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Regression Analysis Time Series Analysis

Regression Analysis Time Series Analysis. Regression Analysis. A statistical technique for determining the best fit line through a series of data. Error. No line can hit all, or even most of the points - The amount we miss by is called ERROR

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Regression Analysis Time Series Analysis

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  1. Regression AnalysisTime Series Analysis

  2. Regression Analysis • A statistical technique for determining the best fit line through a series of data

  3. Error • No line can hit all, or even most of the points - The amount we miss by is called ERROR • Error does not mean mistake! It simply means the inevitable “missing” that will happen when we generalize, or try to describe things with models • When we looked at the mean and variance, we called the errors deviations

  4. What Regression Does • Regression finds the line that minimizes the amount of error, or deviation from the line • The mean is the statistic that has the minimum total of squared deviations • Likewise, the regression line is the unique line that minimizes the total of the squared errors. • The Statistical term is “Sum of Squared Errors” or SSE

  5. Example • Suppose we are examining the sale prices of compact cars sold by rental agencies and that we have the following summary statistics:

  6. Summary Statistics • Our best estimate of the average price would be $5,411 • Our 95% Confidence Interval would be $5,411 ± (2)(255) or $5,411 ± (510) or $4,901 to $5,921

  7. Something Missing? • Clearly, looking at this data in such a simplistic way ignores a key factor: the mileage on the vehicle

  8. Price vs. Mileage

  9. Importance of the Factor • After looking at the scatter graph, you would be inclined to revise you estimate depending on the mileage • 25,000 km about $5,700 - $5,900 • 45,000 km about $5,100 - $5,300 • Similar to getting new test information in decision theory.

  10. Switch to Excel File CarPrice.xls Tab Odometer

  11. The Regression Tool • Tools • Data Analysis • Choose “Regression” from the dialogue box menu.

  12. More Than You Need

  13. Ignore • The ANOVA table • The Upper 95% and Lower 95% stuff.

  14. Stripped Down Output

  15. Interpretation • Our estimated relationship is • Price = $6,533 - 0.031(km) • Every 1000 km reduces the price by an average of $31 • What does the $6,533 mean? • Careful! It is outside the data range!

  16. Quality • The model makes sense: Price is lowered as mileage increases, and by a plausible amount. • The slope: 13.5s from 0! • Occurs randomly, or by chance, with a probability that has 23 zeros! • The R-squared: 0.65: 65% of the variation in price is explained by mileage

  17. Multiple Regression Using More than One Explanatory Variable

  18. Using Excel • No significant changes

  19. To Watch For • Variables significantly related to each other • Correlation Function (Tools Data Analysis) • Look for values above 0.5 or below -0.5 • Nonsensical Results • Wrong Signs • Weak Variables • Magnitude of the T-ratio less than 2 • p-value greater than 0.05

  20. Dummy Variables • Qualitative variables that allow the relationship to shift is a certain factor is present. • Illustrated in the two upcoming examples

  21. Examples House Prices Theme Park Attendance

  22. Time Series Analysis

  23. Time Series Analysis • Various techniques that allow us to • Understand the variation in a time series • Understand the seasonalities and cycles in a time series • Use this understanding to make predictions

  24. Two Techniques • Deseasonalizing based on a moving average • Using Dummy Variables to Isolate the seasonal effects.

  25. Moving Average • Calculate a moving average • Calculate the ratio of the observation to the moving average • Collect all ratios organized by the point in the seasonal cycle • months, if monthly; quarters, if quarterly • Average, and adjust if necessary, to get seasonal adjustment factors

  26. Example Course Kit Example Page 143

  27. Regression • Add dummy variables for all but one seasonal period (i.e., 3 for quarterly, 11 for monthly)

  28. Example Revisit the Course Kit Example Page 143

  29. Edgar Feidler’s Six Rules of Forecasting With thanks to Peter Walker for bringing this to my attention

  30. Forecasting is very difficult, especially if it is about the future

  31. The minute you make a forecast, you know you’re going to be wrong, you just don’t know when or in what direction.

  32. The herd instinct among forecasters make sheep look like independent thinkers

  33. When asked to explain a forecast, never underestimate the power of a platitude

  34. When you know absolutely nothing about a subject, you can still do a forecast by asking 300 people who don’t know anything either.That’s called a survey

  35. Forecasters learn more and more about less and less until they know nothing about anything

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