Forecasting Of Sales

Forecasting of Sales

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Abstract:

Forecasting of sales is important given that production and employment will highly depend on expected sales in future. The paper discusses retail sales levels in 31 countries for the year 2007 and 2008 and also shows the relationship between sales and price index. Results shows that at the 95% level of test the mean sales value for 2007 and 2008 are equal and that as the price index increase the sales level increase.

Introduction:

Consumer expenditure on goods and services is determined by the level of retail sales level, this paper discusses total retail sales level in 31 economies, and data was retrieved from the

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OCED website and contains retail sales level for the year 2007 and 2008. The following is a discussion of the mean values, standard deviation and a hypothesis test to determine whether the sales level in 2008 was greater than sales levels in 2007 at the 0.05% level of test, also discussed is a regression analysis that shows the relationship between the retail sales levels and the consumer price index.

Year 2007 sales level:

Total retail sales for the 31 countries amounted to 3423.7, the mean sales in 2007 amounted to 110.4419 and the standard deviation was 8.59941. Grouping the data in six classes depict that majority of countries sales ranged from 101.5 to 110.5, the following table summarizes the frequencies across the selected ranges.

2007

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frequency

cumulative frequency

% frequency

90.5-100.5

2

2

6.45%

101.5-110.5

17

19

54.84%

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111.5-120.5

9

28

29.03%

121.5-130.5

1

29

3.23%

131.5-140.5

2

31

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6.45%

141.5-150.5

0

31

0.00%

The following chart summarizes the percentage frequencies:

From the above chart it is evident that 56% of the countries had sales in the range 101.5 to 110.5 and only 3% of the countries had sales in the range 121.5-130.5

Year 2008 sales:

The mean sale in 2008 was 111.8193548 and the standard deviation was 12.60535387. Grouping the data in six classes depict that majority of countries sales were in range 101.5 to 110.5, the following table summarizes the frequencies across the selected ranges.

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2008

frequency

cumulative frequency

% frequency

90.5-100.5

5

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5

16.13%

101.5-110.5

13

18

41.94%

111.5-120.5

7

25

22.58%

121.5-130.5

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4

29

12.90%

131.5-140.5

1

30

3.23%

141.5-150.5

1

31

3.23%

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The following chart summarizes the percentage frequencies:

From the above chart it is evident that 42% of the countries had sales in the range 101.5 to

110.5, this means that majority of the countries in both years had sales in the range 101.5 to

110.5

Year 2007 and 2008 sales level:

The following chart summarizes the frequency of the countries with reference to the selected ranges:

The above chart shows that the there was a decline in frequency in 2008 for the range 101.5 to 110.5 and 111.5 to 120.5, however there was an increase in frequency for the range 90.5 to 100.5 and 121.5 to 130.5.

Hypothesis test:

The research question in this paper is whether the mean sales level in 2008 is greater than the mean sales level in 2007; the following are the hypothesis testing steps:

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Step 1:

Stating the hypothesis:

Mean sales in 2008 is greater than mean sales in 2007

Null hypothesis:                      H0: M2008 = M2007

Alternative hypothesis:      Ha: M2008 > M2007

Step 2:

Assumption:

The assumptions in this hypothesis test is that sales data is randomly selected and therefore represents the entire population, also that sales data has a normal distribution and therefore a T test is appropriate, the hypothesis will be tested at the 0.05 level.

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Step 3:

Test statistics:

The hypothesis will be tested using both the Z and T test, for the Z test all the 31 countries will be included and for the T test 29 countries will be included in the test.

The following table shows the results of the T test using Stata:

. ttest sales2007 ==  sales2008, unpaired unequal

Two-sample t test with

unequal variances

Variable    Obs       Mean  Std. Err. Std. Dev.

[95% Conf. Interval

sal~2007 29 109.3828

1.415564 7.623043

106.4831 112.282

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sal~2008 29 110.2241  1.968218 10.59918

106.1924 114.255

diff = mean(sales2007) –  mean(sales2008)

t = -0.347

> 0

Pr(T < t) = 0.3650 Pr(T  > t) = 0.7300

Pr(T > t) = 0.635

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The T calculated value is -0.347, the T critical value is 2.42, given that the critical value is greater then the calculated value we accept the null hypothesis, by rejecting the null hypothesis this means that the sales value for 2007 and 2008 at the 95% level of test are equal.

Z test:

The Z test will involve including n = 30, the following is the calculation of the Z critical and calculated values:

Z calculated = (M2008 – M2007)/ (σ/√n)

Z calculated = 0.048265515

Z critical value at 0.05 = 0.019

Z critical > Z calculated

Given that the critical value is greater then the calculated value we accept the null hypothesis.

Step 4:

Evaluation:

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For the T test the T calculated value is -0.347, the T critical value is 2.42, given that the critical value is greater then the calculated value we accept the null hypothesis, for the Z test Z critical > Z calculated and therefore we accept the null hypothesis.

Step 5:

Interpretation:

Given that we accept the null hypothesis in both cases we reject the alternative hypothesis, this means that at the 95% level of test the 2007 mean sales value is equal to the 2008 mean sales value.

Regression:

Regression analysis involves depicting the relationship between two or more variables; the model estimated will depict the relationship between sales and the consumer price index, the price index data was retrieved from the OCED website.

State output shows that the correlation coefficient for the sales and price index is 0.4636; this shows that there is a positive relationship whereby as one variable increase the other variable is also increasing, also there is a relatively weak relationship between the variables. The following table summarizes the results:

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pi

sal~2008

pi

1.0000

sales2008

0.4636

1.0000

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Regression:

The regression model to be estimated has a constant, the sales level is the dependent variable and price index is the independent variable, the following table summarizes the results:

.

regress sales2008 pi

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Source SS

df MS

Number of obs

= 31

F( 1, 29)

= 7.94

Model 1024.47664

1 1024.47664

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Prob > F

= 0.0086

Residual 3742.37098

29 129.047275 R-squared

= 0.2149

Adj R-squared

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= 0.1878

Total 4766.84762

30 158.894921 Root MSE

= 11.36

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Sales2008 Coef.

Std. Err. t

P>t

[95% Conf.

Interval]

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pi .8674739

.3078788 2.82

0.009

.237791

1.497157

_cons 15.49897

34.24631 0.45

0.654

-54.54259

85.54053

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The estimated model is as follows: sales = 15.5 + 0.8674 PI, this means that the price index has a positive influence on sales whereby as the price index increases the sales levels also increase. This shows that an increase in inflation will lead to an increase in sales, this can be explained by the fact that consumers who have expectations that prices will rise in future will purchase more.

REFERENCE:

OECD (2009) production and sales data and price index data for member and non member countries, retrieved on 3rd December, available at http://stats.oecd.org/index.aspx?querytype=v iew&amp;queryname=91

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