Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480

Similar documents
Regression step-by-step using Microsoft Excel

Simple Methods and Procedures Used in Forecasting

2. What is the general linear model to be used to model linear trend? (Write out the model) = or

Final Exam Practice Problem Answers

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

Module 6: Introduction to Time Series Forecasting

A Primer on Forecasting Business Performance

Outline: Demand Forecasting

Univariate Regression

Regression Analysis: A Complete Example

SPSS Guide: Regression Analysis

Not Your Dad s Magic Eight Ball

Chapter 13 Introduction to Linear Regression and Correlation Analysis

Simple Linear Regression Inference

Module 5: Multiple Regression Analysis

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

MGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal

Premaster Statistics Tutorial 4 Full solutions

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Part 2: Analysis of Relationship Between Two Variables

2013 MBA Jump Start Program. Statistics Module Part 3

Production Planning. Chapter 4 Forecasting. Overview. Overview. Chapter 04 Forecasting 1. 7 Steps to a Forecast. What is forecasting?

Chapter 3 Quantitative Demand Analysis

1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

Theory at a Glance (For IES, GATE, PSU)

Estimation of σ 2, the variance of ɛ

Chapter 23. Inferences for Regression

Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model

Generalized Linear Models

Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.

Ch.3 Demand Forecasting.

Multiple Linear Regression

KSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management

Forecasting Analytics. Group members: - Arpita - Kapil - Kaushik - Ridhima - Ushhan

2) The three categories of forecasting models are time series, quantitative, and qualitative. 2)

Data Analysis Tools. Tools for Summarizing Data

Using R for Linear Regression

August 2012 EXAMINATIONS Solution Part I

THE UNIVERSITY OF CHICAGO, Booth School of Business Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay. Solutions to Homework Assignment #2

Objectives of Chapters 7,8

Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques Page 1 of 11. EduPristine CMA - Part I

Section 1: Simple Linear Regression

Hypothesis testing - Steps

Nominal and Real U.S. GDP

One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups

Indian School of Business Forecasting Sales for Dairy Products

Stock Valuation: Gordon Growth Model. Week 2

Testing for Lack of Fit

USING THE ETS MAJOR FIELD TEST IN BUSINESS TO COMPARE ONLINE AND CLASSROOM STUDENT LEARNING

Time-Series Forecasting and Index Numbers

2. Simple Linear Regression

Forecasting the first step in planning. Estimating the future demand for products and services and the necessary resources to produce these outputs

1.1. Simple Regression in Excel (Excel 2010).

NIKE Case Study Solutions

Didacticiel - Études de cas

Forecasting in supply chains

Chapter 7: Simple linear regression Learning Objectives

5. Linear Regression

Hedge Effectiveness Testing

Demand Forecasting When a product is produced for a market, the demand occurs in the future. The production planning cannot be accomplished unless

Forecasting DISCUSSION QUESTIONS

Factors affecting online sales

TIME SERIES ANALYSIS & FORECASTING

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9

Multiple Regression Analysis A Case Study

11. Analysis of Case-control Studies Logistic Regression

1 Simple Linear Regression I Least Squares Estimation

Chapter 9: Univariate Time Series Analysis

One-Way Analysis of Variance (ANOVA) Example Problem

Slides Prepared by JOHN S. LOUCKS St. Edward s University

Econometrics I: Econometric Methods

Demand forecasting & Aggregate planning in a Supply chain. Session Speaker Prof.P.S.Satish

Demand Management Where Practice Meets Theory

Business Valuation Review

16 : Demand Forecasting

CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

Interaction between quantitative predictors

Causal Forecasting Models

GLM I An Introduction to Generalized Linear Models

SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.

Sales Forecasting System for Chemicals Supplying Enterprises

hp calculators HP 50g Trend Lines The STAT menu Trend Lines Practice predicting the future using trend lines

Elements of statistics (MATH0487-1)

Exponential Smoothing with Trend. As we move toward medium-range forecasts, trend becomes more important.

This chapter will demonstrate how to perform multiple linear regression with IBM SPSS

TIME SERIES ANALYSIS

Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares

Booth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay. Solutions to Midterm

8. Time Series and Prediction

Testing for Granger causality between stock prices and economic growth

Forecasting Methods. What is forecasting? Why is forecasting important? How can we evaluate a future demand? How do we make mistakes?

Chicago Booth BUSINESS STATISTICS Final Exam Fall 2011

We extended the additive model in two variables to the interaction model by adding a third term to the equation.

MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL. by Michael L. Orlov Chemistry Department, Oregon State University (1996)

Time Series Analysis

CHAPTER 11 FORECASTING AND DEMAND PLANNING

Week 5: Multiple Linear Regression

Transcription:

1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480 a) Compute the three week moving averages and forecast the TSX Index forecast for week 7 b) Compute the three week weighted moving averages using 3, 2 and 1 for most recent, second most recent, and third most recent periods. Find the TSX Index forecast for week 7. c) Compute the exponentially smoothed forecasts for weeks 2 to 7 using α = 0.7. d) Calculate the MAD and MAPE for all three methods. Which provides the best forecast for the TSX Index? 2) The following data represents the quarterly piano sales of Sawyer Piano House for 3 consecutive years. Year Quarter Sales (000$) 1 1 4 2 2 3 1 4 5 2 1 6 2 4 3 4 4 14 3 1 10 2 3 3 5 4 16 a) Compute the seasonal indices and normalized indices using overall average sales. b) Compute the seasonal indices and normalized indices using centred moving average sales. c) If the average quarterly forecast for year 4 is $10,000, use the seasonal indices (unnormalized) to calculate seasonally adjusted quarterly forecasts for year 4. 1

3) James Steven has been hired by the Victory Stores, a convenience store, to study how factors such as floor space area, number of parking spaces, and average family income of families in the city affect daily sales. A random sample of 15 stores is obtained and the data are as follows: Sales ($) Floor Area Parking Spaces Income ($ 000) 1840 532 6 44 1746 478 4 51 1812 530 7 45 1806 508 7 46 1792 514 5 44 1825 556 6 46 1811 541 4 49 1803 513 6 52 1830 532 5 46 1827 537 5 46 1764 499 3 48 1825 510 8 47 1763 490 4 48 1846 516 8 45 1815 482 7 43 SUMMARY OUTPUT Regression Statistics Multiple R 0.91397794 R Square 0.83535568 Adjusted R Square 0.79045268 Standard Error 13.4242577 Observations 15 ANOVA df SS MS F Significance F Regression 3 10057.68236 3352.561 18.60356 0.000128518 Residual 11 1982.317643 180.2107 Total 14 12040 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1480.74461 126.3041592 11.72364 1.48E-07 1202.751032 1758.7382 Floor Area 0.73149888 0.163330495 0.000933 0.37201088 1.0909869 Parking Spaces 9.99148739 2.599960572 3.842938 0.002733 Income ($ 000) -2.3082627 1.594675103-1.44748 0.175655-5.818118954 1.2015935 2

a) From the Excel output above determine the regression equation, adjusted coefficient of determination, correlation coefficient, standard error of the estimate. Interpret the meaning of each. b) Interpret the coefficients of each of the independent variables. c) Forecast a sales level for 500 (floor area), 5 (parking spaces) and 50 (Income, 000s). d) Complete the coefficients table by filling in the missing data for t stat (Floor Area) and Lower and Upper 95% confidence limits (Parking Spaces). e) Conduct an overall hypothesis test to determine if the regression equation is significant (useful) in explaining differences in Sales. Use a 5% significance level. f) Conduct individual hypothesis tests to determine which independent variables are significant or should be dropped in explaining differences in Sales. Use a 5% significance level. 4) Complete the following ANOVA table, assuming the sample size is 20. ANOVA df SS MS F Regression 2 18010.21 Residual (Error) 10057.68 Total 3

Definitions and concepts to know 1. Time Series Forecasting 2. Causal Forecasting 3. Qualitative Forecasting (a) Delphi Method (b) Jury of Executive Opinion (c) Sales Force Composite (d) Consumer Market Survey 4. MAD 5. MAPE 6. Trend 7. Seasonal 8. Cyclical 9. Random 10. Moving Average 11. Weighted Moving Average 12. Exponential Smoothing, Smoothing constant or parameter 13. Stationary, Non-stationary 14. ANOVA Table 15. Simple Regression 16. Multiple Regression 17. Correlation Coefficient 18. Coefficient of Determination 19. Standard Error of the Estimate 4

Answers/Solutions 1) a) b) c) Error Actual Week Actual 3 Week Moving Error Error TSX Index Average Forecast 1 8480 2 8470 3 8475 4 8510 8475 35 35 0.0041 5 8500 8485 15 15 0.0018 6 8480 8495-15 15 0.0018 7 8497 Totals 65 0.0077 MAD = 21.7 MAPE = 0.257% Error Actual Week Actual 3 Week Moving Error Error TSX Index Average Forecast 1 8480 2 8470 3 8475 4 8510 8474 36 36 0.0042 5 8500 8492 8 8 0.0009 6 8480 8499-19 19 0.0022 7 8492 Totals 63 0.0073 MAD = 21.0 MAPE = 0.243% Error Actual Week Actual Exponentially Smoothed Error Error TSX Index Forecast α =.7 1 8480 8480 (assumed) 2 8470 8480-10 10 0.0012 3 8475 8473 2 2 0.0002 4 8510 8474 36 36 0.0042 5 8500 8499 1 1 0.0001 6 8480 8500-20 20 0.0024 7 8486 Totals 69 0.0081 MAD = 13.8 MAPE = 0.162% d) Exponential Smoothing provides the best forecast due lowest MAD (13.8) and MAPE (0.162%). 5

2) a) b) Year Quarter Sales Overall Seasonal Seasonal Seasonal Index Average Sales Ratios Index (Normalized) 1 1 4.0 6.17 0.648 1.080 0.270 2 2.0 6.17 0.324 0.486 0.122 3 1.0 6.17 0.162 0.540 0.135 4 5.0 6.17 0.810 1.891 0.473 2 1 6.0 6.17 0.972 Total 3.997 Total 1.000 2 4.0 6.17 0.648 3 4.0 6.17 0.648 4 14.0 6.17 2.269 3 1 10.0 6.17 1.621 2 3.0 6.17 0.486 3 5.0 6.17 0.810 4 16.0 6.17 2.593 Seasonal Ratios Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 1 0.648 0.324 0.162 0.810 2 0.972 0.648 0.648 2.269 3 1.621 0.486 0.810 2.593 Average 1.080 0.486 0.540 1.891 Seasonal Indices Year Quarter Sales Centred Moving Seasonal Seasonal Seasonal Index Average Sales Ratios Index (Normalized) 1 1 4.0 2 2.0 3 1.0 3.25 0.308 0.421 0.110 4 5.0 3.75 1.333 1.556 0.407 2 1 6.0 4.38 1.371 1.321 0.346 2 4.0 5.88 0.681 0.523 0.137 3 4.0 7.50 0.533 Total 3.821 Total 1.000 4 14.0 7.88 1.778 3 1 10.0 7.88 1.270 2 3.0 8.25 0.364 3 5.0 4 16.0 Seasonal Ratios Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 1 0.308 1.333 2 1.371 0.681 0.533 1.778 3 1.270 0.364 Average 1.321 0.523 0.421 1.556 Seasonal Indices 6

c) For Overall Average Year 4 Q1 = 10800 Q2 = 4860 Q3 = 5400 Q4 = 18910 For Centred Average Year 4 Q1 = 13210 Q2 = 5230 Q3 = 4210 Q4 = 15560 In the case of centred average, better to allocate an annual estimate of 40000 with the normalized indices. Year 4 Q1 = 13840 Q2 = 5480 Q3 = 4400 Q4 = 16280 3) a) From Summary Output Regression equation ŷ = 1480.74 + 0.7315x 1 + 9.9915x 2 2.3083x 3 Coefficient of Determination = R 2 = 0.835 Correlation Coefficient = 0.914 Standard Error of Estimate = ±13.424 Meanings - see Practice Q1 and Causal Forecasting Model notes b) For each additional square foot of floor area, we expect sales to increase by 0.7315$, all else being held constant. For each additional parking place, we expect sales to increase by 9.9915$, all else being held constant. For each additional ( 000)$ average income, we expect sales to decrease by 2.3083$ c) $1781 d) t stat (Floor Area) = 4.479; Lower 95% (Parking Spaces) 4.269, Upper 95% (Parking Spaces) 15.714 e) H 0 : β 1 = β 2 = β 3 = 0 H 1 : Not all β s are 0 F Crit = 3.5874. So we reject H 0 and conclude that the linear relationship exists and at least one of the regression coefficients is not zero. 7

f) For Floor Area: For Parking Spaces: For Income: H 0 : β 1 = 0 H 0 : β 2 = 0 H 0 : β 3 = 0 H 0 : β 1 0 H 0 : β 2 0 H 0 : β 3 0 Critical t value = 2.201 (or -2.201) Floor Area and Parking Spaces, we reject the null hypothesis and keep these two variables in the model. We fail to reject the null hypothesis and discard Income as an independent variable. 4) ANOVA df SS MS F Regression 2 36020.42 18010.21 30.442 Residual (Error) 17 10057.68 591.628 Total 19 46078.10 8

2026 © DocPlayer.net Privacy Policy | Terms of Service | Feedback  | Do Not Sell My Personal Information