Lecture 5

Question 1

is it possible that your population mean is not within your sample confidence interval?

Answer 1

yes.

in general, you would be highly unlikely to know the true population mean.

Question 2

is the width of the confidence intervals of all samples in a population the same everywhere?

Answer 2

width of interval may not be the same for all samples in a population, because the population standard deviation is always unknown

Question 3

why in multiple regression, the corresponding value for each IV is not the same as the one in simple regression?

Answer 3

because in multiple regression, the correlation among IVs in their relationship to the DV is partialled out (removed)

in multiple regression equation, each IV’s regression coefficient is independent of the other IV

Question 4

what does intercept indicate in a regression model?

Answer 4

it is the predicted value of DV when an individual scores 0 on the IV

0 cancels out the regression coefficient found in each IV

Question 5

what does it mean when you use an unbiased interval estimator

Answer 5

means that the actual coverage rate will be 95% over the long run

Question 6

what does it mean when you use a biased interval estimator

Answer 6

means that the actual coverage rate would be SMALLER or LARGER than the nominal rate over the long run (eg: 89% or 96%)

Question 7

what does it mean when you use a consistent interval estimator

Answer 7

means that the actual coverage will get closer to 95% over the long run as sample size get larger

Question 8

what does nominal level of coverage rate refers to

Answer 8

it refers to the 95% in the description of a confidence interval

Question 9

what does multiple R-squared = 0.47 mean

Answer 9

means that 47% of all variation is explained by IV 1 and IV 2

Question 10

if sample size is 100, what is the df?

Answer 10

97

df= sample size - numerator df (no of IV) - 1

Question 11

4 things we need in order to calculate R2

Answer 11

1. estimated value (of R2)
2. numerator df (no of IVs)
3. denominator df (n - no of IVs -1)
4. desired level of confidence (0.95)

Question 12

what does it mean if your R2 and adjusted R2 are different

Answer 12

means that the R2 estimate is biased

adj r2 is not unbiased but it’s less biased than r2 estimate

Question 13

what affects the possible difference between R2 and adjusted R2?

Answer 13

• the no. of IVs (eg: 2 IVs vs 20 IVs –> many IVs = greater obs r2, adj r2 would be smaller)
• the sample size (smaller sample = obs r2 larger, adj r2 smaller)

many IVs + large sample size = larger difference between obs r2 and adj r2

Question 14

2 ways to make regression coefficient directly comparable

Answer 14

• standardised partial regression coefficient

- use squared semi-partial correlation

Question 15

how does standardised partial regression coefficient work

Answer 15

• all in standard deviation unit

- transform all obs scores to to z scores (all standardised ot have sd of 1)

Question 16

how do you interpret standardised regression coefficient?

Answer 16

same as reporting unstandardised regression coefficient, but need to acknowledge what the scaling of one unit change represent (which is in standard deviation unit )

Question 17

what does it mean when you have standardised regression coefficient of 0.74 in IV1

Answer 17

means that 1 sd increase in IV1 would result in 0.74 sd increase in DV, holding constant IV2

Question 18

what does it mean when you have standardised regression coefficient of -0.13 in IV2

Answer 18

means that for 1 sd increase of IV2, there would be a decrease of 0.13 in DV, holding constant IV1

Question 19

what is semi-partial correlation

Answer 19

semipartial correlation is the correlation of DV and IV1 when the correlation between IV1 and IV2 has been removed

Question 20

why is squared semi-partial correlation useful?

Answer 20

• it indicates direct correspondence to R2

- it also indicates the unique proportion of variation in the DV explained by each IV

Question 21

assumption of linear regression

Answer 21

• independence of observations
• linearity
• constant variance of residuals (homoscedasticity)
• normality

Question 22

what does independence of observations mean?

Answer 22

one person’s scores is independent to the others’

Question 23

what does linearity mean?

Answer 23

scores on dv are additive linear function of scores on the set of iv

Question 24

what does homoscedasticity mean?

Answer 24

variance of residuals is the same for each score on each iv

Question 25

what does normality mean?

Answer 25

well-modeled by a normal distribution

qqplot –> within the ‘window’ ???

Question 26

how to make sure independence of observation is met?

Answer 26

• don’t duplicate scores (to make bigger sample)

- as long as responses on one variable do not determine the responses on the other

Question 27

scatter plot with LOESS line –> how to tell if non linearity is present?

Answer 27

red dotted line straight or not straight?

Question 28

in multiple regression equation, each coefficient for each IV is called ……..

Answer 28

partial regression coefficient

Question 29

how do you get values of intercept and regression coefficients in multiple linear regression equation?

Answer 29

by the method of Ordinary Least Squares (whereas intercept and regression model is estimated in such a way that would minimise the Sum of Squared residuals)

Question 30

What is a residual score in a linear regression model?

Answer 30

That part of the observed scores on the dependent variable not being explained by the regression model.

Question 31

which summary characteristics are of most interest to us in analysing data using a linear regression model with two independent variables

Answer 31

• The overall strength of prediction of the model (indicated by the size of the R-squared statistic)
• the relative strength of prediction of each independent variable (indicated by the standardised regression coefficient

Question 32

Why might prediction be viewed as indicating an asymmetric relationship?

Answer 32

one variable is defined to have a different function and role in the relationship to any other variables

Question 33

what defines an important deviation score that is central to multiple linear regression?

Answer 33

The predicted Y score deviating from the observed Y score.

Question 34

residual scores can be either positive or negative in value, true or false?

Answer 34

true

Question 35

what is R-squared statistic

Answer 35

It is a measure of the strength of prediction in the regression model.

Question 36

what does R-squared value of 0 mean

Answer 36

no prediction

Question 37

What is the difference between an unstandardised partial regression coefficient and a standardised partial regression coefficient?

Answer 37

A standardised partial regression coefficient is estimated in a multiple linear regression model using z scores rather than observed scores.

• NOT simple linear regression

Question 38

If a standardised regression coefficient is ‒0.25, what does it mean?

Answer 38

decrease in IV1 by 1 sd unit leads to increase of 0.25 unit at DV, holding constant IV2

Question 39

Why is using a straight line function different to displaying a two-dimensional scatterplot of real data ?

Answer 39

Real data would (almost certainly) not form a straight line of individual data values.

If real data formed a straight line in a two-dimensional scatterplot, then this implies that the values of X variable are each perfectly predicting the values of the Y variables.