Regression & Correlation Flashcards by Will Perchard

What does correlation refer to?

Degree to which two quantitative variables are related

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What is commonly used to measure correlation in quantitative parametric data?

Pearsons correlation coefficient

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What does value of correlation coefficient ‘r’ vary between?

-1 to +1

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Units of ‘r’?

None

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When is correlation coefficient not valid?

If data is not independent (paired)

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When can Fishers transformation be used?

To compare two correlation coefficients for hypothesis testing

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What are Partial correlations?

Correlations between two variables after adjusting for a third variable

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What is Spearmans correlation (rho)?

Non-parametric equivalent of Pearsons

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What can Spearmans be used for?

To test association between two variables if at least one is ordinal or
If sample size is small despite being continuous variables
or if non-linearity is suspected or
if non-normal distribution is noted for both variables

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What does Spearmans assume?

Difference between each pair of ordinal variables is the same i.e. the ranks are equidistant

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If the difference between each pair of ordinal variables is not the same, how can one calculate correlation?

Kendalls Tau - appropriate measure of nonparametric correlation

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What does regression statistics help with?

Helps predict what value one variable will be if given a particular value of the other variable

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Explain the formula for simple linear regression

y = a +bx

B = regression coefficient
A = intercept on y axis

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What can simple linear regression predict?

Probable score in Y axis from known score in X axis i.e. dependent variable can be predicted from value of independent variable

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How does one determine the value of a and b for regression?

Using a scattergram and method of least squares

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Explain the method of using a scattergram and method of least squares

Hypothetical straight line is constructed so that its vertical distance from various points of observations on a scattergram is kept to a minimum; this is called the residue.
The sum of the square of residues is kept to a minimum for a regression line of good fit

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What happens in multiple linear regression?

Several independent variables together predict a single dependent variable

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What type of technique is multiple regression?

Multivariate

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What is the name of the independent variables in multiple regression?

Covariates

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What is the name of covariates which may be highly correlated with each other?

Collinearity

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Effect of collinearity?

May disturb the regression

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When is regression coefficient useful?

Examine confounders

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What can be used to express correlation coefficients?

What does square of regression coefficient test?

Goodness of fit or final regression

What is goodness of fit?

Proportion of total variation in dependent variable that can be explained by the independent variable

What does goodness of fit measure?

How well actual outcome (dependent variable) and calculated dependent variable correspond

Values or goodness of fit

0-1

What is the coefficient of variation?

Goodness of fit calculated for Pearsons correlation coefficient

What is needed for linear regression?

Continuous dependent variable

What type of regression is used if dependent variable is binary?

Logistic regression

Why is logistic regression popular?

It can give OR, RR and hazard ratio for independent variables that affect the dependent variable

Test used if variable is continuous, 1 independent & dependent variable

Simple linear regression

Regression test used if continuous data with >1 independent variable and 1 dependent variable

Multiple linear regression

Regression test used if binary data, 1 independent variable and 1 dependent variable

Simple logistic regression

Test used if binary data, >1 independent variable and 1 dependent variable

Multiple logistic regression

What is log-linear analysis used for?

Categorical data

What must be noted in log-linear analysis?

No demarcation between the dependent and independent variable

What data can be used in logistic regression?

Continuous and categorical independent variables

What are Bernoulli random variables?

Variables that have dichotomous outcomes used in logistic regression

What is exponential correlation?

When one demonstrates the exponential relationship of a variable with a factor such as time using log-transformed values plotted against time

What is polynomial regression?

When in non-linearity, the relationship between dependent variable (y) and independent variable (x) is expressed as Y=X(n square)

What is the 1 in 10 rule?

Number of variables studied in multiple regression models must not be greater than 10% of sample size.

1 in 10 rule for logistic regression?

Number of variables must not be greater than 10% of number of events

How can multiple regression be performed

Stepwise regression Forward selection Backward elimination

What happens in stepwise regression?

Coefficient of regression calculated and starts with most significant to least significant independent variable and fits them in stepwise fashion into regression equation.

Disadvantage of stepwise regression

Sometimes statistically significant variables may not be clinically significant

Theory behind forward selection

Confounding factor is associated with both independent and dependent variable If one does not know the confounding variable, they are treated as covariates

What does one often examine in multiple regression

Which is the confounding variable

What happens in forward selection?

While constructing multiple regression equations, if the regression coefficient of a previously added variable changes then either one of the covariates is a confounder; these are retained in the equation irrespective of statistical significance. Latter added covariate is discarded if no change occurs in regression coefficient

What is backward elimination?

Starts with final model - full equation - and tries to discard covariates one by one according to changes that occur in correlation coefficients

In the equation y=a+bx+e what is y?

Dependent variable - outcome of interest

In the equation y=a+bx+e what is a and b?

Constants

In the equation y=a+bx+e what is b?

Slope or regression coefficient

In the equation y=a+bx+e what is x?

Independent variable - predictor of outcome

In the equation y=a+bx+e what is e?

Error. Random variable with mean = 0

In the equation y=a+bx+e what does e represent?

Part of variability of Y which is not explained by relationship with x

What can method of least squares be used for with respect to e (error)?

We can find best linear regression equation with minim variance of e