Report: Demand Analysis, Estimation, Forecasting and Decision Making

This report delves into the intricacies of demand analysis, encompassing demand estimation, forecasting, and the decision-making processes. It begins by outlining the factors influencing consumer demand, such as price, income, and the prices of substitutes and complements. The report then details the methodology for analyzing demand, including data collection, regression analysis using Excel, and the interpretation of OLS parameters. Part 2 presents a case study with a provided demand function, regression results, and the testing of statistical significance for OLS parameters. The report then calculates and interprets coefficients of determination and assesses the significance of the regression model using F-statistics. Part 3 provides demand estimation results and a decision-making scenario for maximizing profit based on the analysis. The report concludes by holding prices constant since any price increment results in a greater decline in demand.

Running Head: Demand Analysis
Demand Estimation, Analysis, Forecasting and Decision Making
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Demand Analysis 2
Demand Estimation, Analysis, Forecasting and Decision Making
Part 1
The demand for a good by consumers is influenced by many variables. However, each
variable has its own proportionate contribution to the changes in demand. There is no single
variable that can have a 100% influence on the quantity demanded. Before anything else, it is
important for one to determine the problem that will underlie the analysis. Barnett (2018) noted
that it’s important for one to begin by broadly defining the market to include all the necessary
factors. Failure to do this might result in surprises resulting from product substitution. Thus, in
order to estimate and analyze consumers’ demand, one need first to identify the most important
variables behind the demand variations. Some of these important variable may include; price,
income, price of substitutes and complements, interest rate, etc. (Amir, 2015).
After identifying the factors influencing demand, the next step is to determine the
population size and thus choose a good sample size. The choice of sample is then followed by
the collection of data on the chosen variables (this may include a period of time e.g. years,
months, etc.). The data is usually collected from secondary sources as the analysis is on historical
data that has been recorded earlier. Any data collected may be important for the analysis whether
it is quantitative or qualitative. For quantitative data, we directly carry out the analysis with the
obtained value. On the other hand, for qualitative data, we introduce a dummy variable. A
dummy variable could be included in a variable like adverting to determine whether it has
influence on consumers’ demand.
After the data has been collected, one is now settled to carry out the analysis. The
analysis start by deciding which variables to include in the analysis (those that seems to have a
greater impact e.g. income and price). All the data are entered into the excel program ready for
analysis. This data may also be imported from the excel file and analyzed on other statistical
programs. In this case, let’s consider analysis on the excel program. Data analysis is done by
regressing the consumers’ demand against the chosen variables. Excel gives a summary results
of the regression. These results includes the OLS parameters which help in directly estimating
the demand equation. This demand equation is the basis for the analysis as it is used in
forecasting the future demand given certain levels of the variables. The results are also used in
determining whether the parameters are significant or not and also the significance of the model
in general. Decisions are made based on these forecasts.

Demand Analysis 3
Part 2
(a)
Demand function
Y = β0 + β1X1 + β2X2
β0 = 114.074
β1 = -9.470
β2 = 0.029
Estimated demand function
Y = 114.074 -9.470X1 + 0.029X2
The regression analysis is carried out in excel to give the following results
SUMMARY
OUTPUT
Regression Statistics
Multiple
R 0.98398
R Square 0.968217
Adjusted
R Square 0.964478
Standard
Error 7.204988
Observati
ons 20
ANOVA
df SS MS F
Significan
ce F
Regressio
n 2 26884.3
13442.
15
258.94
18
1.85614E-
13
Residual 17
882.501
5
51.911
85

Demand Analysis 4
Total 19 27766.8
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 114.0738
29.9311
9
3.8112
01
0.0013
96
50.924497
68
177.22
31
50.924
5
177.22
31
X1
Variable -9.47019
1.81958
1
-
5.2046
7.16E-
05
-
13.309171
2
-
5.6312
1
-
13.309
2
-
5.6312
1
X2
Variable 0.028937
0.00642
2
4.5058
61
0.0003
12
0.0153874
56
0.0424
86
0.0153
87
0.0424
86
(b) Testing for statistical significance of OLS parameters
i) Specify hypothesis
H0: β0 = 0 H0: β1 = 0 H0: β2 = 0
HA: β0 ≠ 0 HA: β1 ≠ 0 HA: β2 ≠ 0
Where β0, β1 and β2 are the estimated values
The null hypothesis if confirmed true means that the parameter fails to be significant
The alternative hypothesis if confirmed true means that the parameter attests to be significant
ii) Obtain calculated t-statistics
t-statistics = ¿ βi−β i¿ /¿
Se ( βi ) ¿ where β i¿ is the hypothesized value = 0
Calculated t for β0 = ¿ β 0−β 0¿/¿
Se ( β 0 ) ¿ = ¿ 114. 074− 0/¿
29.931 ¿ = 3.811
Calculated t for β1 = ¿ β 1−β 1¿ /¿
Se ( β 1 ) ¿ = ¿−9.470− 0/¿
1.820 ¿ = -5.205
Calculated t for β2 = ¿ β 2−β 2¿ /¿
Se ( β 2 ) ¿ = ¿ 0.029− 0 /¿
0.006 ¿ = 4.506
iii) Obtaining critical t from table assuming 5% significance level
Critical t = tn-k, (ᵜ/2) where ᵜ is the significance level, n is sample size and k is number of variables.
n = 20, k =3, ᵜ = 0.05

Demand Analysis 5
Critical t = t17, (0.025)
= 2.110
iv) Comparing t with t critical
If t calculated ˃ critical t, reject H0
If t calculated < critical t, do not reject H0
β0 = 3.811 ˃ 2.110, reject H0
β1 = -5.205 < 2.110, do not reject H0
β2 = 4.506 ˃ 2.110, reject H0
In this case, β0 and β2 are significant at 5% significance level, while β1 is not significant at 5%
significance level.
c) Coefficients of determination
Unadjusted coefficient of determination (R2) = 0.968
Adjusted coefficient of determination ( R2) = 0.964
d) Significance of the regression model (F-statistics)
The calculated F from the regression result summary is 258.942
F critical = Fk-1, n-k, ᵜ
= F2, 17, 5%
= 3.590
Decision criteria
If F calculated ˃ F critical, reject H0
If F calculated < F critical, fail to reject H0
In this case 258.942 ˃ 3.590, reject H0 saying that the regression model is not statistically
significant and conclude that at 5% significance level, our model is statistically significant.
Part 3
Demand estimation results
β0 = 114.074
β1 = -9.470
β2 = 0.029
β0 tells us that the average demand is 114.074
β1 tells us that an increase in price by a units results in demand falling by 9.470
β2 tells us that an increase in income by a unit results in demand rising by 0.029

Demand Analysis 6
Given these estimations the expected demand is 114.074 is price and demand does not change.
The decision to be made in order to maximize profit is to hold prices constant since any price
increment is resulting in a greater decline in demand; this is irrespective of the rise in income
since income rise is resulting in a very small increment in demand.

Demand Analysis 7
Bibliography
Amir. (2015). Factors influencing demand. Retrieved from http://www.economicsguide.me/?
page_id=2026.
Barnett, W. (2018). Four Steps to Forecast Total Market Demand. Retrieved from
https://hbr.org/1988/07/four-steps-to-forecast-total-market-demand.
Chand, S. (2015). Managerial Economics: Meaning, Scope, Techniques & other Details.
Retrieved from http://www.yourarticlelibrary.com/managerial-economics/managerial-
economics-meaning-scope-techniques-other-details/24730.
Dummies.com. How to Use the t-Table to Solve Statistics Problems - dummies. Retrieved from
http://www.dummies.com/education/math/statistics/how-to-use-the-t-table-to-solve-
statistics-problems/.