Chapters 32 and 33: Correlation and Regression Flashcards
What does correlation do?
It quantifies the association between two continuous variables.
How do you find the coefficient of variation?
Divide the Standard Deviation by the mean
Does the coefficient of variation have units?
No
What is the coefficient of variation useful for?
It is useful for comparing the Standard Deviation to the mean and for comparing the scatter of variables measured in different units.
What is another term for correlation?
Covariation
What does the Correlation Coefficient (r) measure?
It measures the direction and magnitude of the linear correlation.
What are the values for the Correlation Coefficient?
-1 to 1
What does zero mean in regard to the Correlation Coefficient?
Zero means no correlation
What does a positive Correlation Coefficient mean?
It means the variables increase or decrease together.
What does a negative Correlation Coefficient mean?
It means the variables are inversely related.
In regard to the Correlation Coefficient, what does a 95% CI mean?
It means there is a 95% chance that the CI (of r) includes the population correlation coefficient.
The CI is not symmetrical unless…why?
the r=0 because r cannot be greater than 1.0 or
When is the Correlation Coefficient more symmetrical?
When the CI is large.
What is r squared?
The fraction of the variance shared between the two variables.
In correlation, what is the null hypothesis?
The null hypothesis is that there is no correlation.
What does r squared mean?
It’s the effect size for correlation.
What do r squared values indicate?
They indicate the amount of variation shared or explained.
What assumptions are made with correlations?
-Random, independent observations
-Normal distributions (of X and Y values).
• Paired (X & Y) observations from one population
• Assumes all covariation is linear
• Or won’t be detected if nonlinear
-No outliers
• X values are not experimentally controlled.
Describe what the Spearman correlation is.
It is a rank-based nonparametric test that is similar to a
Pearson’s correlation test.
What are the steps and rules for a Spearman correlation test?
- Separately rank X and Y values.
2. Perform the same steps as a Pearson correlation test but with the ranks.
What are the benefits of a Spearman correlation test?
It doesn’t assume a Gaussian distribution and it doesn’t suffer from outliers.
What does linear regression determine?
It determines the best linear model to represent the causal relationship between X and Y.
What is the X variable in linear regression?
The independent variable
What is the Y variable in linear regression?
The dependent variable
How does linear regression fit?
Linear regression fits the ‘best fit line’ through a graph of data points.
Line equation:
Y = mX + b
Linear regression must also account for…
variability
What does linear regression not do?
It does not find the line that comes closest to the points on the graph.
What does linear regression minimize?
It minimizes the vertical distances (residuals) of the points from the line.
What does correlation assume?
Correlation assumes a linear relationship in which both X and Y values exhibit error.
What does linear regression assume?
Linear regression assumes that X values are measured without error, but all of the error exists in Y
In either correlation or linear regression, what does the best fit line minimize?
The sum of the squared distances between the line and all of the points
Why is this a squared distance?
It is a squared distance because doing that finds the best midpoint between points.
What are we using in order the estimate the best linear model?
The values of the parameters of the linear model
What is the null hypothesis for simple linear regression?
The null hypothesis states that the line of best fit has a slope of 0.
What is the essentially equivalent to?
Essentially equivalent to the null of no correlation.
The P values for linear regression and correlation are…
identical.
