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Summary Correlation and Multiple Regression Notes
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- The University Of Nottingham (UON)
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Cornell notes templateCorrelation and Multiple Regression: Theory
o Concepts of correlation and partial correlation explained
o Terms: multiple, linear and regression explained
o Prediction error and goodness of fit explained
o Interpreting f-ratio for multiple linear regression
o Calculating effect sizes (Cohen’s f²)
Factors effecting multiple linear regression described and how to deal with each
, Cornell notes template
o
Part one – correlation
o What is o an association/ dependency between two independently observed
correlation? variables (a statistical relationship bet. 2 variables)
o can use a scatterplot to visualise it, with each data point being a single
subject
o Analysis of in a regression analysis the beta coefficients (standardised coefficients beta)
correlation give the direction of the effect
o basic statistical question is: how strong is the association between x and
y?
score should be: 0.0 when x and y are completely independent of each
other, 1.0 when they are identical to one another, -1.0 when they are
exactly inverse to one another.
o One such score is called the Pearson correlation coefficient
o If x is large then y is small
n
o Arithmetic mean:
∑ xi
i
x=
n
o Covariance n
o Variance/ standard deviation:
∑ ( xi −x ) 2
i
Var x =
n−1
√
n
∑ ( x i−x )2
i
Std .x =
n−1
n
o Correlation:
∑ ( x i−x ) ∙ ( y i− y )
i
Corr x , y =
Std x ∙ Std y
- R squared is a
o Dispersion or scaling of variables
measure of n
goodness of
fit o Covariance:
∑ ( x i− x ) ∙ ( y i− y )
i
Cov x , y =
n−1
o The more similar the values of factors, the greater the product
o The more similar the values of variables x and y are the greater the
covariance
o Covariance has a similarity to variance but rather than squaring the
o Pearson
individual differences (IDs) we take IDs from x mean and y mean and
coefficients then we multiply them
o Negative correlation = large values in x and small values in y
- Sum of squares regression model calculation:
- R-squared = 1- (SSR / SST) – also seen on page 4
Goodness of fit, R Squared , is defined based on the amount of explained
variance relative to the total amount of variance, SST . SSR is used to
represent the amount of unexplained variance.
-
o Measures of o
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