Week 8
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What are the key features of correlation?
• has no response and explanatory variables • has no model formula for predicting one variable from the other • both variables must be normally distributed • ranges from -1 to 1 (with no units)
What are the key features of regression?
• has a response variable (Y) and explanatory variable (X) • has a model formula that predicts Y from X • only Y must be normally distributed • slope can be any value (in units of Y per X)
Overall difference between correlation and regression?
correlation is simpler but regression is more useful and flexible
What is α in linear regression?
is the line intercept (mean age when black-on-nose is 0)
What is β in linear regression?
is the line slope (change in age per unit of change in black-on-nose)
What is εi in linear regression?
εi (the residual) is the difference between Yi and the line
What is the line of best fit?
line minimises differences, is called the line of best fit
What is least squares?
is a method for estimating parameters of linear models - by minimising the residual sum of squares (the sum of these green bits squared)
What are the assumptions of linear regression?
A1. Y is linearly related to X (the linear model is appropriate) A2. The distribution of Y values is normal at all values of X A3. The variance of Y values is equal at all values of X A4. Values of Y are randomly sampled at all values of X
What are assumptions ANOVA?
same as linear but replace X with groups A1. Y is linearly related to groups(the linear model is appropriate) A2. The distribution of Y values is normal at all values of groups A3. The variance of Y values is equal at all values of groups A4. Values of Y are randomly sampled at all values of groups