Lecture 13 - Regression Analysis

Question 0

What kinds of mathematical models can be used in regression analysis?

Answer 0

Range from very simple (few parameters) to very complex (many parameters)

Question 1

What is regression analysis?

Answer 1

A technique to fit a mathematical model to data

Question 2

What is the simplest non-trivial model that can be used in regression analysis?

Answer 2

The linear model - y = a + bx

Question 3

What are the regression coefficients in the linear model?

Answer 3

a and b

Question 4

What can regression analysis be used for?

Answer 4

Predicting the value of y for a given value of x - extrapolation/interpolation

Question 6

How do you carry out a regression analysis on SPSS?

Answer 6

Analyse|Regression|Linear… Statistics, tick ‘estimates’ and ‘confidence intervals’.
Need to know which way the dependency goes

Question 7

In a regression analysis on SPSS, what are the different outputs and of those, which are useful?

Answer 7

variables entered
* model summary (r and r^2)
ANOVA
*** coefficients (a and b)
residuals

Question 8

In a regression analysis SPSS output, what does the R Square mean?

Answer 8

It is the percentage of variance explained by the IV. E.g. .496=49.6%

Question 9

Using the coefficients regression analysis output box on SPSS, how would you predict values of y for x?

Answer 9

y = a + bx
In the unstandardised coefficients box the top one is a and the bottom b, and the confidence intervals can also be used to give the likely range.

Question 10

What is the difference between correlations and regression analysis?

Answer 10

Correlations show a relationship and the contribution of noise, but not what the relationship is, whereas regression analysis tells what the relationship is but not whether it is real - a regression analysis will always yield coefficients, even if they’re meaningless.

Question 11

What does a regression analysis with multiple IVs look at?

Answer 11

Each IV’s contribution to the DV and the plane of best fit.

Question 12

What is the regression analysis equation for two IVs?

Answer 12

z = ax + by + c

Question 13

How do you carry out a multiple IV regression analysis in SPSS?

Answer 13

Analyse|Regression|Linear

Question 14

How is the output for a multiple IV regression analysis in SPSS different to the output of a single IV analysis?

Answer 14

There are additional coefficients, still in alphabetical order though!

Question 15

What is the problem with using more than 1/2 IVs in a regression analysis?

Answer 15

As the number of variables increases, it becomes harder to portray the data. 3-D graphs are confusing.

Question 16

What is linear regression analysis good for?

Answer 16

Making simple quantitative models and fitting them to data.