s Honestly Significant Difference (HSD).15 ANOVA: Linear models with a single categorical explanatory variable.14.10 Exercise: Compare t-tests with randomisation tests (optional).

14.8 Exercise: Sex differences in fine motor skills.

14.5 A paired t-test is a one-sample test.

14.3 Doing it “by hand” - where does the t-statistic come from?.13.3 Exercise: Sexual selection in Hercules beetles.13.1.1 Calculate the observed difference.11.5 Comparing normal and Poisson distributions.10.2 “Facets” - splitting data across panels.9.3 Exercise: Temperature effects on egg laying dates.8.6 Exercise: Wrangling the Amniote Life History Database.5.11 Exercise: Californian bird diversity.5.1 Missing values, infinity and “non-numbers”.

Excel linear regression formula 16.6