Lecture 103 - Linear Regressions

Question 1

Assumptions in Linear Regressions can be remembered with the mnemonic LINE:

L –>

I –>

N –>

E –>

Can you make inferences (extrapolate) from linear regressions?

Answer 1

L –> Linear

I –> Independence of errors (Y value is NOT correlated with residuals and IS correlated with fits)

N –> Normally Distributed

E –> Equality of Variance

NO! The relationship between variables can only be said to be true for the sample/data set.

Question 2

Correlation coefficient (r) measures what?

Keep in mind r² allows you to obtain an absolute value for r (corrects for negatives). Re-scaling and applying this value to the data set provides a proportion of variability for an association –> essentially it shows if the variability in a data set is due to variability in the measured variables or in the measurements, themselves.

Answer 2

Correlation coefficient (r) measures the closeness of data points to the line of best fit –> larger r = closer to the line. Remember that r ranges from -1 to +1, where the absolute value describes how close to the line of best fit the data points are, and the sign (+ or -) describes whether the correlation is positive or negative (upward or downward slope).