AI:回归预测

本章首先介绍时间序列预测模型的特征,移动平均模型并举例说明。紧接着介绍了计算预测精确度的方法包括均方误差(MSE)、平均绝对误差(MAD)、平均绝对百分比偏差(MAPE),并通过比较这几种方法讲述各自特征,随后举例介绍指数平滑模型,线性回归预测、多元回归分析、逻辑回归等内容。
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1.回归预测 ( Regression and Forecasting )

2.时间序列预测模型 Two important features: Uses historical data for the phenomenon we wish to forecast. We seek a routine calculation to apply to a large number of cases and that may be automated, without relying on qualitative information about the underlying phenomena. Two types of forecasting: Short Time and Long Term Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 2

3.Three Components of Time Series Behavior Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 3

4.The n -period moving average builds a forecast by averaging the observations in the most recent n periods: where x t represents the observation made in period t , and A t denotes the moving average calculated after making the observation in period t . 移动平均模型 Chapter 7 Copyright © 2013 John Wiley & Sons, Inc.

5.Convention We adopt the following convention for the steps in forecasting: Make the observation in period t Carry out the necessary calculations Use the calculations to forecast period ( t + 1) Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 5

6.Worksheet for Calculating Moving Averages Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 6

7.What Number of Periods to Include in Moving Average? There is no definitive answer, but there is a trade-off to consider. Suppose the mean of the underlying process remains stable: If we include very few data points, then the moving average exhibits more variability than if we include a larger number of data points. In that sense, we get more stability from including more points. Suppose there is an unanticipated change in the mean of the underlying process: If we include very few data points, our moving average will tend to track the changed process more closely than if we include a larger number of data points. In that case, we get more responsiveness from including fewer points. Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 7

8.Moving-Average Calculations in a Stylized Example Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 8

9.Comparison of 4-week and 6-week Moving Averages Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 9

10.MEASURES OF FORECAST ACCURACY MSE: the Mean Squared Error between forecast and actual MAD: the Mean Absolute Deviation between forecast and actual MAPE: the Mean Absolute Percent Error between forecast and actual Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 10

11.Comparison of Measures of Forecast Accuracy The MAD calculation and the MAPE calculation are similar: one is absolute, the other is relative. MAPE is usually reserved for comparisons in which the magnitudes of two cases are different. Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 11

12.The Exponential Smoothing Model Exponential smoothing weighs recent observations more than older ones. Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 12 Where α (the smoothing constant) is some number between zero and one. S t is the smoothed value of the observations (our “best guess” as to the value of the mean) Our forecasting procedure sets the forecast F t+1 = S t .

13.Comparison of Weights Placed on k -year-old Data Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 13

14.Worksheet for Exponential Smoothing Calculations Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 14

15.Comparison of Smoothed and Averaged Forecasts Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 15

16.Trend Model Calculations with a Trend in the Data Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 16

17.HOLT’S METHOD This more flexible procedure uses two smoothing constants, as shown in the following formulas: Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 17

18.HOLT’S METHOD This more flexible procedure uses two smoothing constants, as shown in the following formulas: Chapter 7 Copyright © 2013 John Wiley & Sons, Inc. 17

19.Forecasting With Linear Regression

20.Rectangular coordinate Two quantitative variables One variable is called independent (X) and the second is called dependent (Y) Points are not joined No frequency table Linear Regression

21.Example

22.Scatter diagram of weight and systolic blood pressure

23.Scatter diagram of weight and systolic blood pressure

24.Scatter plots The pattern of data is indicative of the type of relationship between your two variables: positive relationship negative relationship no relationship

25.Positive relationship

26.

27.Negative relationship Reliability Age of Car

28.No relation

29.Correlation Coefficient Statistic showing the degree of relation between two variables