Stats Year 2 - Man

Question 1

SSR

Answer 1

The sum of the square if the distance away from any point to y bar

Question 2

SSR + SSE

Answer 2

The total variance on the y axis

Question 3

Regression line will always pass through (…) so if you know that and the gradient, you know the line

Answer 3

x bar, y bar

Question 4

SSE

Answer 4

Sum of squares of errors
sum ((actual y - predicted y)squared)

Question 5

Linear regression measures

Answer 5

Causal relationship between two variables

Question 6

Regression analysis fits … line to a … plot

Answer 6

straight, scatter

Question 7

Mulitple linear regression is superior to classical linear progression because:

Answer 7

1. It allows us to perform all the calculations in one go
2. It determines the contribution of each independednt variable
3. The result is a model that can predict the DV using two or more IVs
4. The model is usually good or adequate without all IVs

Question 8

Limitation of multiple linear regression

Answer 8

Process is iterative, so each step depends on the previous

Question 9

How to run multiple linear regression?

Answer 9

1. Make an initial model and run with lm
2. Remove the variable with the highest p value
3. Repeat until all variables have a p value less than 0.05

Question 10

ANOVA test of successive models in MLR

Answer 10

Tells us whether there is a significant difference in the performance of each model.
Value within range is good
Value outside of range means that they are significantly different

Question 11

AIC

Answer 11

An assessment of how well the model is doing given the number of DVs.
Want to minimise the AIC
Model will stop running when removing a variable will increase the AIC

Question 12

AIC equation

Answer 12

AIC = 2k - 2 ln(L)

where k is the number of parameters in the model and L is the maximum likelihood of …

Question 13

Using AIC to compare models

Answer 13

AIC < 2 means models are similarly good
AIC 4-7 means one model is probably better
AIC > 10 means there is stron g evidence that the lower model is better.

Question 14

Principle Component Analysis

Answer 14

A tool for exploring the structure of multivariate data.

Question 15

PCA as a Data Reduction Technique

Answer 15

Allows us to reduce the number of variables to a manageable number of new variables or components without sacrifising too much information

Question 16

What do the new variables represent in PCA

Answer 16

The variance in the data set
If the data represents measurements from model cars that are all exactly to scale but have different sizes, then the only variable would be size.
additional differences cause additional variables

Question 17

Limitations of PCA

Answer 17

Not a test, hence no hypotheses
Categorical variables cannot be used.
Missing values cannot be accomodated

Question 18

Assumption of PCA

Answer 18

Assumes variables are continuous or on an interval scale

Question 19

Two types oof PCA

Answer 19

Covariance or correlation matrix

Question 20

Covariance matrix

Answer 20

Applies more weight to some variables than others depending on their variance.
Use when scales are similar.

Question 21

Correlation matrix

Answer 21

Effectively expresses each variable (column of matrix) in standard deviation units, giving each variable equal weight

Question 22

Standardised measurement for PCA

Answer 22

Standardised measurement = (measurement - mean of that type of measurement)/SD of that type of measurement

This is the same as the Z score

Question 23

The first PC expresses the … portion of the variance, the second the next … and so on

Answer 23

Biggest

Question 24

What to look for in a scree plot?

Answer 24

An obvious elbow which tells us which PC are the most important

Question 25

Best way to visualise what’s happening on the first two PCs is by …

Answer 25

Using a biplot.
Variables plotted closely together are closely correlated.

Question 26

Arrows in a biplot indicate…

Answer 26

…the contribution of each variable to each component

Question 27

Hierarchical, Agglomerative Cluster Analysis

Answer 27

A technique for exploring the structure of complex multivariaet data.
Aims to find groups of objects with the data and represent it graphically.

Question 28

Three principle stages in classical clustering

Answer 28

1. Transforming or scaling the data
2. Producing a triangular distance matrix between all possible pairs of objects
3. Making clusters.

Question 29

Transformation in clustering

Answer 29

PCA of correlations effectively rescales the variables to unit variance so no single variance overpowers the model.
Usual procedure is to convert each variable to a set of Z scores.

Question 30

Distance matrix

Answer 30

Gives the distance between each object and any other

Question 31

Making clusters

Answer 31

Methods for this diverge based on how differences between groups are defined.

Question 32

Strengths of clustering

Answer 32

Variables can be of any type provided the distance metric is appropriate.
Many procedures allow for missing values

Question 33

Cophenetic Correlation

Answer 33

Simplest measure of how well a particular dendrogram fits the distance matrix
Correlation between distance matrix and matrix of distances between clusters as shown in dendrogram

Question 34

Limitations of clustering

Answer 34

Depends on how clusters are defined
Depends on how distances between clusters are defined.

Question 35

Height on dendrogram

Answer 35

Indicates the degree of similarity between two variables.
Lower height of horizontal connector = more similar

Question 36

Cophenetic function

Answer 36

Creates a triangular distance matrix from the dendrogram.
Values will be repeated because distances between variables are not shown over distances between clusters