Demand Estimation by Regression Method – Some Statistical Concepts for application ( All the formulae marked in red for remembering. The rest is for your concept)

In case of demand estimation working with data on sales and prices for a period of say 10 years may lead to the problem of identification. In such a case the different variables that may have changed over time other than price, may have an impact on demand more rather than price. In order to void this problem of identification what we adopt is the techniques of demand estimation through regression process in order to distinguish the effects of different variables on demand. In order to understand the basic working and application of the model, let us start with two variable model

Two-variable Regression model
To find out the relation between two variables X & Y, usually a linear relation is estimated. If it is non-linear one then we convert it into log-linear to estimate the equation. Among the scatter of points in plane X-Y, we try to fit in the best line that can estimate the relationship. Here Y is the dependent variable and X is the independent variable. Let us take the example given in Salvatore. Let demand be the function of advertisement expenditure by the particular firm. Then the scatter diagram will show as the ad. Exp. Increases the sales volume will rise. In order to estimate the relationship of Sales (Y), on ad. Exp. (X), we regress the following equation,

In order to establish this relation we need to estimate a and b with the help of the data set on Y and X. we use a technique called ordinary least squares technique in order to find out the best fitted line. In order to do so, we minimize the sum of squared errors (measure of overall variation of estimated sales from observed sales), assuming that the sum of error is equal to zero. Thus the error is given by,

Thus we need to minimize the above in such a way that the estimated values minimize the above error variance....

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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...

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DemandEstimation
Seydou Diallo
Strayer University
ECO 550: Managerial Economics
Dr. Fereidoon Shahrokh
November 4, 2014
Background
I work for Snack-Eeze. We are the leading brand of low-calorie, frozen microwavable food. We estimate the following demand equation for our product using the data from 26 supermarkets around the country for the month of April.
QD = -2,000 - 100P + 15A + 25PX + 10I
(5,234) (2.29) (525) (1.75) (1.5)
R2 = 0.85 n = 120 F = 35.25
Your supervisor has asked you to compute the elasticities for each independent variable. Assume the following values for the independent variables:
Q = Quantity demanded of 3-pack units
P (in cents) = Price of the product = 200 cents per 3-pack unit
PX (in cents) = Price of leading competitor’s product = 300 cents per 3-pack unit
I (in dollars) = Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = $5,000
A (in dollars) = Monthly advertising expenditures = $640
Compute the elasticities for each independent variable. Note: Write down all of your calculations.
McGuigan, Moyer, and Harris state that elasticity is merely a ratio of the percentage change in quantity to the percentage change in a determinant (2013). Therefore, we will use the following formula.
The formula for finding price...

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DemandEstimation
ECO 550: Managerial Economics and Globalization
/2015
Jason M Brown
1. Compute the elasticity for each independent variable.
When P=500 Px-600 I=$5,500 A=$10,000 and M=5,000, using the regression equation:
QD = -5,200 -4,200(500) +5.2(600) +5.2(5,500) +0.20) (10,000) +0.25(5,000) =17,650
Price Elasticity = (P/Q) (∆Q/∆P)
From the regression equation: ∆Q/∆P=-42
So price elasticity (EP) = (p/Q) (-42) (500/17650) =-1.19
Ec=20(600/17650) =0.68
EA= (P/Q) (0 .20) (10,000/17,650) =0.11
EI= (P/Q) (5.2) (5,500/17,650) = 1.62
EM= (P/Q) (0.25) (5,000/17,650) =0.07
2. Determine the implications for each of the computed elasticity for the business in terms of short term and long-term pricing strategies. Provide a rationale in which you cite your results.
Price Elasticity is -1.19. That is a 1% increase in price of the product will make quantity demanded to drop by 1.19%. Thus, the demand for this product is somewhat elastic. Consequently, increase in income may drive consumers away.
Cross-price elasticity is 0.68 that is if the price of the competitor’s product goes up by 1% then quantity demanded of this product will increase by 0.68%. This product is fairly inelastic to a competitor’s price and there exist no need to be concerned about the competitor since their pricing won’t affect sales.
Income-elasticity is 1.62. This indicates that a 1% rise in the average area income will...

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DemandEstimation
Dhruvang kansara
Eco 550, Assignment 1
Professor: Dr, Guerman Kornilov
January 27, 2014
1. Compute the elasticity for each independent variable. Note: Write down all of your calculations.
According to our Textbooks and given information, When P = 8000, A = 64, PX = 9000, I = 5000, we can use regression equation,
QD = 20000 - 10*8000 + 1500*64 + 5*9000 + 10*5000 = 131,000
Price elasticity = (P/Q)*(dQ/dP)
From regression equation, dQ/dP = -10.
So, price elasticity EP= (P/Q) * (-10) = (-10) * (8000 / 131000) = -0.61
Similarly,
EA = 1500 * 64 / 131000 = 0.73
EPX = 5 * 9000 / 131000 = 0.34
EI = 10* 5000 / 131000 = 0.38
2. Determine the implications for each of the computed elasticities for the business in terms of short-term and long-term pricing strategies. Provide a rationale in which you cite your results.
Price elasticity is -0.61 which means a 1% increase in price of the product causes quantity demanded to drop by 0.61%. So, the demand of the product is relatively inelastic. Therefore, increase in price may not have large impact on the customers.
Advertisement elasticity is 0.73, meaning 1% increase in advertising expenses increases quantity demanded by only 0.73%. So, demand is relatively inelastic to advertising. Therefore, more advertisement won’t necessarily mean that firm can raise the price because it...

...Introduction
This presentation on RegressionAnalysis will relate to a simple regression model. Initially, the regression model and the regression equation will be explored. As well, there will be a brief look into estimated regression equation. This case study that will be used involves a large Chinese Food restaurant chain.
Business Case
In this instance, the restaurant chain's management wants to determine the best locations in which to expand their restaurant business. So far the most successful locations have been near college campuses. This opinion is based on the positive numbers that quarterly sales (y) reflect and the size of the student population (x). Management's mindset is that over all, the restaurants that are within close proximity to college campuses with large student bodies generate more sales than restaurants located near campuses with small student bodies.
In the sample box below, xi is the size of the student population (in thousands) and yi is the quarterly sale (in thousands of dollars). The value for xi and yi for all of the 10 Chinese Food restaurants given in the sample are reflected as follows:
Sample Data:
(measured in 1,000s) (measured in $1,000s)
Restaurant Student Population Quarterly Sales
(i) (xi) (yi)
1 2 58
2 6 105
3 8 88
4 8 118
5 12 117
6 16 137
7 20 157
8 20 169
9 22 149
10 26 202
Methodology
Given 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...

...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 figures:
|Forecast |104 |112 |125 |132 |
|Actual | 95 |108 |128 |136 |
Problem 4 [16]
Sales of industrial vacuum cleaners at Larry Armstrong Supply Co. over the past 13 months are shown below:
|Month |Jan. |Feb. |March |April |May |June |July |
|Sales (in thousands) |11 |14 |16 |10 |15 |17 |11 |
|Month |Aug. |Sept. |Oct. |Nov. |Dec. |Jan. | |
|Sales (in thousands) |14 |17 |12 |14 |16 |11 | |
a) Using a moving average with 3 periods, determine the demand for vacuum cleaners for next February. [2]
b) Using a weighted moving average with 3 periods, determine the demand for vacuum cleaners for February. Use 5, 3, and 2 for the weights of the most recent, second most recent, and third most recent periods, respectively. For...

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