Diploma in StatisticsIntroduction to Regression

Lecture 6.1 1

Introduction to RegressionLecture 6.1

• Review Laboratory 2

• More on indicators

• More on logs

• General issues in regression

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 2

Introduction to RegressionLecture 6.1

• Review Laboratory 2

– estimating time series components– do big mammals have big brains?

Minitab

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 3

Introduction to RegressionLecture 6.1

• Review Laboratory 2

• More on indicators

– two-sample t-tests– one way ANOVA– two regressions

• More on logs

• General issues in regression

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 4

More on Indicators;two regressions

1086420

8

7

6

5

4

3

2

1

Temperature

Gas

Scatterplot of Gas vs Temperature

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 5

More on Indicators;two regressions

Homework

Create two subsets of the Gas Consumption data corresponding to Before and After Insulation. Calculate separate regressions. Compare with the results using an indicator.

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 6

Introduction to RegressionLecture 6.1

• Review Laboratory 2

– estimating time series components– do big mammals have big brains?

• More on indicators

– two-sample t-tests– one way ANOVA– two regressions

• More on logs

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 7

More on logs• The log transformation

– Normalises skew distributions

– equalises unequal standard deviations

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 8

More on logs• The log transformation

– converts multiplicative models to additive

XY

XloglogYlog

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 9

Introduction to RegressionLecture 6.1

• Review Laboratory 2

• More on indicators

• More on logs

• General issues in regression

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 10

General Issues in Regression

• Degree of control of the study environment

• Stability of relationships

• Extrapolation

• Predicting explanatory variables

• Large data sets

– many cases

– many variables

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 11

General Issues in Regression

Beware of

• undiagnosed regression equations

• small samples

– representative?

– wide prediction interval

• changing systems

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 12

General Issues in Regression

Exploratory data analysis invariably

• raises unanticipated issues,

• helps clarify issues,

• though not necessarily resolving them

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 13

General Issues in Regression

"The justification sometimes advanced that a multiple regression analysis on observational data can be relied upon if there is

an adequate theoretical background

is utterly specious and

disregards the unlimited capability of the human intellect for producing plausible explanations by the carload lot".

K.A. Brownlee (1965) "Statistical Theory and Methodology", New York, Wiley.

Diploma in StatisticsIntroduction to Regression

Lecture 6.1 14

Reading

SA § 1.6, §§8.7 - 8.8

Hamilton Ch. 3, pp. 84 - 95, Ch. 5, pp. 148 - 158