Regression

Question 1

What does a correlation allow us to do?

Answer 1

allows us to quantify / measure the strength and direction of a relationship.

Question 2

What does a Pearson’s correlation assume, and what are it’s outputs?

Answer 2

A Pearson’s correlation assumes that a relationship is linear (straight line). It’s reports a t-value, r(cor), and p-value. Only r(cor) and p needed to report

Question 3

How does a Spearman’s test work? What does it assume?

Answer 3

A Spearman’s test assumes monotonicity. In ascending order it ranks on x- and y-axis in and plots them. Prints s-value, s(rho), and pvalue

Question 4

What are the main characteristics of a regression line?

Answer 4

outcome v (Y) = slope X + intercept.

Question 5

What is the slope and what is the intercept.

Answer 5

The slope is what value the regression line begins on the y-axis. The intercept is how much (+ or -) y is predicted to change for every unit increase along the x-axis of the line is affected for every 1 unit along the x-axis. IF x = zero, y = the intercept.

Question 6

Why do we always square^2 our test equations?

Answer 6

So our postivites and neatives don’t cancel out.

Question 7

What other name is the slope know as?

Answer 7

Diversity. An lm function will print the intercept and diversity scores

Question 8

What is a regression line called when it has one outcome variable and two predictor variables?

Answer 8

Regression coefficient

Question 9

Why does variation allocation change when you add new predictors?

Answer 9

R now has the data to express more accurately which variables account for the variation. Additional varaibles claim variation.

This is the same for ANOVA

Question 10

What does an interaction variable indicate?

Answer 10

That the affect of variable 1 is going to depend on variable 2

Question 11

What does a postive and negative interaction do to a reression sheet (3D), and what does it imply for the relationship?

Answer 11

Pos’ interction: bends the sheet up. This means that as V1 increases it is likely to have more of an effect on V2.

Neg’ interaction: bends the sheet down. this means as V1 increases it is likely to have less affect on V2.

Question 12

What does the printed f-statistic tell us in regression?

Answer 12

This represents how well our whole model fits the varation.

Question 13

What does a t-statistic tell us in regression?

Answer 13

How likely it is to get a regression line for that variable if the null was true. Null = no difference between regression line and Y- mean or ‘flat line’

Question 14

What are the two sources of variance used to calculate if a regression model is significant?

Answer 14

Model Sum of Sqaures (SSmod)
Residual Sum of Squares (SSres)

Question 15

What is the (SSmod) calculating?

Answer 15

The difference between regression line predictions and mean Y. Null: predicts no difference between regression line and mean.

df = k

Question 16

What is the (SSres) calculating?

Answer 16

The difference between the data and regression line predictions

Question 17

How are the df’s calculated for (SSmod) and (SSres), and what are these figures analogous to?

Answer 17

(SSmod): df = k, analogous to SSb.
(SSres): df = N - K -1)

Question 18

Taking (SSmod) and (SSres), how would they most likely appear if model was significant.

Answer 18

Similar to ANOVA we would want high (SSmod), indicating that regression like was more different from mean Y, and low (SSres), meaning are regression line more accureatly captured the data.

(SSres) = Less noise

Question 19

What is the effect size in a regression model representing?

R^2

Answer 19

How well does the overall regression model actually account for the outcome varaible

Question 20

How is effect size calculated for regression?

Answer 20

R^2 = 1 - SSres / SStotal
zero = when model does nothing
one = when model is perfect fit

Printed as multiple R-squared.

Question 21

How else can you get R^2?

Answer 21

Pearson’s correlation (r) squared.

R^2 also acheived by, 1 - SSres / SStotal

Question 22

What do you need to do before comparing the effect of differenet varibles?

Answer 22

Convert them into a z-score.

Question 23

What is a standardised cofficients?

Answer 23

Varaibles that have been converted into a z-score. Denoted as beta β

Not to be confused with b(slope)

Question 24

Why are standardised cofficents useful?

Answer 24

Standardising our cofficents to a z-score allows us to compare the affect of each varaible.