Personal Consumption Expenditures, Personal Income, and CPI
1980 – 2011

April 24, 2010

Abstract
The goal of this paper is to estimate the relationship between personal consumption and personal income among all Americans over the past 30 years. The data includes annual records for the four variables between the years 1980 and 2011. I have analyzed this data using the Ordinary Least Squares Method and ran a regression analysis in order to observe the relationship between my variables. In my model, I have used Real Personal Consumption Expenditures (PCE) as my independent variable, while the dependent variable is Real Disposable Personal Income Per-Capita. As well, I included two explanatory variables in my model which are the Consumer Price Index (CPI) and a Coincident Index. The model finds a positive relationship between personal consumption expenditures and personal income. It also shows that inflation is positively related to the independent variable of personal consumption. However the model demonstrates that there is an insignificant relationship between personal consumption and the Coincident Index. We can conclude that personal income has an effect on personal consumption and that there is a positive correlation between these two variables. Therefore, in general, we can assume according to this model that as personal income increases, personal consumption also increases.

1. Introduction
Our economy is an ever-changing system that is affected by an infinite number of factors. Some of these factors include personal consumption, personal income, and inflation. I have chosen to look at how these factors may influence one another within the American economy. More specifically, I have chosen to research the influence of income, inflation, and the Coincidence Index on Americans’ consumption expenditures. I believe that individuals’ consumption expenditures may vary based on two main factors: A change in these individuals’ income and a...

...Introduction to Econometrics coursework
For the assignment I will examine whether or not a linear regression model is suitable for estimating the relationship between Human development index (HDI) and its components. Linear Regression is a statistical technique that correlates the change in a variable to other variable/s, the representation of the relationship is called the linear regression model.
Variables are measurements of occurrences of a recurring event taken at regular intervals or measurements of different instances of similar events that can take on different possible values. A dependent variable is a variable whose value depends on the value of other variables in a model. Hence, an independent variable is a variable whose value is not dependent on other variables in a model.
The dependent variable here is HDI and this will be regressed against the independent variables which include Life expectancy at birth, Mean years of schooling, expected years of schooling and Gross National Income per capita Hence we can model this into Yi = b0 + b1 xi + b2 xi + b3 xi + b4 xi + where Y is HDI, β0 is a constant, β1 β2 β3 β4 are the coefficients and denotes for random/error term.
R2 is how much your response variable (y) is explained by your explanatory variable (x). The value of R2 ranges between 0 and 1, and the value will determine how much of the independent variable impacts on the dependent variable. The R2 value will show how reliable the...

...Course Home - Course Project
| | Print This Page |
Course Project: AJ DAVIS DEPARTMENT STORES
Introduction | Project Part A: Exploratory Data Analysis | Project Part A: Grading Rubric | Project Part B: Hypothesis Testing and Confidence Intervals | Project Part B: Grading Rubric | Project Part C: Regression and Correlation Analysis | Project Part C: Grading Rubric
| |
Introduction | |
AJ DAVIS is a department store chain, which has many credit customers and wants to find out more information about these customers. A sample of 50 credit customers is selected with data collected on the following five variables:
1. LOCATION (Rural, Urban, Suburban)
2. INCOME (in $1,000's – be careful with this)
3. SIZE (Household Size, meaning number of people living in the household)
4. YEARS (the number of years that the customer has lived in the current location)
5. CREDIT BALANCE (the customers current credit card balance on the store's credit card, in $).
The data appears below, and is available in Doc Sharing Course Project Data Set as an EXCEL file:
LOCATION | INCOME($1000) | SIZE | YEARS | CREDIT BALANCE($) |
Urban | 54 | 3 | 12 | 4016 |
Rural | 30 | 2 | 12 | 3159 |
Suburban | 32 | 4 | 17 | 5100 |
Suburban | 50 | 5 | 14 | 4742 |
Rural | 31 | 2 | 4 | 1864 |
Urban | 55 | 2 | 9 | 4070 |
Rural | 37 | 1 | 20...

...ECO
1 chapter
An overview of regression analysis
Econometrics – literally ,,economic measurement” is the quantitative measurement and analysis of actual economic and business phenomena.
Econometrics has three major uses:
1) Describing economic reality
2) Testing hypothesis about economic theory
3) Forecasting future economic activity
The simplest use of econometrics is description.
For most goods, the relationship between consumption and disposable income is expected to be positive, because an increase in disposable income will associated with increase in the consumption of the goods.
Consumer demand for a particular commodity often can be thought of as relationship between the quantity demanded (Q) and the commodity’s price (P), the price of a substitute good (Ps), and disposable income (Yd).
The second and perhaps most common use of econometrics is hypothesis testing – the evaluation of alternative theories with quantitative evidence.
Normal good – one for which the quantity demanded increases when disposable income increases.
The third and most difficult use of econometrics is to forecast or predict what is likely to happen next quarter, next year, or further into the future, based on what has happened in the past.
Nonexperimental quantitative research:
1) Specifying the models or relationships to be studied
2) Collecting the data needed to...

...Case Project
1a)
The histograms of page cost, circulation and median income are all skewed to the right because the majority of the data lies to the left of the mean and the tail on the right side is longer than that on the left side.
b)
There seems to be a strong logarithmic type of relationship between page cost and circulation and a slightly noticeable linear relationship between page cost and median income. As for the scatterplot between page cost and percent male, the points appear to be scattered randomly because percent male does not affect page cost.
2
a) The multiple regression model is statistically useful overall because at least one
independent variable is significant as shown below.
H0: No linear relationship
Ha: At least one X variable affects Y
F = MSR/MSE = 5177553908/184850796 = 28.009
Reject H0 at 5% level of significance since p value = 0 < 0.05 when Fα is based on
3 numerator and 40 denominator degrees of freedom
b) pagecost = - 7640 + 5.17 circ - 10.2 percmale + 1.19 medianincome
c) Page cost is expected to increase by an estimated $5.17 for each projected
thousand increase in readers, decrease by an estimated $10.2 for each percent
increase in male among the predicted readership and increase by an estimated
$1.19 for each dollar increase in median household income.
We would recommend keeping circulation and median household income of...

...UNIVERSITY OF MACAU FACULTY OF BUSINESS ADMINISTRATION BACHELOR'S DEGREE PROGRAMME
ECIF311 ECONOMETRICS II
Second Semester 2010-2011
Instructor Contacts P. S. Tam Office: L430 (Thursday 4:00 p.m. - 7:00 p.m. Or By appointment.) Phone: 8397-4756 Email: pstam@umac.mo Friday 1:00 p.m. - 4:00 p.m. J207 http://webcourse.umac.mo
Class Website
Description:
This course focuses on basic econometric techniques, emphasizing both technical derivations and practical applications. The linear regression model will be reviewed using matrix algebra, and its limitations addressed. Topics on dynamic models, random regressors, simultaneous equations models, and time series econometrics will be covered. If time permits, panel data models and qualitative and limited dependent variable models will also be discussed. Upon completing this course, students are expected to be able to undertake their own econometric analysis.
Prerequisite:
ECIF310 or equivalent. In general, knowledge in basic economic theory, calculus, probability and statistics is required.
Textbook:
Hill, R.C., Griffiths, W.E., and Lim, G.C. Principles of Econometrics, Third Edition. John Wiley & Sons, Inc. 2008. Griffiths, W.E., Hill, R. C., and Lim, G.C. Using EViews for Principles of Econometrics, Third Edition. John Wiley & Sons, Inc. 2008. (They are available from the university bookstore as a bundle with student discount.)...

...
MATH533: Applied Managerial Statistics
PROJECT PART C: Regression and Correlation Analysis
Using MINITAB perform the regression and correlation analysis for the data on SALES (Y) and CALLS (X), by answering the following questions:
1. Generate a scatterplot for SALES vs. CALLS, including the graph of the "best fit" line.
Interpret.
After interpreting the scatter plot, it is evident that the slope of the ‘best fit’ line is positive, which indicates that sales amount varies directly with calls. As call increases, the sales amount increases as well.
2. Determine the equation of the "best fit" line, which describes the relationship between
SALES and CALLS.
The equation of the ‘best fit’ line or the regression equation is SALES(Y) = 9.638 + 0.2018 CALLS(X1)
3. Determine the coefficient of correlation. Interpret:
MINTAB Results:
Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES(Y) and CALLS(X1) = 0.871
P-Value = 0.000
The coefficient of correlation is 0.871. The correlation coefficient is positive so this indicates a positive or direct relationship between the variables. The correlation coefficient is far from the P-Value of 0.000. This means that there is an extremely low chance that Sales and Calls results are wrong and we can be confident in interpretation.
4. Determine the coefficient of determination. Interpret.
MINTAB Results:
S = 2.05708 R-Sq = 75.9% R-Sq(adj) = 75.7%
The index of...

...PROJECT C MATH 533
INSTRUCTOR Prof AMIR SADRAIN
1. Generate a scatterplot for CREDIT BALANCE vs SIZE
Regression Analysis: Credit Balance ($) versus Size
2. Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE.
There is a slight positive relationship between credit balance and size
The regression equation is
Credit Balance ($) = 2591 + 403 Size
3. Determine the coefficient of correlation. Interpret.
The coefficient is 403.for any increase in size, the credit balance will change by beta-hat
4. Determine the coefficient of determination. Interpret.
The coefficient of determinations is R2 which is 56.6% Indicates the percentage of the total sample variation of credit balance value accounted for by the model. R2A 55.7% indicates the percentage of the variation of the credit balance value accounted for by the model adjusted for the sample size and the number of beta parameter in the model
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value. Since the p-value is 0.000 and less than α =.05 we reject the Ho and conclude that there is sufficient evidence to do so.
6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain. We can expect the model to prediction of credit balance to be within 260.162 x2...

...1. Scatterplot for Credit Balance vs Size
Analyzing the scatterplot credit balance vs size, it seems like size (x) will be a good predictor of credit balance (y). The line has a positive slope, and shows that when x increase per 1 unit, y will change by the slope.
2. Equation that describes the relationship between Credit Balance vs Size
Y = β0 + β1
β0 : y – intercept
β1 : slope
Credit Balance($) = 2591.44 + 403.221 Size
3. Coefficient of correlation
R = √R2
R = √ 0.5662 = 0.75246262
When we have a high coefficient of correlation like 0.75, means that there is a strong linear relationship between the credit balance and the size.
4. Coefficient of determination
R2 = 0.5662 = 56.62 %
The coefficient of determination means that there is a 56.62 % of the sample variation in credit balance that can be explained by the model.
5. Test the utility of the regression model
The model is useful because the P-Value is less than α , so it can be use to predict the true mean of credit balance.
P- Value = 0.000000
α = 0.05
6. My opinion about using Size to predict Credit Balance
There is strong evidence supported by the findings in question 1 to 5, that using size to predict credit balance is a good model.
7. 95 % confidence interval for β1
Term Coef SE Coef T P 95% CI
Size 403.22 50.946 7.9147 0.000 ( 300.79, 505.66)
We are 95 % confidence that the...