The document analyzes the relationship between retail and food service sales (dependent variable) and three economic indicators (independent variables) using regression analysis. It finds that a regression model with personal income, CPI, and interest rate provides the best fit with an F-statistic below 0.05. The coefficients suggest retail sales increase with personal income and interest rate, and increase with CPI.
There is a moderately positive correlation between the Yen/USD exchange rate and Japan's inflation rate based on data from January 2008 to September 2010. Statistical analysis including least squares regression, Pearson's correlation coefficient, and a chi-squared test show the rates are related and dependent on each other. However, limitations include potential time lags between collecting the exchange rate and inflation data each month, as well as external economic factors that could influence the relationship.
This document discusses inflation, appreciation, and depreciation. It provides examples of how to calculate future values when given an original price, inflation/appreciation rate, and number of years. A 3-step process is outlined for calculating future values: 1) identify the variables (original price, rate, years), 2) write the compound interest formula, 3) substitute the values into the formula. The document also describes how a graphics calculator can be used to model appreciation over time by creating a table and graph of the changing value.
Este documento presenta los conceptos básicos de programación en Arduino. Explica la estructura básica de los programas de Arduino, que consiste en las funciones void setup() y void loop(). setup() se ejecuta una vez al inicio para configurar las variables y pins, mientras que loop() contiene el código principal que se ejecuta de forma continua. También describe conceptos como variables, tipos de datos, operadores lógicos y de control de flujo para programar en Arduino.
There is a moderately positive correlation between the Yen/USD exchange rate and Japan's inflation rate based on data from January 2008 to September 2010. Statistical analysis including least squares regression, Pearson's correlation coefficient, and a chi-squared test show the rates are related and dependent on each other. However, limitations include potential time lags between collecting the exchange rate and inflation data each month, as well as external economic factors that could influence the relationship.
This document discusses inflation, appreciation, and depreciation. It provides examples of how to calculate future values when given an original price, inflation/appreciation rate, and number of years. A 3-step process is outlined for calculating future values: 1) identify the variables (original price, rate, years), 2) write the compound interest formula, 3) substitute the values into the formula. The document also describes how a graphics calculator can be used to model appreciation over time by creating a table and graph of the changing value.
Este documento presenta los conceptos básicos de programación en Arduino. Explica la estructura básica de los programas de Arduino, que consiste en las funciones void setup() y void loop(). setup() se ejecuta una vez al inicio para configurar las variables y pins, mientras que loop() contiene el código principal que se ejecuta de forma continua. También describe conceptos como variables, tipos de datos, operadores lógicos y de control de flujo para programar en Arduino.
Ann J. Pilsworth is seeking a records management or document control position. She has over 15 years of experience in records management, document control, and administrative roles. Her skills include expertise in Microsoft Office, Livelink, FOIP regulations, and establishing and maintaining document tracking and filing systems. Her professional history includes roles managing documentation for pipeline integrity projects, maintaining records for Shell Canada, and administrative functions for Premay Equipment Limited. She is currently pursuing a Records Management Certificate.
Este documento presenta la resolución de un ejercicio sobre sistemas eléctricos modelados por ecuaciones diferenciales. Se halla la función de transferencia H(s) del sistema cuando la entrada es un impulso unitario. Luego, se calcula la carga q(t) cuando la entrada es un escalón de 300 voltios, y finalmente la corriente i(t) a partir de q(t). El proceso involucra aplicar transformadas de Laplace y sus propiedades para resolver las ecuaciones diferenciales.
The document analyzes key economic factors of the United States economy, including GDP, exports, imports, investments, government expenditures, and interest rates from 2009 to 2011. It finds that the US has maintained stable GDP growth and moderate unemployment while being the largest economy and manufacturer in the world. The US also has the largest foreign investments and debt levels relative to GDP.
This document provides details on a fieldwork report for a traversing exercise conducted by students. It includes an introduction to traversing, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rod. The objectives and field data from the exercise are presented. Calculations are shown for angular errors and adjustments, determining lengths using stadia measurements, and calculating latitudes, departures and station coordinates. Small errors were found and corrected using compass rule adjustments. The summary provides an acceptable level of accuracy and demonstrates the techniques learned for conducting a traversing survey.
This document contains the fieldwork report for a traversing survey conducted by students using a theodolite. It includes an introduction to traversing surveys, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rods. The objectives of the fieldwork and field data collected are presented. Calculations of angular errors and adjustments, length measurements using stadia methods, and course latitude and departure are shown. A table of station coordinates and graph are included. The report discusses achieving the required accuracy and applying compass rule corrections. It is concluded that the objectives were met by obtaining necessary data to analyze and adjust errors in the closed loop traverse.
This document provides the results of a site surveying fieldwork report on levelling. The objectives were to find elevation differences between points and establish points at given elevations. Apparatus used included an automatic level, levelling rod, tripod, and spirit level. Levelling was conducted between 11 points including a benchmark. Results showed an error of -0.009m. Using the height of collimation and rise/fall methods, reduced levels were calculated and adjusted using error distribution. The maximum allowable error was +/-39.799mm, so the levelling was acceptable. The fieldwork helped obtain necessary data to complete the report.
The document provides an overview of the SMART Tunnel in Kuala Lumpur, Malaysia. Some key points:
1) The SMART Tunnel was constructed to manage stormwater and reduce flooding in Kuala Lumpur following massive floods.
2) It is 9.7km long and runs from Kampung Berembang Lake to Taman Desa Lake, making it the longest stormwater tunnel in Southeast Asia.
3) The tunnel has three sections - a lower channel to receive stormwater and upper/middle decks for motor vehicles. During severe storms, water is diverted into the lower channel and traffic is evacuated from the motorway section.
4) The tunnel was
This document provides information about a fieldwork report for a site surveying course. It includes an introduction to levelling, the objective of the fieldwork, apparatus used including an automatic level, levelling rod, tripod and spirit level. Levelling results were presented using the height of collimation and rise/fall methods. Adjusted results were shown after distributing a small error. The levelling was found to be acceptable as the error of closure was within the allowed maximum. The document concluded the fieldwork was successfully completed to obtain data for the report.
Multiple regression allows examination of the linear relationship between one dependent variable (sales of bar) and two or more independent variables (price of bar and promotion expenditure). The multiple regression equation fits a plane to the data points to predict monthly sales based on price and promotion. The results show that price and promotion are significant predictors of sales, with an increase in price predicted to decrease sales and an increase in promotion predicted to increase sales. The model explains 75.8% of the variation in sales.
This document provides an overview of regression analysis, including:
- Regression analysis is used to study the relationship between variables and predict one variable from another. It can be linear or non-linear.
- Simple regression involves one independent and one dependent variable, while multiple regression involves two or more independent variables.
- The method of least squares is used to determine the regression equation that best fits the data by minimizing the sum of the squared residuals.
The document discusses a company called 3DP that is considering two options - launching a new 3D printer product or selling the patent license. It provides information on the estimated costs of product development and market potential for the product. It also provides details on a potential offer from another company to purchase the patent license. The document asks two questions: 1) Calculate the expected monetary value of the two options and recommend the decision based on financial considerations. 2) Calculate the exchange rate change needed to change the recommended decision and its probability.
1) Simple linear regression models the relationship between a dependent variable (Y) and a single independent variable (X) as a linear equation. It finds the line of best fit to the data and uses this to estimate or predict future values of Y based on X.
2) The document provides an example of using simple linear regression to model the relationship between weekly sales (Y) and advertising expenditures (X) for a retail merchant. It estimates the regression equation and uses this to predict sales for a given expenditure level.
3) Key outputs of the simple linear regression analysis are presented, including estimating the regression coefficients, testing their significance, calculating confidence intervals and analyzing the variance (ANOVA).
Consumer price index number and uses of cpiNadeem Uddin
The document discusses consumer price index (CPI), which is used to measure inflation. It provides examples of calculating CPI using the Laspeyre formula under the aggregate expenditure method and weighted average of price relatives method. CPI is used to measure changes in cost of living and purchasing power over time. It also discusses how CPI can be used to calculate real income by adjusting current income for inflation. Higher CPI indicates higher inflation and lower purchasing power of money.
8
The document provides an overview of marketing engineering and response models. It discusses linear regression models, which assume a linear relationship between dependent and independent variables. Key points include:
1) Linear regression finds coefficients that minimize error between actual and predicted dependent variable values.
2) Diagnostics include R-squared, standard error, and ANOVA tables comparing explained, residual, and total variation.
3) Models can forecast sales and profits given marketing mix changes.
4) Logit models are used when dependent variables are binary or limited ranges, predicting choice probabilities rather than continuous preferences.
The document provides information about statistics and economics tutorials being offered after school, including regression analysis, correlation, and the normal distribution. It gives examples of calculating rank correlation, finding regression equations, and using the standard normal distribution table. It also explains key aspects of the normal distribution like the 68-95-99.7 rule and how to calculate probabilities using the normal distribution function in Excel.
The document provides information about an afterschool program called Centre for Social Entrepreneurship that offers a comprehensive program in social and spiritual entrepreneurship. It is open and free for all. It also provides contact information for Dr. T.K. Jain, the head of the afterschool centre located in Bikaner, India.
This document provides an overview of demand forecasting methods. It discusses qualitative and quantitative forecasting models, including time series analysis techniques like moving averages, exponential smoothing, and adjusting for trends and seasonality. It also covers causal models using linear regression. Key steps in forecasting like selecting a model, measuring accuracy, and choosing software are outlined. The homework assigns practicing examples on least squares, moving averages, and exponential smoothing from a textbook.
This document discusses how a company's total risk exposure depends on the correlations between changes in market variables that affect its gains and losses. It provides an example where the company gains or loses $10 million based on one-standard deviation changes in two market variables. If the variables are highly positively correlated, the company's total exposure is very high, but if they are highly negatively correlated, the exposure is quite low since losses in one variable will likely be offset by gains in the other. This shows it is important for risk managers to estimate both the volatilities and correlations of relevant market variables when assessing risk exposures.
This document discusses various methods for sales forecasting including moving average methods and exponential smoothing. It provides examples of how to calculate 3-month and 4-month moving averages and uses data to forecast the 16th month. Exponential smoothing is explained using an equation and example data. Limitations of moving average methods are outlined. Straight line and linear regression forecasting methods are demonstrated through examples calculating forecasts for years 2016-2017 and for a town's cooler demand based on population.
This document discusses various measures of central tendency including the arithmetic mean, geometric mean, harmonic mean, and median. It provides formulas and examples for calculating each measure. The arithmetic mean is the most commonly used average and is calculated by summing all values and dividing by the total number of items. The geometric mean considers the product of values while the harmonic mean is best for data involving rates or proportions. The median is the middle value when values are arranged in order.
1. The document outlines the process of estimating demand functions using statistical techniques, including identifying variables, collecting data, specifying models, and estimating parameters.
2. Linear and nonlinear models are discussed for relating dependent and independent variables, with the linear model being most common. Estimating techniques include ordinary least squares regression.
3. Regression results can be used to interpret relationships between variables and make predictions, though correlation does not necessarily imply causation. Testing procedures evaluate the model fit and significance of relationships.
Ann J. Pilsworth is seeking a records management or document control position. She has over 15 years of experience in records management, document control, and administrative roles. Her skills include expertise in Microsoft Office, Livelink, FOIP regulations, and establishing and maintaining document tracking and filing systems. Her professional history includes roles managing documentation for pipeline integrity projects, maintaining records for Shell Canada, and administrative functions for Premay Equipment Limited. She is currently pursuing a Records Management Certificate.
Este documento presenta la resolución de un ejercicio sobre sistemas eléctricos modelados por ecuaciones diferenciales. Se halla la función de transferencia H(s) del sistema cuando la entrada es un impulso unitario. Luego, se calcula la carga q(t) cuando la entrada es un escalón de 300 voltios, y finalmente la corriente i(t) a partir de q(t). El proceso involucra aplicar transformadas de Laplace y sus propiedades para resolver las ecuaciones diferenciales.
The document analyzes key economic factors of the United States economy, including GDP, exports, imports, investments, government expenditures, and interest rates from 2009 to 2011. It finds that the US has maintained stable GDP growth and moderate unemployment while being the largest economy and manufacturer in the world. The US also has the largest foreign investments and debt levels relative to GDP.
This document provides details on a fieldwork report for a traversing exercise conducted by students. It includes an introduction to traversing, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rod. The objectives and field data from the exercise are presented. Calculations are shown for angular errors and adjustments, determining lengths using stadia measurements, and calculating latitudes, departures and station coordinates. Small errors were found and corrected using compass rule adjustments. The summary provides an acceptable level of accuracy and demonstrates the techniques learned for conducting a traversing survey.
This document contains the fieldwork report for a traversing survey conducted by students using a theodolite. It includes an introduction to traversing surveys, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rods. The objectives of the fieldwork and field data collected are presented. Calculations of angular errors and adjustments, length measurements using stadia methods, and course latitude and departure are shown. A table of station coordinates and graph are included. The report discusses achieving the required accuracy and applying compass rule corrections. It is concluded that the objectives were met by obtaining necessary data to analyze and adjust errors in the closed loop traverse.
This document provides the results of a site surveying fieldwork report on levelling. The objectives were to find elevation differences between points and establish points at given elevations. Apparatus used included an automatic level, levelling rod, tripod, and spirit level. Levelling was conducted between 11 points including a benchmark. Results showed an error of -0.009m. Using the height of collimation and rise/fall methods, reduced levels were calculated and adjusted using error distribution. The maximum allowable error was +/-39.799mm, so the levelling was acceptable. The fieldwork helped obtain necessary data to complete the report.
The document provides an overview of the SMART Tunnel in Kuala Lumpur, Malaysia. Some key points:
1) The SMART Tunnel was constructed to manage stormwater and reduce flooding in Kuala Lumpur following massive floods.
2) It is 9.7km long and runs from Kampung Berembang Lake to Taman Desa Lake, making it the longest stormwater tunnel in Southeast Asia.
3) The tunnel has three sections - a lower channel to receive stormwater and upper/middle decks for motor vehicles. During severe storms, water is diverted into the lower channel and traffic is evacuated from the motorway section.
4) The tunnel was
This document provides information about a fieldwork report for a site surveying course. It includes an introduction to levelling, the objective of the fieldwork, apparatus used including an automatic level, levelling rod, tripod and spirit level. Levelling results were presented using the height of collimation and rise/fall methods. Adjusted results were shown after distributing a small error. The levelling was found to be acceptable as the error of closure was within the allowed maximum. The document concluded the fieldwork was successfully completed to obtain data for the report.
Multiple regression allows examination of the linear relationship between one dependent variable (sales of bar) and two or more independent variables (price of bar and promotion expenditure). The multiple regression equation fits a plane to the data points to predict monthly sales based on price and promotion. The results show that price and promotion are significant predictors of sales, with an increase in price predicted to decrease sales and an increase in promotion predicted to increase sales. The model explains 75.8% of the variation in sales.
This document provides an overview of regression analysis, including:
- Regression analysis is used to study the relationship between variables and predict one variable from another. It can be linear or non-linear.
- Simple regression involves one independent and one dependent variable, while multiple regression involves two or more independent variables.
- The method of least squares is used to determine the regression equation that best fits the data by minimizing the sum of the squared residuals.
The document discusses a company called 3DP that is considering two options - launching a new 3D printer product or selling the patent license. It provides information on the estimated costs of product development and market potential for the product. It also provides details on a potential offer from another company to purchase the patent license. The document asks two questions: 1) Calculate the expected monetary value of the two options and recommend the decision based on financial considerations. 2) Calculate the exchange rate change needed to change the recommended decision and its probability.
1) Simple linear regression models the relationship between a dependent variable (Y) and a single independent variable (X) as a linear equation. It finds the line of best fit to the data and uses this to estimate or predict future values of Y based on X.
2) The document provides an example of using simple linear regression to model the relationship between weekly sales (Y) and advertising expenditures (X) for a retail merchant. It estimates the regression equation and uses this to predict sales for a given expenditure level.
3) Key outputs of the simple linear regression analysis are presented, including estimating the regression coefficients, testing their significance, calculating confidence intervals and analyzing the variance (ANOVA).
Consumer price index number and uses of cpiNadeem Uddin
The document discusses consumer price index (CPI), which is used to measure inflation. It provides examples of calculating CPI using the Laspeyre formula under the aggregate expenditure method and weighted average of price relatives method. CPI is used to measure changes in cost of living and purchasing power over time. It also discusses how CPI can be used to calculate real income by adjusting current income for inflation. Higher CPI indicates higher inflation and lower purchasing power of money.
8
The document provides an overview of marketing engineering and response models. It discusses linear regression models, which assume a linear relationship between dependent and independent variables. Key points include:
1) Linear regression finds coefficients that minimize error between actual and predicted dependent variable values.
2) Diagnostics include R-squared, standard error, and ANOVA tables comparing explained, residual, and total variation.
3) Models can forecast sales and profits given marketing mix changes.
4) Logit models are used when dependent variables are binary or limited ranges, predicting choice probabilities rather than continuous preferences.
The document provides information about statistics and economics tutorials being offered after school, including regression analysis, correlation, and the normal distribution. It gives examples of calculating rank correlation, finding regression equations, and using the standard normal distribution table. It also explains key aspects of the normal distribution like the 68-95-99.7 rule and how to calculate probabilities using the normal distribution function in Excel.
The document provides information about an afterschool program called Centre for Social Entrepreneurship that offers a comprehensive program in social and spiritual entrepreneurship. It is open and free for all. It also provides contact information for Dr. T.K. Jain, the head of the afterschool centre located in Bikaner, India.
This document provides an overview of demand forecasting methods. It discusses qualitative and quantitative forecasting models, including time series analysis techniques like moving averages, exponential smoothing, and adjusting for trends and seasonality. It also covers causal models using linear regression. Key steps in forecasting like selecting a model, measuring accuracy, and choosing software are outlined. The homework assigns practicing examples on least squares, moving averages, and exponential smoothing from a textbook.
This document discusses how a company's total risk exposure depends on the correlations between changes in market variables that affect its gains and losses. It provides an example where the company gains or loses $10 million based on one-standard deviation changes in two market variables. If the variables are highly positively correlated, the company's total exposure is very high, but if they are highly negatively correlated, the exposure is quite low since losses in one variable will likely be offset by gains in the other. This shows it is important for risk managers to estimate both the volatilities and correlations of relevant market variables when assessing risk exposures.
This document discusses various methods for sales forecasting including moving average methods and exponential smoothing. It provides examples of how to calculate 3-month and 4-month moving averages and uses data to forecast the 16th month. Exponential smoothing is explained using an equation and example data. Limitations of moving average methods are outlined. Straight line and linear regression forecasting methods are demonstrated through examples calculating forecasts for years 2016-2017 and for a town's cooler demand based on population.
This document discusses various measures of central tendency including the arithmetic mean, geometric mean, harmonic mean, and median. It provides formulas and examples for calculating each measure. The arithmetic mean is the most commonly used average and is calculated by summing all values and dividing by the total number of items. The geometric mean considers the product of values while the harmonic mean is best for data involving rates or proportions. The median is the middle value when values are arranged in order.
1. The document outlines the process of estimating demand functions using statistical techniques, including identifying variables, collecting data, specifying models, and estimating parameters.
2. Linear and nonlinear models are discussed for relating dependent and independent variables, with the linear model being most common. Estimating techniques include ordinary least squares regression.
3. Regression results can be used to interpret relationships between variables and make predictions, though correlation does not necessarily imply causation. Testing procedures evaluate the model fit and significance of relationships.
The document discusses uses of the Consumer Price Index (CPI) including calculating purchasing power and real income. Purchasing power decreases as prices rise, shown through examples comparing the CPI to income levels over several years. Real income is calculated by deflating current income by the CPI to account for inflation. Examples show how current income may rise nominally while real income decreases due to higher inflation. The final example demonstrates calculating real GDP and GNP by deflating current values using the CPI.
The presentation aims to explain the meaning of ECONOMETRICS and why this subject is studied as a separate discipline.
The reference is based on the book "BASIC ECONOMETRICS" by Damodar N. Gujarati.
For further explanation, check out the youtube link:
https://youtu.be/S3SUDiVpUGU
1. The document discusses econometrics and the linear regression model. It outlines the methodology of econometric research which includes stating a theory or hypothesis, specifying a mathematical model, specifying an econometric model, obtaining data, estimating parameters, hypothesis testing, forecasting, and using the model for policy purposes.
2. It provides an example of specifying Keynes' consumption function as the mathematical model C= β1 + β2X where C is consumption and X is income. For the econometric model, an error term is added to allow for inexact relationships.
3. Assumptions of the classical linear regression model are discussed including the error term being uncorrelated with X, having a mean of zero,
AIOU Code 802 Introduction To Macroeconomics Semester Spring 2022 Assignment ...Zawarali786
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اگر آپ تعلیمی نیوز، رجسٹریشن، داخلہ، ڈیٹ شیٹ، رزلٹ، اسائنمنٹ،جابز اور باقی تمام اپ ڈیٹس اپنے موبائل پر فری حاصل کرنا چاہتے ہیں ۔تو نیچے دیے گئے واٹس ایپ نمبرکو اپنے موبائل میں سیو کرکے اپنا نام لکھ کر واٹس ایپ کر دیں۔ سٹیٹس روزانہ لازمی چیک کریں۔
نوٹ : اس کے علاوہ تمام یونیورسٹیز کے آن لائن داخلے بھجوانے اور جابز کے لیے آن لائن اپلائی کروانے کے لیے رابطہ کریں۔
Here are some key areas where we could implement the two leadership styles and use training vs coaching:
Transactional leadership:
- Day to day operations
- Setting goals and KPIs
- Performance reviews
- Reward and recognition programs
Transformational leadership:
- Communicating and inspiring vision/mission
- Leading change initiatives
- Developing future leaders
- Strategic planning
Training:
- Onboarding new employees
- Technical/compliance topics
- Hard/tangible skills development
Coaching:
- Leadership development
- Soft skills enhancement
- Career development
- Change management
- High potential employees
- Addressing performance issues
The areas listed would be good
This document outlines a daily, weekly, and monthly reporting structure for a fitness club.
Daily reports include risk elimination checks, conference calls for various departments, follow ups on plans and goals, inspections of club and results, and end of day updates.
Weekly reports focus on plan reviews, target achievements, and SWOT analyses.
Monthly reports include forecast reviews, action plans by department, master plans with reviews and close-out plans, initiatives to increase revenue and reduce costs, and rota plans for campaigns, events, bonuses and incentives.
This 6-week personalized fitness program is designed for Carter Steven, a 32-year-old male weighing 94 kg who wants to lose 15-20 pounds and build muscle in his arms and core. The program includes warm-up and stretching, lower and upper body weight circuits, 10 and 20 minutes of cardio on a cross trainer or exercise bike, and a cool down with stretching. The weight circuits target major muscle groups and aim to generate muscle burn between 12-15 seconds. Heart rate is monitored during cardio sessions with targets ranging from 90-159 bpm.
Razvan Ion Gabriel received a Certificate of Completion from Johnson Health Tech for completing the Kranking Sales Training course on August 19, 2014. The certificate was issued by Jocelyn Vande Velde and includes the identification number 970606054.
The document analyzes stock market indices and their statistical properties. It examines the DAX, NASDAQ, and Straits Times indices for stationarity, mean, standard deviation, skewness, kurtosis, and autocorrelation at different time intervals. The analysis finds that while the raw indices are non-stationary, their returns are stationary. It also calculates descriptive statistics for index returns and residuals at the daily, 5-day, 10-day, and 15-day frequencies. Autocorrelation and normality tests reveal some lag significance and non-normal residual distributions.
The document analyzes the relationship between retail and food service sales (dependent variable) and three economic indicators (independent variables) using regression analysis. It finds that a regression model with personal income, CPI, and interest rate provides the best fit for the data, with each variable having a statistically significant relationship to sales.
1. 1. Download data for at least 4 economic variables that you think are related.
Make sure they have the same frequency (daily, weekly, monthly or yearly data) and the
same number of observations- you need contemporaneous values for all variables. The
sample should include at least 30 observations. Compute means, standard deviations,
skewness and kurtosis for all the variables and built histograms to characterize their
distributions. Describe and graph the data. Show your sources.
Month
Y(Retail and food services
sales) mil. $
X 1
( Total
disponible
personal Income)
bil. $
X 2
(Consumar price
index - CPI)
X 3
(Interest
rate) %
2007-
Jan. 329,736 11,640.70 202.416 8.25
Feb. 324,287 11,713.80 203.499 8.25
Mar. 375,294 11,788.20 205.352 8.25
Apr. 359,619 11,815.80 206.686 8.25
May 392,640 11,843.00 207.949 8.25
Jun. 377,695 11,858.10 208.352 8.25
Jul. 373,405 11,906.90 208.299 8.25
Aug. 388,846 11,931.90 207.917 8.25
Sept. 354,721 12,024.50 208.49 7.75
Oct. 369,434 12,065.10 208.936 7.5
Nov. 378,619 12,132.00 210.177 7.5
Dec. 427,225 12,227.20 210.036 7.25
2008-
Jan. 343,616 12,258.00 211.08 6
Feb. 345,010 12,294.00 211.693 6
Mar. 374,208 12,349.20 213.528 5.25
Apr. 370,352 12,336.50 214.823 5
May 399,773 12,522.10 216.632 5
Jun. 380,389 12,524.10 218.815 5
Jul. 385,985 12,409.70 219.964 5
Aug. 385,211 12,462.60 219.086 5
Sept. 353,128 12,468.90 218.783 5
Oct. 352,847 12,435.00 216.573 4
Nov. 338,774 12,376.10 212.425 4
Dec. 388,025 12,257.70 210.228 3.25
2009-
Jan. 313,864 12,160.20 211.143 3.25
Feb. 303,504 12,072.20 212.193 3.25
Mar. 333,230 12,047.30 212.709 3.25
Apr. 334,767 12,110.50 213.24 3.25
May 353,263 12,310.80 213.856 3.25
Jun. 349,960 12,189.00 215.693 3.25
Jul. 353,617 12,148.30 215.351 3.25
Aug. 359,221 12,173.80 215.834 3.25
1
2. Sept. 330,260 12,169.70 215.969 3.25
Oct. 344,716 12,178.70 216.177 3.25
Nov. 345,700 12,237.40 216.33 3.25
Dec. 408,576 12,300.70 215.949 3.25
2010-
Jan. 321,550 12,324.30 216.687 3.25
Feb. 317,961 12,337.20 216.741 3.25
Mar. 369,339 12,389.40 217.631 3.25
Apr. 366,002 12,478.50 218.009 3.25
May 375,699 12,532.80 218.178 3.25
Jun. 369,031 12,540.00 217.965 3.25
Jul. 372,451 12,559.80 218.011 3.25
Aug. 373,373 12,622.10 218.312 3.25
Sept. 355,549 12,619.30 218.439 3.25
Sources: www.census.gov (retail and food services sales), www.bea.gov (personal
income), www.bls.gov (CPI), www.bankofcanada.ca (interest rate).
• Means:
x =
n
xi∑
y = 360454.9333 – The mean of retail and food services sales in USA beginning with
January 2007 to September 2010 is 360454.9333.
1x = 12225.40222 – The mean of personal income in USA beginning with January 2007
to September 2010 is 12225.40222.
2x = 213.4701333 – The mean of the consumer price index in USA beginning with
January 2007 to September 2010 is 213.4701333.
3x = 4.95 – The mean of the interest rate in USA beginning with January 2007 to
September 2010 is 4.95.
• Standard deviation:
σ = 2
σ =
n
xxi∑ − 2
)(
yσ = 26036.6843 – The degree of dispersion of the retail and food services sales in USA
from the mean value is 250.7240547.
1xσ = 250.7240547 – The degree of dispersion of personal income in USA from the
mean value is 250.7240547.
2xσ = 4.54299426 - The degree of dispersion of consumer price index in USA from the
mean value is 4.54299426.
2
3. 3xσ = 2.027929979 - The degree of dispersion of interest rate in USA from the mean
value is 2.027929979.
• Skewness:
sˆ = 1/n*∑=
−n
i
i xx
1
3
)(
σ
ysˆ = 0.034228706 – The degree of asymmetry of the sales distribution around its mean is
0.034228706. In this case, the skewness is positive and that indicates a distribution with
an asymmetric tail extending towards more positive values.
1
ˆxs = -0.491795728 - The degree of asymmetry of the income distribution around its
mean is -0.491795728. In this case, the skewness is negative and that indicates a
distribution with an asymmetric tail extending towards more negative values.
2
ˆxs = -0.629726058 - The degree of asymmetry of the CPI distribution around its mean is
-0.629726058. In this case, the skewness is negative and that indicates a distribution with
an asymmetric tail extending towards more negative values.
3
ˆxs = 0.705329021 - The degree of asymmetry of the interest rate distribution around its
mean is 0.705329021. In this case, the skewness is positive and that indicates a
distribution with an asymmetric tail extending towards more positive values.
• Kurtosis:
k y = 0.016183697 – Positive kurtosis indicates a relatively peaked distribution of sales.
k 1x = -0.426401663, k 2x = -0.505730192, k 3x = -1.19736224 – Negative kurtosis
indicates a relatively flat distribution of this three economic indicators: personal income,
CPI and interest rate.
3
4. Histogram for Y
0
2
4
6
8
10
12
14
16
303504 324124.1667 344744.3333 365364.5 385984.6667 406604.8333 More
Bin
Frequency
0%
20%
40%
60%
80%
100%
120%
Frequency Cumulative %
Histogram for X1
0
2
4
6
8
10
12
14
11640.7
11804.26667
11967.83333
12131.4
12294.96667
12458.53333
M
ore
Bin
Frequency
0%
20%
40%
60%
80%
100%
120%
Frequency Cumulative %
4
6. 2. Select the dependent variable and build a multiple regression model that makes
economic sense. Run a battery of regressions of the dependent variable on all
combinations of one, two and three other variables. Create the ANOVA table in each
case. What do you observe? Comment on the values you obtained for the coefcients.
Compute the regression statistics in Excel by minimizing the sum of squared residuals
(using Solver), and using Regression in the Data Analysis tool-pack. Verify that you
obtained the same values for the coefficients irrespective of the method used. Create a
summary table of the results and interpret it.
• Combinations of one:
Model 1.1. Dependent variable: y=Sales
Independent variable: x=Personal Income
y=114575.8743(b 0 ) + 20.11214474(b 1 )*x
For a personal income of 0, the sales will be around 115000. But from an economic point
of view the coefficient b 0 has no relevance.
The coefficient b 1 tells us that each additional unit of personal income adds an average
of about 20 to the sales.
Model 1.2. Dependent variable: y=Sales
Independent variable: x= Consumer price index
y=15.38986188 + 0.016202352x
For a CPI=0, the value of sales will be around 15. But from an economic point of view
the coefficient b 0 has no relevance.
The coefficient b 1 tells us that each additional unit of CPI adds an average of about
0.02% to the value of sales.
Model 1.3. Dependent variable: y= Sales
Independent variable: x= Interest rate
y= 342427.657 + 3641.873998x
For an interest rate=0 the value of sales will be around 343000.
6
7. The coefficient b 1 tells us that if the interest rate increases with 1 unit, it adds an
average of about 3642 to the value of sales.
We have compared the value of Significance F for the three models of regression
and we have observed that the Model 1.2 is the best model of one combination because it
is the single one with Significance F <0.05.
• Combinations of two
Model 2.1. Dependent variable: y= sales
Independent variable: x 1 =personal income; x 2 = CPI;
y= 156310.0338+ 64.04961164 x 1 -2711.795584 x 2
For a personal income of 0, the sales will be around 157 000. The value of 64 for b 1
means that if personal income increases by one unit while CPI remains constant, sales
will increase by aprox.64. The value of -2712 for b 2 means that if CPI increases by one
unit while personal income remains constant, sales will decrease by aprox. 2712.
Model 2.2. Dependent variable: y= sales
Independent variable: x 1 =CPI; x 2 = interest rate;
y= -652741.257+ 4479.369565 x 1 + 11512.03473 x 2
For a CPI of 0, the sales will be around -652742. The value of 4480 for b 1 means that if
CPI increases by one unit while interest rate remains constant, sales will increase by
aprox. 4480. The value of 11512 for b 2 means that if interest rate increases by one unit
while CPI remains constant, sales will increase by aprox. 11512.
Model 2.3. Dependent variable: y= sales
Independent variable: x 1 =personal income; x 2 = interest rate;
y= -614274.5472+ 10040.83217x 1 +75.66437034 x 2
For a personal income of 0, the sales will be around -614280. The value of 10041 for b 1
means that if personal income increases by one unit while interest rate remains constant,
sales will increase by aprox. 10041. The value of 75 for b 2 means that if interest rate
increases by one unit while personal income remains constant, sales will increase by
aprox. 75.
7
8. We have compared the value of Significance F for the three models of regression
and we have observed that the Model 2.2 and Model 2.3. are relevant models of two
combinations because they both have Significance F <0.05.
• Combinations of three
Model 3.1. Dependent variable: y= sales
Independent variable: x 1 =personal income; x 2 = CPI; x 3 = interest rate;
y= -722949.6462+ 56.23933624 x 1 + 1594.680709 x 2 + 11199.87269 x 3
The value of 56 for b 1 means that if personal income increases by one unit while CPI
and interest rate remain constant, sales will increase by aprox. 56. The value of 1595 for
b 2 means that if CPI increases by one unit while personal income and interest rate
remain constant, sales will increase by aprox. 1595. The value of 11120 for b 3 means
that if interest rate increases by one unit while personal income and CPI remain constant,
sales will increase by aprox. 11120.
Because Significance F for this model is lower than 0.05 we can say this model is
a relevant one.
0
50.000
100.000
150.000
200.000
250.000
300.000
350.000
400.000
450.000
2007-Jan.
Apr.
Jul.
Oct.
2008-Jan.
Apr.
Jul.
Oct.
2009-Jan.
Apr.
Jul.
Oct.
2010-Jan.
Apr.
Jul.
Oct.
Y(Retail and food services
sales)
All-period Average
8
13. Summary Table (using Solver)
Model
1.1
Model
1.2
Model
1.3
Model
2.1
Model
2.2
Model
2.3
Model
3.1
Constant
term 0,002454 -263970,1 -2345620 0,028035 26,00248 0,033276 0,018979
Coefficient
for
Personal
Income
28,32852 27,84473 28,30651 27,83183
Coefficient
for
CPI
-53687091 27,68454 1563,78 27,12872
Coefficient
for
Interest
rate
324285,6 1594,853 27,6845 31,8367
As we can see comparing the tables above, the values for the coefficients differ
from one method to another. We have obtained some values for the coefficients using
Regression and other values using Solver.
From the Summary tables we can observe that the values of the regression
coefficients associated with a given independent variable are differents for each model.
The values depend on what independent variables are included in the model.
We consider that Model 3.1. is the one we should rely on because it takes into
consideration the largest number of factors (independent variables) that can influence the
sales.
3. For two of the variables previously chosen remake the analysis we did in class:
1. Compute all-period average, 3 month Moving Average and Exponential Somoothing
with alpha = 0.2 and alpha = 0.3. 2. Decide on what method you could use for
forecasting using the precision coefficients. 3. Compute seasonality indexes and the
trend. 4. Use the Winter model to compute forcasts for 5 months into the future for the
two variables. Use the minimization of the sum of squared residuals to find the
exponential smoothing coefficients.
The two variables we have chosen are: Retail and food services sales and
Consumer Price Index.
13
14. 1) The values we have obtained for SALES in October using the three methods are
written in the following table:
All-period average 3 month MA ES with alpha=0.2 ES with alpha=0.3
October 360455 367124 362635.615 364451.6811
The values we have obtained for CPI in October using the three methods are written
in the following table:
All-period average 3 month MA ES with alpha=0.2 ES with alpha=0.3
October 213 218 217.7 218.05
2) SALES
All-period average 3 month MA ES with alpha=0.2 ES with alpha=0.3
MAD 21995.43 20694 21454.1 20509.2
MSE 738611259.2 753598800.7 727653365.6 703430711.2
MAPE 6.18% 5.78% 5.96% 5.71%
OCT. 360455 367124 362635.615 364451.6811
As we can see from the table above, the lowest values of the precision coefficients
are the ones obtained using the exponential smoothing with alpha=0.3 method. This
means that the value forcasted for October is the closest to the actual value (364451.6811
is the best value forcasted for October).
CPI
All-period average 3 month MA ES with alpha=0.2 ES with alpha=0.3
MAD 4.07 1.5 2.42 1.92
MSE 21.82 4.09 8.44 5.71
MAPE 1.89 % 0.7% 1.13% 0.9%
OCT. 213 218 217.7 218.05
As we can see from the table above, the lowest values of the precision coefficients
are the ones obtained using the three month Moving Average method. This means that
the value forcasted for October is the closest to the actual value (218 is the best value
forcasted for October).
3)
14