Math 155 Introduction to Statistical Modeling

Fall 2013 Spring 2014

STATISTICS Human intuition is notoriously bad at assessing complex situations. For example, we tend to remember and overemphasize the significance of striking but rare events, which leads to poor decision making. Part of the remedy lies in systematically collecting and analyzing data, the science of statistics. Complexity arises naturally in the interplay of many possibly related phenomena, so we must deal with multiple variables throughout.

A model is a representation that is made for a specific purpose. In this course, we create and analyze linear models that may help to explain variation in data we care about, perhaps to provide a summary of some population characteristics, frequently  about the relation between several traits. Statistical methods will enable us to determine whether there is support for our model in the data.

More precisely, a model is based on a sample of the conceivable data.  Precision is how much the model might change if we had used a different sample. Population variation is why different samples give different models. Since population variation can be gauged from variation within the sample, statistics can give us a reasonable understanding of the precision of a sample based model.

Course components

  • Descriptive statistics
  • Linear models
  • Multiple linear regression
  • Analysis of variance
  • Confidence intervals and hypothesis testing