Lecture 3_Regression Intro

Question 1

What is the Centroid?

Answer 1

Point defined by plotting the means of 2 variables

• represents the center of the cloud of points

Question 2

A regression line must …

Answer 2

• pass through the centroid

* come as close as possible to all points (therefore, the sum of the squared residuals will be as small as possible).

Question 3

What does the slope (b) of a bivariate regression line tell us?

Answer 3

the amount Y is expected to change when X changes by 1 unit.

Question 4

What does the intercept (a) of a bivariate regression line tell us?

Answer 4

the predicted value for Y when X = 0.

Question 5

What does the Method of Least Squares guarantee?

Answer 5

the line will come as close as possible to all the data points (the e values will be as small as possible).

Question 6

What is the calculation process for the Method of Least Squares?

Answer 6

1st - calculate the slope (b = ∑cross-products (SCP) / SSx)

2nd - calculate intercept (a = Y̅ - bX̅)

Question 7

Why doesn’t the calculation of the slope in Method of Least Squares use SSy in the denominator?

Answer 7

because it is using scores on X to predict scores on Y

Question 8

∑e = ? (hint: Method of Least Squares)

Answer 8

∑e = 0 (always!)

Question 9

Because of the Method of Least Squares, e^2 is always …

Answer 9

the smallest possible value

Question 10

Standard Error

Answer 10

SE = (e²/ N)^(1/2)

• the amount on average that predicted Y values differ from observed Y scores (similar to V and SD calculation)

Question 11

What are 3 ways to think about variance?

Answer 11

• the average squared deviation of the
subjects’ scores from the mean of their scores.
• a measure (in squared units) of how
much the subjects differ amongst themselves.
• of the variable X, is the expectation of its square minus the square of its expectation.

Question 12

How does sample size (N) effect the estimation of population variance?

Answer 12

A larger N improved accuracy (the difference between 4 and 5 is large compared to the difference between 99 and 100)

Question 13

Is R² effected by sample size?

Answer 13

No.

R² = SS(regression) / SS(total)

Question 14

What is the Mean Square (MS)?

Answer 14

A variance estimate

MS = SS/df

Question 15

How do we interpret R²?

Answer 15

the proportion of variation in Y explained by variation in X.

Question 16

How do we test the Significance of the proportion of Variation explained (R²)?

Answer 16

With an F test

F = [SS(regression)/ df1 ] / [SS(residual)/ df2]

Question 17

How do we test the Significance of a regression coefficient (b)?

Answer 17

with a t Test

t = b / SE(b)

Question 18

Confidence Interval (CI)

Answer 18

CI = b ± [t(critical) × SE(b)]

• an estimated range of values with a given high probability of covering the true population value