L4 - Intro Regression

Question 1

What is a residual value?

Answer 1

It is the value of the deviation of a data point from a slop line, relative to the y axis.

Question 2

What should the sum of squared residuals be if you have a good slope line?

Answer 2

zero!

Question 3

What is the method of least squares?

Answer 3

It is a method that finds the best location for the straight line function because it estimates values for the slope, and the intercept that minimises the sum of squared residuals.

Question 4

What are the two fundamental equations in the linear regression model?

Answer 4

• Full regression equation

- Regression model equation

Question 5

How do the full regression equation and the regression model equation differ?

Answer 5

‘Model’ equations will always have a predicted Y score on the LHS, and no residual score on RHS (e)

Question 6

of x and y, which is the dv and iv?

Answer 6

X - INDEPENDENT

Y - DEPENDENT

Question 7

What is a and b in the regression equations?

Answer 7

a - intercept

b - slope

Question 8

What is a partial regression coefficient?

Answer 8

The regression slope parameter, noted as b, in multiple linear regression.

(Regression w/ 2 or more IVs)

Question 9

What are the two features we focus on in the linear regression model?

Answer 9

• The strength of the overall prediction model

- The strength of the prediction of each individual IV considered separately within the overall model.

Question 10

Does strong prediction in the overall model imply that each individual IV is a good predictor?

Answer 10

No!

Question 11

What does R Squared measure?

Answer 11

This indicates the strength of prediction in the overall model.

Question 12

What are the 3 sources of variability in scores on the DV?

Answer 12

• Observed scores on the DV (SStotal)
• Predicted scores on the DV (SSReg, variation accounted for by the model)
• Difference between observed and predicted scores (SSRes, variation not accounted for by the model)

Question 13

What is the formula for R squared?

Answer 13

R squared = SS Reg / SS Total

Question 14

What is the formula for SS total?

Answer 14

SSTotal = SS Reg + SS Res

Question 15

What is the formula for SS Reg?

Answer 15

SS Reg = SS total - SS Res

Question 16

What is a good value of R squared?

Answer 16

1 = no residuals! everything has been predicted by the model

The closer R squared is to 1, the stronger the prediction.

Question 17

What is the multiple correlation coefficient?

Answer 17

This is the square root of R square… = R

where 0 ≤ R ≤ 1

R is also a sample statistic for measuring the strength of prediction. It equals the PEARSON CORRELATION between OBSERVED SCORES AND PREDICTED SCORES ON THE DV.

Question 18

What is statistic represents the pearson correlation between observed scores and predicted scores on the DV?

Answer 18

R!

Square root of R squared!

Question 19

What are the 3 ways we can assess the strength of individual IVs in linear regression?

Answer 19

• Unstandardised (partial) regression coefficient
• Standardised (partial) regression coefficient
• the squared semipartial correlation correlation (for multiple regression)

Question 20

what is the regression coefficient?

Answer 20

“b” in the regression equations

the slope

Question 21

What is the unstandardised simple regression coefficient?

Answer 21

This is the EXPECTED CHANGE in observed scores on the DV for A UNIT CHANGE in the observed raw score on the IV.

since it’s not standardised, it’s difficult to know what’s big or small.

Question 22

what does it mean when a regression coefficient is positive?

Answer 22

That an INCREASE in scores on the IV = expected INCREASE in scores on the DV.

or the other way round.

Question 23

What does it mean when a regression coefficient is negative?

Answer 23

That an INCREASE in scores on the IV = expected DECREASE in scores on the DV.

or the other way round.

Question 24

What are standardised regression coefficients?

Answer 24

This is the expected change in Z SCORE UNITS on the DV for a change of ONE STANDARD DEVIATION on the IV.

When standardised,

• The intercept (a) is always zero, so it’s left out of the full regression equation
• the regression coefficient is notated as beta.

Question 25

What is an unstandardised partial regression coefficient?

Answer 25

This coefficient indicates the expected change in scores on the DV for a unit change on the FOCAL IV, when holding constant scores on all over IV’s in the regression model

• -> multiple regression.
• -> only 1 IV changing

Question 26

What is a standardised partial regression coefficient?

Answer 26

It indicates the expected change in standard deviation units on the DV, for one standard deviation increase (or decrease) on the focal IV, when holding constant scores on all over IVS.

Question 27

What is the semipartial correlation?

Answer 27

This is the pearson correlation between scores on the DV and that part of scores on an IV that are NOT ACCOUNTED FOR by the model.

(residual scores)

alternative that is used to assess the strength of prediction of each IV on regression model.

Question 28

What can the regression intercept tell us?

Answer 28

It tells us the expected value on the DV when all scores on the IV are equal to zero!!!

intercept is always zero when standardised!
(if metric is arbitrary, then score of zero is often meaningless, so generally we are not interested in making inferences based on intercept)