M5: Introduction to Regression

Question 1

What does X and Y stand for?

Answer 1

X = Explanatory variable
Y = Response variable

Question 2

Scatterplot

Answer 2

Plot of Y vs X measured on the same individual

Question 3

Interpretations (DOTS)

Answer 3

Direction - Positive/Negative
Outliers
Trend - Linear, nonlinear
Strength - Weak/Moderate/Strong

Question 4

What is the purpose of correlation(r)?

Answer 4

Summarize the direction and strength of the straight line relationship between x and y

Question 5

Interpretation of r

Answer 5

Strength | 0 - 1
Sign | Direction

Question 6

Regression line purpose

Answer 6

Line that best fits through the middle of the points

Question 7

Regression line notation

Answer 7

y = a + bx

Question 8

Least Squares Regression method

Answer 8

a) Find the line that minimizes the prediction errors
b) Line goes through the middle of the points.
c) Minimize the sum of squared residuals
d) Passes through the point (x-, y-)

Question 9

Residuals formula

Answer 9

Observed - Predicted
y - y^

Question 10

Coefficient of Determination (R^2)

Answer 10

Percent of variability in y explained by the linear regression on x

Question 11

b

Answer 11

r (stdv y / stdv x)

Question 12

a

Answer 12

a = y_ - bx_