Method for studying the relationship between one dependent variable (e.g. weight) and two or more independent variables simultaneously (e.g. exercise, diet, water intake, age, gender...)
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For multiple linear regression model all you need is..
in the coefficients Bi. Each Bi is essential to extract valuable information from the model:
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Looking for association in multiple linear regression model:
Test Bi to check if variable xi is significantly associated with the outcome y.
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Interpretation of association in multiple linear regression model:
If variable xi is significantly associated with the outcome y (a), Bi gives the clue on how to interpret the association. In particular, Bi represents the change in average in y for one unit change in xi (holding all other x’s fixed).
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Hypothesis testing on Bi
H0 : Bi = 0. Ha : Bi /=/ 0. If p< 0.05, we accept
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Purposes of multiple regression model
– Association – Prediction – Account of confounding variables
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Cofounding variables
A situation in which the association between a explanatory variable (e.g exercise (x1)) and outcome (e.g. weight (y)) is distorted by the presence of another variable (e.g. hours of free time (x2)).
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If not taken into account, confounding variables can cause two major problems:
– Increase variance in the estimation of B1 – Introduce bias in the estimation of B1
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Bias means..
.. how much on an average are the estimated coefficients B different from the actual value.
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Variance means..
.. how different will B estimations will be if different samples are taken from the same population.
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Dealing with multiple cofounders
All confounders are adjusted for by including them simultaneously as additional predictors
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R2..
how well the regression line/hyperplane approximates the real data points. Also known as the goodness of fit.
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An R2 of 1 indicates..
that the regression line/hyperplane perfectly fits the data.
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Adjusted R2 as a measure for model selection
Adjusted R2 is a modified version of
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Other cards in this set
Card 2
Front
For multiple linear regression model all you need is..
Back
in the coefficients Bi. Each Bi is essential to extract valuable information from the model:
Card 3
Front
Looking for association in multiple linear regression model:
Back
Card 4
Front
Interpretation of association in multiple linear regression model:
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