Case Study: Analysis of Regression

Assistant Professor

JIMS, Kalkaji

The idea of this study is to understand the concept of Regression analysis and its application in order to develop a model for predicting approximately the values of the variables dependent on one another.

United Colors of Benetton is a retail chain in the business of casual and formal wear. Using the pull strategy, the company has been investing in advertising to attract more customers. The top management wants to know how the impact of the advertising on the sales in the past. For this purpose, a research agency was consulted, who collected data from the finance department of the company. The research agency collected information on sales ($ 1000) and advertising expenditure (($ 1000) for the last 30 months.

Month	Advertising Expenditure (X)	Sales(Y)
1	49	14
2	40	9
3	50	15
4	46	13
5	44	12
6	52	15
7	54	15
8	58	16
9	56	15
10	60	18
11	49	14
12	40	9
13	50	15
14	46	13
15	44	12
16	52	15
17	54	15
18	58	16
19	56	15
20	60	18
21	49	14
22	40	9
23	50	15
24	46	13
25	44	10
26	52	15
27	54	15
28	58	16
29	56	13
30	63	16

The research agency was also given the task of

1. Developing a model for forecasting the future sales for any particular level of advertising budget.i.e. Find the regression relationship between the two variables, Sales and the advertising expenditure.

2. Estimate the value of sales approximately if an amount of $ 4000 is spent on Advertising.

In business Decision Making, it becomes imperative to comprehend and examine the impact of one or more variables on a particular variable. As in the above example we studied the impact of advertising expenditure on sales. Hence it is important for the firms to understand the nature of relationship between the variables. That’s when we use the concept of Regression, it used to study the cause and effect relationship among variables.

Primarily, it analyzes the functional relationship among the variables. Perhaps, one can say that a regression technique aims at examining the functional relationship among the variables and then estimating the value of dependent variable on the basis of the values of the independent variables.

 In order to estimate the nature of relationship between the variables, following calculation has to be done.

Month	Advertising Expenditure (X)	Sales(Y)	XY	X2
1	49	14	686	196
2	40	9	360	81
3	50	15	750	225
4	46	13	598	169
5	44	12	528	144
6	52	15	780	225
7	54	15	810	225
8	58	16	928	256
9	56	15	840	225
10	60	18	1080	324
11	49	14	686	196
12	40	9	360	81
13	50	15	750	225
14	46	13	598	169
15	44	12	528	144
16	52	15	780	225
17	54	15	810	225
18	58	16	928	256
19	56	15	840	225
20	60	18	1080	324
21	49	14	686	136
22	40	9	360	81
23	50	15	750	225
24	46	13	598	169
25	44	10	440	100
26	52	15	780	225
27	54	15	810	225
28	58	16	928	256
29	56	13	728	169
30	63	16	1008	256
Total	1530	420	21808	6042

From the above calculation, we get the number of pair of observations= N= 30.

 =  = 14

 =  = 51

 = 6042

 = 21808

So the regression coefficients would be

 =  = 2.395

a= –

a= 17.47

The estimated model is Y = 17.47 + 2.395 X

From the estimated relationship, it can be said that $ 1000 expenditure in advertising is expected to bring increase in sales by $2400.

This model used for forecasting, if the company decides to invest $ 4000 in the advertising in the next month, the total sales expected can be calculated as:

Sales= 17.47 + 2.395(4) = 27.07

The sales are approximately to be $ 27070.

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