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This review covers the fundamental concepts of regression analysis in time series. It introduces the regression function Y = f(X), where Y is dependent on the independent variable X. Key statistical elements, like the error term ε and predicted values Ŷ, are explained. The course emphasizes Excel-based calculations while ensuring students grasp crucial statistics such as R², F-statistic, SSR, SSE, and SST. Understanding the relationship between X and Y is critical, and methods to establish this relationship are discussed. Practical applications in Excel will be explored through in-class examples.
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Time Series From regression to time series
Regression: Y = f(X), where X is some independent variable, and f( ) is linear. The function that relates the actual data points is… Y = β0 + β1X + ε Y …where the “ε” term is the vertical error in the estimate. Ŷ = b0 + b1X …where the “hat” on Y indicates it is a predicted value only! X ε = Y - Ŷ
Summary of statistics from previous example. In this class, Excel-based computer calculations will be used instead of calculator output. However, students should still know what these statistics are.
r2 s F = MSR/SSE = (SSR/k)/SSE SSR SSE SST Probability of no relationship Intercept slope
To establish that there IS a relationship between X and Y, you must REJECT the possibility that there is NO relationship between X and Y. Generally speaking, this means that you want small SSE’s and big SSR’s, and therefore a big F-statistic.
The hard copy of this “self test) will be handed out in class.
