Multiple regression model of sale prediction based on the information about day of the weeks, holidays, and sales promotions elena-tulainova@yandex.ru looking opportunity to work as an analyst in retail/food industry

1. As any other retail company in food industry, revenue may be affected by many different factors,
such as season, awareness of customers, location, age of the company, and etc. There are many
different ways to predict the sales in the future based on the experience in the past.
One of the ways to predict sales is building the regression model based on the significant factors.
During the last year and a half, company was collecting data about its revenue: day, revenue of that
day, and number of orders.
For building multiple regression model there was a need of adding additional information to the
data set. For instance, “days” were converted into three variables: “year”, “month”, and “day of the
week”. In addition, dummy variables were added for 11 month and 6 days of the week. Also,
additional variable “holiday”, that can potentially influence the sales, was added to the data set.
The response variable for Multiple regression model is “Revenue” and predicted variables include
Year, February, March, April, May, June, July, August, September, October, November, December,
Holiday, Monday, Tuesday, Wednesday, Thursday, Saturday, and Sunday.
After running the multiple regression on the software the following equation was build:
Sales = 60782.467 + 6299.3567*Year+64.674037*February+1111.6888
*March+1612.0077*April +5245.2574*May+7535.7937*June+ 18703.282*July+16775.916
August+13967.956 September+10346.342*October+9214.7979* November+5881.4187 *December-
27277.269*Monday-24640.78 *Tuesday-11204.269 *Wednesday+10031.046 *Thursday-27260.071
*Saturday-28896.612 *Sunday
where January /Friday were chosen to be interception.

2. Parameter Estimate Std. Err. Alternative DF T-Stat P-value
Intercept 60782.467 2433.0199 ≠ 0 588 24.982314 <0.0001
Year 6299.3567 1025.005 ≠ 0 588 6.1456838 <0.0001
February 64.674037 2096.0356 ≠ 0 588 0.03085541 0.9754
March 1111.6888 2055.2442 ≠ 0 588 0.54090352 0.5888
April 1612.0077 2092.8673 ≠ 0 588 0.77023882 0.4415
May 5245.2574 2045.5038 ≠ 0 588 2.5642864 0.0106
June 7535.7937 2066.248 ≠ 0 588 3.6470907 0.0003
July 18703.282 2076.2135 ≠ 0 588 9.0083619 <0.0001
August 16775.916 2078.3279 ≠ 0 588 8.071833 <0.0001
September 13967.956 2592.4881 ≠ 0 588 5.3878572 <0.0001
October 10346.342 2574.7308 ≠ 0 588 4.0184171 <0.0001
November 9214.7979 2592.5503 ≠ 0 588 3.5543371 0.0004
December 5881.4187 2557.4269 ≠ 0 588 2.2997407 0.0218
Holiday 31711.132 1955.9221 ≠ 0 588 16.212881 <0.0001
Monday -27277.269 1717.2913 ≠ 0 588 -15.883892 <0.0001
Tuesday -24640.78 1715.4465 ≠ 0 588 -14.364062 <0.0001
Wednesday -11204.269 1715.3106 ≠ 0 588 -6.5319183 <0.0001
Thursday 10031.046 1713.7723 ≠ 0 588 5.8531962 <0.0001
Saturday -27260.071 1713.6991 ≠ 0 588 -15.907152 <0.0001
Sunday -28896.612 1719.6078 ≠ 0 588 -16.804188 <0.0001
Table 1. Parameter estimates
Source DF SS MS F-stat P-value
Model 19 1.9297489e11 1.0156573e10 79.572676 <0.0001
Error 588 7.5051704e10 1.2763895e8
Total 607 2.6802659e11
Table 2. Analysis of variance table for multiple regression model
Summary of fit:
Root MSE: 11297.741
R-squared: 0.72
R-squared (adjusted): 0.7109

3. Building multiple regression model will show the importance of each chosen parameters (p-value)
and percentage of all data which can be predicted using this model (R-squared adjusted). R-squared is
equal 0.7109 meaning that about 70% of the data are to the fitted regression model and almost 30% are
not.
Overall, the p-value of the model is < 0.0001 which prove that the parameters are not equal 0.
Some of the individual p-values, for instance for February, March, and April, are higher than
0.05. Typically, the coefficient p-values are determining which parameter to keep in the regression
model. At the same time, excluding couple of months from the model will be causing the inability to
predict the sale during those months.
No doubt, to be sure that the model is valid following conditions should be checked. First
assumption is that the errors around the idealized regression model at any specified values of the X-
variables follow a Normal model. The Graph 1. is a histogram for residuals. It is proving that
residuals are normally distributed.
Graph 1.

4. The second condition is Condition of Plot Thickness. The scatterplot (Graph 2) of residuals against
predicted values shows no obvious changes in the spread about the line
Graph 2.
The last condition, Nearly Normal Condition: A histogram of the residuals is unimodal and symmetric.
.
Graph 3.

5. The completing those condition allows us to use the result of multiple regression model.
Index/time plot (Graph 4) is showing the Revenues and Predicted Variable for the all period of
time.
Graph 4.
Predicted Variables are more stable than Revenues. With the same mean, they have very different
standard deviations (Table 3). No doubt, the positive differences can be explain by unaccounted
parameters such as promotions, sales, or coupons distributed before that day. For instance, the
negative differences would be explain by hardware failure or negative weather conditions when
customers doesn’t want to step up outside for shopping from their houses.
Column Mean Std. dev. Coef. of var.
Revenues 63194.778 21013.316 33.251666
Pred. Values 63194.778 17830.193 28.21466
Table 3. Summary statistics

6. In addition, it is good to remember that the model build on the past experience. In the future, at any
point of time, any parameters, or relationship between them may be changed. Therefore, regression
model will be changed.