Regression Analysis Time Series Analysis Copyright 2001 Alan

Regression Analysis Time Series Analysis © Copyright 2001, Alan Marshall 1

Regression Analysis èA statistical technique for determining the best fit line through a series of data © Copyright 2001, Alan Marshall 2

Error è No line can hit all, or even most of the points - The amount we miss by is called ERROR è Error does not mean mistake! It simply means the inevitable “missing” that will happen when we generalize, or try to describe things with models è When we looked at the mean and variance, we called the errors deviations © Copyright 2001, Alan Marshall 3

What Regression Does è Regression finds the line that minimizes the amount of error, or deviation from the line è The mean is the statistic that has the minimum total of squared deviations è Likewise, the regression line is the unique line that minimizes the total of the squared errors. è The Statistical term is “Sum of Squared Errors” or SSE © Copyright 2001, Alan Marshall 4

Example è Suppose we are examining the sale prices of compact cars sold by rental agencies and that we have the following summary statistics: © Copyright 2001, Alan Marshall 5

Summary Statistics è Our best estimate of the average price would be $5, 411 è Our 95% Confidence Interval would be $5, 411 ± (2)(255) or $5, 411 ± (510) or $4, 901 to $5, 921 © Copyright 2001, Alan Marshall 6

Something Missing? è Clearly, looking at this data in such a simplistic way ignores a key factor: the mileage on the vehicle © Copyright 2001, Alan Marshall 7

Price vs. Mileage © Copyright 2001, Alan Marshall 8

Importance of the Factor è After looking at the scatter graph, you would be inclined to revise you estimate depending on the mileage u 25, 000 km about $5, 700 - $5, 900 u 45, 000 km about $5, 100 - $5, 300 è Similar to getting new test information in decision theory. © Copyright 2001, Alan Marshall 9

Switch to Excel File Car. Price. xls Tab Odometer © Copyright 2001, Alan Marshall 10

The Regression Tool è Tools u Data Analysis ä Choose “Regression” from the dialogue box menu. © Copyright 2001, Alan Marshall 11

More Than You Need © Copyright 2001, Alan Marshall 12

Ignore è The ANOVA table è The Upper 95% and Lower 95% stuff. © Copyright 2001, Alan Marshall 13

© Copyright 2001, Alan Marshall 14

Stripped Down Output © Copyright 2001, Alan Marshall 15

Interpretation è Our estimated relationship is è Price = $6, 533 - 0. 031(km) u Every 1000 km reduces the price by an average of $31 u What does the $6, 533 mean? ä Careful! © Copyright 2001, Alan Marshall It is outside the data range! 16

Quality è The model makes sense: Price is lowered as mileage increases, and by a plausible amount. è The slope: 13. 5 s from 0! u Occurs randomly, or by chance, with a probability that has 23 zeros! è The R-squared: 0. 65: 65% of the variation in price is explained by mileage © Copyright 2001, Alan Marshall 17

Multiple Regression Using More than One Explanatory Variable © Copyright 2001, Alan Marshall 18

Using Excel è No significant changes © Copyright 2001, Alan Marshall 19

To Watch For è Variables significantly related to each other u Correlation Function (Tools Data Analysis) u Look for values above 0. 5 or below -0. 5 è Nonsensical u Wrong è Weak Results Signs Variables u Magnitude of the T-ratio less than 2 u p-value greater than 0. 05 © Copyright 2001, Alan Marshall 20

Dummy Variables è Qualitative variables that allow the relationship to shift is a certain factor is present. è Illustrated in the two upcoming examples © Copyright 2001, Alan Marshall 21

Examples House Prices Theme Park Attendance © Copyright 2001, Alan Marshall 22

Time Series Analysis © Copyright 2001, Alan Marshall 23

Time Series Analysis è Various techniques that allow us to u Understand the variation in a time series u Understand the seasonalities and cycles in a time series u Use this understanding to make predictions © Copyright 2001, Alan Marshall 24

Two Techniques è Deseasonalizing based on a moving average è Using Dummy Variables to Isolate the seasonal effects. © Copyright 2001, Alan Marshall 25

Moving Average è Calculate a moving average è Calculate the ratio of the observation to the moving average è Collect all ratios organized by the point in the seasonal cycle u months, if monthly; quarters, if quarterly è Average, and adjust if necessary, to get seasonal adjustment factors © Copyright 2001, Alan Marshall 26

Example Course Kit Example Page 143 © Copyright 2001, Alan Marshall 27

Regression è Add dummy variables for all but one seasonal period (i. e. , 3 for quarterly, 11 for monthly) © Copyright 2001, Alan Marshall 28

Example Revisit the Course Kit Example Page 143 © Copyright 2001, Alan Marshall 29

Edgar Feidler’s Six Rules of Forecasting With thanks to Peter Walker for bringing this to my attention © Copyright 2001, Alan Marshall 30

Forecasting is very difficult, especially if it is about the future © Copyright 2001, Alan Marshall 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. © Copyright 2001, Alan Marshall 32

The herd instinct among forecasters make sheep look like independent thinkers © Copyright 2001, Alan Marshall 33

When asked to explain a forecast, never underestimate the power of a platitude © Copyright 2001, Alan Marshall 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 © Copyright 2001, Alan Marshall 35

Forecasters learn more and more about less and less until they know nothing about anything © Copyright 2001, Alan Marshall 36