Section 10 - MATH 11400 Statistics

 MATH 11400 	Statistics 1	2008-09

10. Linear Regression: Confidence Intervals and Hypothesis Tests

Aims | Objectives | Reading | Handouts & Problem Sheets | Questions | Links

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Aims

In the last section we used hypothesis tests to compare samples from distributions that differed in some qualitative factor. In this section we return to the simple linear regression model and use confidence intervals and hypothesis tests to investigate the pattern of variation of the mean value of a response variable Y with the corresponding value of a quantitative predictor variable x.

Objectives

The following objectives, together with those of the previous section, will help you to assess how well you have mastered the relevant material. By the end of this section you should be able to:

State the model assumptions for the simple Normal linear regression model.

Derive the mean, variance and distribution of the estimators of the slope and intercept of the fitted regression line, and calculate the corresponding standard errors.

Construct exact confidence intervals for the values of both the slope and the intercept.

Perform standard hypothesis tests on the values of both the slope and the intercept.

Use the summary() command in R to calculate confidence intervals and perform hypothesis tests on the values of both the slope and the intercept.

Handouts and Problem Sheets

Copies of Handouts, Problem Sheets and Solution Sheets for the unit will be made available each week on the Statistics 1 course pages on Blackboard.

Questions - set this week

PROBLEM SHEET 10 -- Questions 1, 2, 3

Interesting links

A number of links to linear regression applets were already given on the web page for section 4.

In addition to the links given there, the Rice Virtual Lab in Statistics has other regression-related applets; for example an applet that allows you to investigate the underlying concept of regression towards the mean and another that allows you to examine the effects of the reliability of X and Y on a number of the components of the regression analysis.

Note that I have no control over the content or availability of these external web pages. The links may be slow to load, or may sometimes fail altogether - please email me to report if a link goes down. Similarly applets may be slow to load or run, but beware that you may experience problems if you try to exit them before they have finished loading.

Return to the Statistics1 information page

Dr E J Collins,
Department of Mathematics,
University of Bristol, Bristol, BS8 1TW, UK
Email: E.J.Collins@bristol.ac.uk
Telephone: +44 (0) 117 928 7977; Fax: +44 (0) 117 928 7999