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Summary Regression Notes

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A summary of notes from the lecture

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  • January 18, 2024
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  • 2021/2022
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Regression

Part 1

Correlation vs regression
 Correlation looks at relationship between variables
 Regression asks how does the variable x predict variable y?

Correlation into simple regression
 When you have data for both age and height, correlation tells you the strength of
the relationship – useful
 In some situations only part of the data is provided. E.g. I might want to guess what
height my 9 yr old will be next year.
 Regressions is used to make a simple prediction in cases such as these
 Simple regression (one predictor
o Predictor > outcome/criterion variable
o Age > height

Multiple regression
 But other variables that contribute to height such as nutrition and parent height. A
child with poor nutrition and or shorter parents may not reach same height as one
with good nutrition and or tall parents at the same age
 If we want to make a good prediction we must quantify how much these variables
influence height and to what degree relative to each other. Multiple regression can
be used to answer these questions.
 Nutrition – age – parent height > height
 Predictor – predictor – predictor > outcome/criterion variable

Regression key terms
 ‘Independent variables’ are now predictor variables
 ‘Dependent variables’ are now outcome/ criterion variables
 The overall ‘model fit’ is R/R2
 The strength of predictors is shown by its beta values
o Positive betas = positive predictor
o Negative beta = negative predictor
o These above are similar to covariance/correlations

Formula fun
 Intro to data modelling – GLM
 Tests a linear model to predict values of an outcome variable from one or more
predictor variables
 One predictor = simple regression
 More than one predictor = multiple regression

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