### STATISTICS FOR ECONOMISTS: A BEGINNING

The material on which my introductory quantitative methods in economics class at the University of Toronto was based is presented below. It is designed to be used along with any reasonable statistics textbook. The problems at the ends of the chapters are questions from mid-term and final exams at both the St. George and Mississauga campuses of the University of Toronto. They were set by Gordon Anderson, Lee Bailey, Greg Jump, Victor Yu and others including myself.

The freely available statistics program XLispStat, written by Luke Tierney at the University of Minnesota, can be used both as somewhat of a tutorial for the material here as well as to do basic statistical computations. The first 106 pages of Statistics and Econometric Using XLispStat (stemlisp.ps -- 2500k) PDF version (stemlisp.pdf -- 1128k) are well worth working through in conjunction with the material below if one wants to achieve a solid basic understanding of statistical concepts.

This material should be useful for people who have studied statistics some time ago and need a review of what they are supposed to have learned. Indeed, one could learn statistics from scratch from this material alone, although those trying to do so may find the presentation somewhat compact, requiring slow and careful reading and thought as one goes along.

I would especially like to thank my colleague Gordon Anderson who has answered so many of my questions and clarified so many issues for me in basic statistics that he deserves the status of mentor.

Introduction: Data Sets and Summary Statistics (ecs1.pdf -- 233k)
Sample Test (statest1.pdf -- 25k) Answers (statans1.pdf -- 47k)

Probability (ecs2.pdf -- 160k)
Sample Test (statest2.pdf -- 35k) Answers (statans2.pdf -- 45k)

Common Probability Distributions (ecs3.pdf -- 259k)
Sample Test (statest3.pdf -- 28k) Answers (statans3.pdf -- 75k)

Statistical Sampling: Point and Interval Estimation (ecs4.pdf -- 192)
Sample Test (statest4.pdf -- 34k) Answers (statans4.pdf -- 73k)

Tests of Hypotheses (ecs5.pdf -- 165)
Sample Test (statest5.pdf -- 40k) Answers (statans5.pdf -- 65k)

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses (ecs6.pdf -- 99)
Sample Test (statest6.pdf -- 44k) Answers (statans6.pdf -- 77k)

Inferences About Population Variances and Tests of Goodness of Fit and Independence (ecs7.pdf -- 146)
Sample Test (statest7.pdf -- 31k) Answers (statans7.pdf -- 77k)

Simple Linear Regression (ecs8.pdf -- 170)
Sample Test (statest8.pdf -- 36k) Answers (statans8.pdf -- 80k)

Multiple Regression (ecs9.pdf -- 225)
Sample Test (statest9.pdf -- 54k) Answers (statans9.pdf -- 62k)

Analysis of Variance (ecs10.pdf -- 165)
Sample Test (statest10.pdf -- 32k) Answers (statans10.pdf -- 72k)

Some interactive computer-assisted learning modules, written by John Hattie of the University of Auckland, are worth working through. They work in DOS, so you must use DOSBOX if you are working in Mac OS X or MS-Windows Vista or 7.

• Modules on Summation Notation:

Download the self-extracting zip file sumnot.exe (134k) and put it in a DOS directory. When you enter `sumnot' (with out the apostrophe characters) in that directory the file will disgorge its contents, which will consist of three files---simpsum.exe, doubsum.exe and sumrules.exe. Run these three programs in order by entering the root file names `simpsum', `doubsum' and `sumrules' (without the apostrophe characters).

• Module on The Central Limit Theorem:

Download the executable file clt.exe (77k), put it in a DOS directory and run it by entering `clt'.

• Module on Hypothesis Testing:

Download the executable file hypotest.exe (110k), put it in a DOS directory and run it by entering `hypotest'.