Linear Regression - Week 11

Question 1

Define linear regression

Answer 1

Fits a line through data to predict one variable from another
(How to optimally guess variables info about each other)

Y = a + b X

Question 2

Define intercept and slope

Answer 2

Intercept : Predicted criterion value when predictor = 0
Slope : Predicted change in criterion value when predictor changes by one unit

Question 3

How can we predict one variable from another?

Answer 3

• Substitute actual X value in equation OR use graph to find average value

Question 4

Why is best prediction ≠ perfect prediction?

Answer 4

• Residuals (prediction errors)
• Some are neg and some are pos but sum always = 0

Question 5

Define extrapolation

Answer 5

• Using regression values outside the realm of the original data
• Sometimes the intercept in an extrapolation

Question 6

How is R^2 used to evaluate the strength of a fit of linear regression?

Answer 6

Tells us what proportion of variability in the response variable is explained

If r = 0 : predicted scores are all the same
If r = 0<r<1 : some linear relationship

S^2 predicted scores + S^2 residuals = S^2 true scores

Question 7

How is a slope tested for statistical significance?

Answer 7

CI measured using B, sample size, and standard error

Question 8

Define pro-regression

Answer 8

How much response variable changes for one-unit change in predictor
(INDEPENDENT OF RANGE)

Question 9

Define pro-correlation

Answer 9

Universal unit where we can compare relationships across different pairs of variables and we understand result when we are unfamiliar with variables concerned

Question 10

Explain what regression to the mean means

Answer 10

• Predicted scores are less extreme than predictor scores