A marketing manager wishes to forecast corporate sales for the coming year and to understand better the factors that influence them.
Sales Forecast Regression Exercise
INSEAD MBA Core Course UDJ
INSEAD
The Problem
Sales Drivers
The manager believes that sales depend upon
personal disposable income, dealers' allowances prices, product development expenditures, capital investments, advertising, sales expenses, total industry advertising, and some random effects.
The Data
Personal Disposable Income in Millions of Dollars. (PDI)
Dealers' Allowances in Thousands of Dollars. (DEALS)
Price in Dollars. (PRICE)
Product Development in Thousands of Dollars. (R&D)
Capital Investments in Thousands of Dollars. (INVEST)
Advertising in Thousands of Dollars. (ADVERTIS)
Sales Expenses in Thousands of Dollars. (EXPENSE)
Total Industry Advertising in Thousands of Dollars. (TOTINDAD)
Company Sales in Thousands of Dollars. (SALES)
Summary Statistics
| PDI | DEALS | PRICE | R.D | INVEST | ADVERTIS | EXPENSE | TOTINDAD | SALES | |
|---|---|---|---|---|---|---|---|---|---|
| min | 268.000 | 104.000 | 56.200 | 7.740 | -49.570 | 12.460 | 154.050 | 59.610 | 4033.130 |
| 25% | 358.000 | 120.000 | 63.133 | 12.995 | 9.473 | 40.025 | 205.725 | 136.660 | 4767.525 |
| median | 415.000 | 130.000 | 69.075 | 19.655 | 60.310 | 65.790 | 224.250 | 242.995 | 5103.850 |
| mean | 406.100 | 129.125 | 69.372 | 19.587 | 57.508 | 60.334 | 232.727 | 238.441 | 5078.957 |
| 75% | 455.250 | 138.000 | 75.455 | 24.907 | 113.860 | 83.208 | 266.335 | 315.253 | 5376.128 |
| max | 554.000 | 152.000 | 82.330 | 35.740 | 148.450 | 96.070 | 328.250 | 428.980 | 6180.060 |
| std | 70.765 | 12.845 | 7.821 | 7.880 | 61.538 | 26.087 | 43.924 | 110.407 | 513.181 |
Histogram of the Dependent Variable SALES
Time Series of Sales
An interactive chart of the SALES time series (Place the mouse on the plot to see daily values, and zoom using click-and-drag with the mouse in the smaller graph below)
Correlation Matrix
| PDI | DEALS | PRICE | R.D | INVEST | ADVERTIS | EXPENSE | TOTINDAD | SALES | |
|---|---|---|---|---|---|---|---|---|---|
| PDI | 1.00 | -0.05198 | 0.5818 | 0.1628 | 0.1066 | 0.2057 | 0.9017 | -0.05611 | 0.7301 |
| DEALS | -0.05198 | 1.00 | 0.0442 | 0.008086 | -0.09995 | -0.1096 | -0.0409 | -0.1528 | 0.01248 |
| PRICE | 0.5818 | 0.0442 | 1.00 | 0.4371 | -0.08938 | 0.2764 | 0.6387 | -0.2135 | 0.2949 |
| R.D | 0.1628 | 0.008086 | 0.4371 | 1.00 | 0.1673 | 0.1269 | 0.3628 | -0.1295 | 0.04157 |
| INVEST | 0.1066 | -0.09995 | -0.08938 | 0.1673 | 1.00 | 0.238 | 0.1956 | -0.1008 | 0.4239 |
| ADVERTIS | 0.2057 | -0.1096 | 0.2764 | 0.1269 | 0.238 | 1.00 | 0.144 | -0.1986 | 0.5306 |
| EXPENSE | 0.9017 | -0.0409 | 0.6387 | 0.3628 | 0.1956 | 0.144 | 1.00 | -0.04053 | 0.6675 |
| TOTINDAD | -0.05611 | -0.1528 | -0.2135 | -0.1295 | -0.1008 | -0.1986 | -0.04053 | 1.00 | -0.1802 |
| SALES | 0.7301 | 0.01248 | 0.2949 | 0.04157 | 0.4239 | 0.5306 | 0.6675 | -0.1802 | 1.00 |
Just one of the many possible plots...
Our Regression Model
SALES = b1*PDI + b2*DEALS + b3*PRICE + b4*R.D + b5*INVEST + b6*ADVERTIS + b7*EXPENSE + b8*TOTINDAD
Regression Output
| Estimate | Std. Error | t value | Pr(> |t|) | |
|---|---|---|---|---|
| (Intercept) | 3027.6336 | 572.3599 | 5.29 | 0.0000 |
| PDI | 3.3723 | 1.4137 | 2.39 | 0.0234 |
| DEALS | 4.6953 | 3.0103 | 1.56 | 0.1290 |
| PRICE | -18.1112 | 7.4927 | -2.42 | 0.0217 |
| R.D | -9.9033 | 6.0021 | -1.65 | 0.1090 |
| INVEST | 1.6895 | 0.7157 | 2.36 | 0.0247 |
| ADVERTIS | 8.2907 | 1.6445 | 5.04 | 0.0000 |
| EXPENSE | 4.4434 | 2.5076 | 1.77 | 0.0862 |
| TOTINDAD | -0.4427 | 0.3646 | -1.21 | 0.2339 |
R-squared: 0.8338 , Adjusted R-squared: 0.791
F-statistic: 19.4449 with 8 and 31 degrees of freedom
Residual standard error: 234.6363 with 31 degrees of freedom
The Residuals Plot (Time Series)
One of the many Residual plots...
Histogram of the Residuals
