**Syllabus: M349R**

APPLIED REGRESSION AND TIME SERIES

**Textbook: Bowerman and Koehler,**Forecasting, Time Series, and Regression, **Fourth Edition**

**Responsible parties**: Mark Maxwell and Gustavo Cepparo

**Prerequisite**

Mathematics 339J or 339U, and 358K or 378K, with a grade of at least C- in each.

**Description of the Course****:**The purpose of this course is to provide students in actuarial science, statistics and applied disciplines with an introduction to simple and multiple regression methods for analyzing relationships among several variables, and to elementary time series analysis. The emphasis will be on fitting suitable models to data, evaluating models using numerical and graphical techniques and interpreting the results in the context of the original problem, as opposed to derivation of mathematical properties of the models. At the end of this course students will be able to analyze many kinds of data in which one variable of interest is thought to depend on, or at least be related to, several other measured quantities, and some kinds of data collected over time or in some other serial manner.

**Course Goals and Overview:**

Incoming Students should be very familiar with descriptive statistics, simple regression, the logic of statistical inference, hypothesis tests and confidence intervals for means and proportions. M349R is a computer intensive course starting with an introduction to R and gradually moving towards SAS. The focus of the course is on hands-on data analysis. Students will work on projects with real data, identifying and stating the problems, planning/solving and concluding/reflecting. The textbook will be supplemented with R/SAS code and additional topics.

**Timing **

A typical semester has 42-44 MWF days. The syllabus contains topics for 35 class days and an additional 6 class days with Optional Topics. There are 3 class days for midterms or review.

Calendar (Lecture by lecture) M349R (approximate calendar with 38 days three times a week and 6 days for Optional Topics)

1 |
The Univariate Model (as a base model) and Randomization (Two sample and Matched Pairs Test). |

2 |
One sample t and Checking conditions with Bootstrap distributions. |

3 |
The Bivariate Model vs Univariate Model. Simple Regression. The Least Squares estimator. |

4 |
Root Mean Square Error and Adequate Predictor. |

5 |
Inference on Regression and Residual Plots. |

6 |
Continue with Inference on Regression and Coefficient of Determination. |

7 |
Calculating Standard Errors for Confidence Intervals and Prediction Intervals |

8 |
Total Regression and Partial Regression (Correlation and Partial Correlation). Simpson’s Paradox. |

9 |
Multiple Regression and Interpreting Coefficients. |

10 |
Residual Plots (again) in the context of Multiple Regression |

11 |
Overall F-test and Individual t-tests. Dummy Variables |

12 |
Continue with Dummy Variable notation. One-way Anova from Regression and Traditional Approach. |

13 |
Interaction, Partial F-test. |

14 |
More Practice with Dummy Variables and Variance Covariance Matrix and Ancova. |

15 |
Continue with Ancova. |

16 |
Collinearity. |

17 |
Continue with Collinearity. |

18 |
Residual Analysis (Hat-values, DfFits, DfBetas, Studentized Residuals). |

19 |
Continue with Residual Analysis. |

20 |
Continue with Residual Analysis. |

21 |
Heteroskedasticity. |

22 |
Continue with Heteroskedasticity. |

23 |
Continue with Heteroskedasticity. |

24 |
Autocorrelation in Regression and in Time Series Regression. Dummy variables for Seasonal Models in Time Series Regression with AR(1) errors structure. |

25 |
An example of a Random Walk. The intercept model in TS Regression. |

26 |
Moving Average and Random Walk (Calculate: Expectation, Variance, Covariance and Correlation for MA(1), MA(2) and AR(1)) |

27 |
MA(1) and AR(1) (SAS). |

28 |
Correlograms (ACF and PACF). |

29 |
Estimation MLE and Method of Moments (MoM). |

30 |
Four steps of Arima Modeling (Backshift Notation) |

31 |
Four steps of Arima Modeling (Model Comparison) |

32 |
Intro to Seasonal Models (Box Jenkins Models) |

33 |
Continue with Seasonal (Multiplicative Backshift Notation) |

34 |
Continue with Seasonal |

35 |
Review Seasonal and Nonseasonal |

optional |
Two out of three Optional Topics (below): Intervention Models and Building a Transfer Function Model (if time permits). |

optional |
Intervention Models and Building a Transfer Function Model |

optional |
Intervention Models and Building a Transfer Function Model |

optional |
Linear Probability Model and Logistic Regression Model |

optional |
Linear Probability Model and Logistic Regression Model (if time permits) |

optional |
Delta Method for one and two parameters (Confidence Intervals and Hypothesis Testing) (if time permits) |