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Biostats > Chapters 32 and 33: Correlation and Regression > Flashcards

Chapters 32 and 33: Correlation and Regression Flashcards

1
Q

What does correlation do?

A

It quantifies the association between two continuous variables.

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2
Q

How do you find the coefficient of variation?

A

Divide the Standard Deviation by the mean

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3
Q

Does the coefficient of variation have units?

A

No

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4
Q

What is the coefficient of variation useful for?

A

It is useful for comparing the Standard Deviation to the mean and for comparing the scatter of variables measured in different units.

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5
Q

What is another term for correlation?

A

Covariation

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6
Q

What does the Correlation Coefficient (r) measure?

A

It measures the direction and magnitude of the linear correlation.

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7
Q

What are the values for the Correlation Coefficient?

A

-1 to 1

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8
Q

What does zero mean in regard to the Correlation Coefficient?

A

Zero means no correlation

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9
Q

What does a positive Correlation Coefficient mean?

A

It means the variables increase or decrease together.

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10
Q

What does a negative Correlation Coefficient mean?

A

It means the variables are inversely related.

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11
Q

In regard to the Correlation Coefficient, what does a 95% CI mean?

A

It means there is a 95% chance that the CI (of r) includes the population correlation coefficient.

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12
Q

The CI is not symmetrical unless…why?

A

the r=0 because r cannot be greater than 1.0 or

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13
Q

When is the Correlation Coefficient more symmetrical?

A

When the CI is large.

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14
Q

What is r squared?

A

The fraction of the variance shared between the two variables.

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15
Q

In correlation, what is the null hypothesis?

A

The null hypothesis is that there is no correlation.

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16
Q

What does r squared mean?

A

It’s the effect size for correlation.

17
Q

What do r squared values indicate?

A

They indicate the amount of variation shared or explained.

18
Q

What assumptions are made with correlations?

A

-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.

19
Q

Describe what the Spearman correlation is.

A

It is a rank-based nonparametric test that is similar to a

Pearson’s correlation test.

20
Q

What are the steps and rules for a Spearman correlation test?

A
  1. Separately rank X and Y values.

2. Perform the same steps as a Pearson correlation test but with the ranks.

21
Q

What are the benefits of a Spearman correlation test?

A

It doesn’t assume a Gaussian distribution and it doesn’t suffer from outliers.

22
Q

What does linear regression determine?

A

It determines the best linear model to represent the causal relationship between X and Y.

23
Q

What is the X variable in linear regression?

A

The independent variable

24
Q

What is the Y variable in linear regression?

A

The dependent variable

25
Q

How does linear regression fit?

A 
Linear
regression fits
the ‘best fit
line’ through a
graph of data
points.
26
Q

Line equation:

A

Y = mX + b

27
Q

Linear regression must also account for…

A

variability

28
Q

What does linear regression not do?

A

It does not find the line that comes closest to the points on the graph.

29
Q

What does linear regression minimize?

A

It minimizes the vertical distances (residuals) of the points from the line.

30
Q

What does correlation assume?

A 
Correlation
assumes a linear
relationship in
which both X
and Y values
exhibit error.
31
Q

What does linear regression assume?

A 
Linear regression
assumes that X
values are
measured
without error,
but all of the
error exists in Y
32
Q

In either correlation or linear regression, what does the best fit line minimize?

A

The sum of the squared distances between the line and all of the points

33
Q

Why is this a squared distance?

A

It is a squared distance because doing that finds the best midpoint between points.

34
Q

What are we using in order the estimate the best linear model?

A

The values of the parameters of the linear model

35
Q

What is the null hypothesis for simple linear regression?

A

The null hypothesis states that the line of best fit has a slope of 0.

36
Q

What is the essentially equivalent to?

A

Essentially equivalent to the null of no correlation.

37
Q

The P values for linear regression and correlation are…

A

identical.

Biostats (21 decks)

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