We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byCarla Kennison
Modified over 2 years ago
© Copyright 2001, Alan Marshall1 Regression Analysis Time Series Analysis
© Copyright 2001, Alan Marshall2 Regression Analysis è A statistical technique for determining the best fit line through a series of data
© Copyright 2001, Alan Marshall3 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 Marshall4 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 Marshall5 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 Marshall6 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 Marshall7 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 Marshall8 Price vs. Mileage
© Copyright 2001, Alan Marshall9 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 Marshall10 Switch to Excel File CarPrice.xls Tab Odometer
© Copyright 2001, Alan Marshall11 The Regression Tool è Tools u Data Analysis ä Choose “Regression” from the dialogue box menu.
© Copyright 2001, Alan Marshall12 More Than You Need
© Copyright 2001, Alan Marshall13 Ignore è The ANOVA table è The Upper 95% and Lower 95% stuff.
© Copyright 2001, Alan Marshall14
© Copyright 2001, Alan Marshall15 Stripped Down Output
© Copyright 2001, Alan Marshall16 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! It is outside the data range!
© Copyright 2001, Alan Marshall17 Quality è The model makes sense: Price is lowered as mileage increases, and by a plausible amount. The slope: 13.5 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 Marshall18 Multiple Regression Using More than One Explanatory Variable
© Copyright 2001, Alan Marshall19 Using Excel è No significant changes
© Copyright 2001, Alan Marshall20 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 Results u Wrong Signs è Weak Variables u Magnitude of the T-ratio less than 2 u p-value greater than 0.05
© Copyright 2001, Alan Marshall21 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 Marshall22 Examples House Prices Theme Park Attendance
© Copyright 2001, Alan Marshall23 Time Series Analysis
© Copyright 2001, Alan Marshall24 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 Marshall25 Two Techniques è Deseasonalizing based on a moving average è Using Dummy Variables to Isolate the seasonal effects.
© Copyright 2001, Alan Marshall26 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 Marshall27 Example Course Kit Example Page 143
© Copyright 2001, Alan Marshall28 Regression è Add dummy variables for all but one seasonal period (i.e., 3 for quarterly, 11 for monthly)
© Copyright 2001, Alan Marshall29 Example Revisit the Course Kit Example Page 143
© Copyright 2001, Alan Marshall30 Edgar Feidler’s Six Rules of Forecasting With thanks to Peter Walker for bringing this to my attention
© Copyright 2001, Alan Marshall31 Forecasting is very difficult, especially if it is about the future
© Copyright 2001, Alan Marshall32 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 Marshall33 The herd instinct among forecasters make sheep look like independent thinkers
© Copyright 2001, Alan Marshall34 When asked to explain a forecast, never underestimate the power of a platitude
© Copyright 2001, Alan Marshall35 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 Marshall36 Forecasters learn more and more about less and less until they know nothing about anything
Chapter 12 Multiple Regression
Chapter 13 Multiple Regression
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 12-1 Chapter 12 Simple Linear Regression Statistics for Managers Using.
Regression Analysis Using Excel. Econometrics Econometrics is simply the statistical analysis of economic phenomena Here, we just summarize some of the.
Introduction to Multiple Regression Lecture 11. The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & 2 or more.
EQT 373 Chapter 3 Simple Linear Regression. EQT 373 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value.
Chapter 12 - Forecasting Forecasting is important in the business decision-making process in which a current choice or decision has future implications:
Applied Quantitative Analysis and Practices LECTURE#23 By Dr. Osman Sadiq Paracha.
OPIM 303-Lecture #8 Jose M. Cruz Assistant Professor.
Lecture 10: Correlation and Regression Model.
Statistics for Managers Using Microsoft® Excel 5th Edition
Topic 10 - Linear Regression Least squares principle - pages 301 – – 309 Hypothesis tests/confidence intervals/prediction intervals for regression.
Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 13-1 Statistics for Managers Using Microsoft® Excel 5th Edition Chapter.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 14-1 Chapter 14 Introduction to Multiple Regression Basic Business Statistics 10 th Edition.
Lecture 4 Introduction to Multiple Regression
Linear Regression Example Data
Correlation and Linear Regression
Correlation and Linear Regression. Evaluating Relations Between Interval Level Variables Up to now you have learned to evaluate differences between the.
Introduction to Linear Regression and Correlation Analysis
© 2017 SlidePlayer.com Inc. All rights reserved.