BRUNEL UNIVERSITY Master of Science Degree examination Specimen Exam Paper 2005-2006 EC5002: Modelling Financial Decisions and Markets EC5030: Introduction to Quantitative Methods Time allowed: 1.5 hours Answer all of question 1 and at least two other questions

1. COMPULSORY Provide brief answers to all the following: (a) A sample of 20 observations corresponding to the model: Y = + X + u, gave the P P P following data: (X X)2 = 215:4, (Y Y )2 = 86:9, and (X X)(Y Y ) = 106:04. Estimate . (5 marks) (b) Prove that r2 = byx bxy , where byx is the least-squares (LS) slope in the regression of Y on X , bxy is the LS slope in the regression of X on Y , and r is the coe¢ cient of correlation between X and Y . (5 marks) (c) Present four alternative in‡ ation/unemployment regressions. (5 marks) (d) Give one reason for autocorrelated disturbances. (5 marks) (e) Explain how we might use the Breusch-Godfrey statistic to test estimated residuals for serial correlation. (5 marks) (f) The following regression equation is estimated as a production function for Q: lnQ = 1:37 + 0:632 lnK + 0:452 lnL, cov(bk ; bl ) = 0:055;

(0:257) (0:219)

where the standard errors are given in parentheses. Test the hypothesis that capital (K ) and labor (L) elasticities of output are identical. (5 marks) Continued (Turn over)

1

ANSWER TWO QUESTIONS FROM THE FOLLOWING: 2. (a) Economic theory supplies the economic interpretation for the predicted relationships between nominal (in‡ ation) uncertainty, real (output growth) uncertainty, output growth, and in‡ ation. Discuss …ve testable hypotheses regarding bidirectional causality among these four variables. (25 marks) + yt

(b) An investigator estimates a linear relation for German output growth (yt ): yt = 1 + ut , t = 1850; : : : ; 1999. The values of …ve test statistics are shown in Table 1: Discuss the results. Is the above equation correctly speci…ed? (10 marks)

3. (a) i) Show how various examples of typical hypotheses …t into...

...REGRESSIONANALYSIS
Correlation only indicates the degree and direction of relationship between two variables. It does not, necessarily connote a cause-effect relationship. Even when there are grounds to believe the causal relationship exits, correlation does not tell us which variable is the cause and which, the effect. For example, the demand for a commodity and its price will generally be found to be correlated, but the question whether demand depends on price or vice-versa; will not be answered by correlation.
The dictionary meaning of the ‘regression’ is the act of the returning or going back. The term ‘regression’ was first used by Francis Galton in 1877 while studying the relationship between the heights of fathers and sons.
“Regression is the measure of the average relationship between two or more variables in terms of the original units of data.”
The line of regression is the line, which gives the best estimate to the values of one variable for any specific values of other variables.
For two variables on regressionanalysis, there are two regression lines. One line as the regression of x on y and other is for regression of y on x.
These two regression line show the average relationship between the two variables. The regression line of y on x gives the most probable...

...
Unit 5 – RegressionAnalysis
Mikeja R. Cherry
American InterContinental University
Abstract
In this brief, I will demonstrate selected perceptions of the company Nordstrom, Inc., a retailer that specializes in fashion apparel with over 12 million dollars in sales last year. I will research, review, and analyze perceptions of the company, create graphs to show qualitative and quantitative analysis, and provide a summary of my findings.
Introduction
Nordstrom, Inc. is a retailer that specializes in fashion apparel for men, women and kids that was founded in 1901. The company is headquartered in Seattle, Washington with over 61,000 employees world-wide as of February 2, 2013. (Business Wire, 2014)
Nordstrom, Inc. offers on online store, e-commerce, retail stores, mobile commerce and catalogs to its consumers. It operates 117 full-line stores within the United States and 1 store in Canada, 167 Nordstrom Rack stores, 1 clearance store under the Last Chance Banner, 1 philanthropic treasure & bond store called Trunk Club and 2 Jeffrey boutiques. The option of shopping online is also available at www.nordstrom.com along with an online private sale subsidiary Hautelook. They have warehouses, also called fulfillment centers, which manages majority of their shipping needs that are located in Cedar Rapids, Iowa. (Business Source Premier, 2014)
Nordstrom, Inc. continues to make investments in their e-commerce...

...associated with a β1 change in Y.
(iii) The interpretation of the slope coefficient in the model ln(Yi ) = β0 + β1 ln(Xi ) + ui is as
follows:
(a) a 1% change in X is associated with a β1 % change in Y.
(b) a change in X by one unit is associated with a β1 change in Y.
(c) a change in X by one unit is associated with a 100β1 % change in Y.
(d) a 1% change in X is associated with a change in Y of 0.01β1 .
(iv) To decide whether Yi = β0 + β1 X + ui or ln(Yi ) = β0 + β1 X + ui fits the data better, you
cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear
model.
(d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regression functions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...
(vi) The following are properties of the logarithm function with the exception of
(a) ln(1/x) = −ln(x).
(b) ln(a + x) = ln(a) + ln(x).
(c) ln(ax) = ln(a) + ln(x).
(d) ln(xa) = aln(x).
(vii) In the log-log model, the slope coefficient indicates
(a) the effect that a unit change in X has on Y.
(b) the elasticity of Y with respect to X.
(c) ∆Y/∆X.
(d)
∆Y
∆X
×
Y
X
(viii) In the...

...RegressionAnalysis Exercises
1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres.
|Fertilizer Used |Yield of Corn |
|120 |138 |
|80 |112 |
|100 |129 |
|70 |96 |
|88 |119 |
|75 |104 |
|110 |134 |
a. With the amount of fertilizer used as an independent variable and yield of corn as a...

...deviation of the data can influence overall result including confidence level. And he thinks that’s why we should have large enough data if possible to strengthen our conclusion.
2. RegressionAnalysis Jake recently learned a very interesting statistical topic, regressionanalysis. Although he can tell the investment returns on DJIA and AT&T are somewhat dependent, he can’t tell how much one influences the other. Additionally he isn’t sure that there is any significant time trend in DJIA and AT&T. So now he is going to do regressionanalysis by using collected data.
a) Time Trend in AT&T In order to do a hypothesis test with time trend and the investment return on AT&T, firstly he marked the data from March 2008 to September 2012 from 1 to 54. Then he set time trend as the independent variable (denoted x) and the investment return on AT&T as the dependent variable (denoted y), and used Excel program to see the regression result by using “Data Analysis” as below.
Table 2. Regression result with the investment return on AT&T against time trend
Cohort 2- Team 5
Page 7
He can now make an estimated regression line, ̂ = b0 + b1x, here is b0 and b1 are called the least squares point estimates of and and b0 is -2.276, b1 is 0.1043 (Coefficients of Table 2). Therefore the estimated regression line is ̂ = -2.276...

...l
RegressionAnalysis
Basic Concepts & Methodology
1. Introduction
Regressionanalysis is by far the most popular technique in business and economics for
seeking to explain variations in some quantity in terms of variations in other quantities, or to
develop forecasts of the future based on data from the past. For example, suppose we are
interested in the monthly sales of retail outlets across the UK. An initial dataanalysis would
summarise the variability in terms of a mean and standard deviation, but the variation from
outlet to outlet could be very large for a variety of reasons. The size of the local market, the
size of the shop, the level of competition, the level of advertising, etc.. would all influence the
sales volume from outlet to outlet. This is where regressionanalysis can be useful. A
regressionanalysis would seek to model the influence of these factors on the level of sales. In
statistical terms we would be seeking to regress the variation in sales ⎯ the dependent
variable ⎯ upon several explanatory variables such as advertising, size, etc..
From a forecasting point of view we can use regressionanalysis to develop predictions. If we
were asked to make a forecast for the monthly sales of a proposed new outlet in, say, Oxford,
we can simply compute the average outlet sales and put this...

...Assignment # 1
Forecasting (Total marks: 100)
Following 10 Problems are for submission
Problem 1: [12]
Registration numbers for an accounting seminar over the past 10 weeks are shown below:
|Week 1 2 3 4 5 6 7 8 9 10 |
|Registrations 24 23 28 30 38 32 36 40 44 40 |
a) Starting with week 2 and ending with week 11, forecast registrations using the naive forecasting method. [2]
b) Starting with week 3 and ending with week 11, forecast registration using a two-week moving average. [3]
c) Starting with week 5 and ending with week 11, forecast registrations using a four-week moving average. [3]
d) Plot the original data and the three forecasts on the same graph. Which forecast smoothes the data the most? Which forecast responds to change the best? [4]
Problem 2 [4]
Given the following data, use exponential smoothing (( = 0.3) to develop a demand forecast. Assume the forecast for the initial period is 5.
|Period 1 2 3 4 5 6 |
|Demand 7 9 5 9 13 8 |
Problem 3 [6]
Calculate (a) MAD and (b) MSE for the following forecast versus actual sales...

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