Strategies For Starting A Business And Advertising: Analysis And Predictions

Summary of Business Strategies

Two friends Gregor and Ilya have recently completed their studies and are interested in setting up a business. They have adopted three different strategies to do that.

Strategy 1: Rent a fairly expensive location to set up an office for their business and where their potential customers are located.

Strategy 2: To rent a comparatively cheaper place in the neighbouring suburb.

Strategy 3: Not to set up a business at all.

            The estimates of profit and loss from the business in a favourable and unfavourable market are given in the following table:

• Ilya is an optimist and likes to take risks. Thus, the strategy chosen by Ilya will be Strategy 1, where the profitable amount is maximum.

• On the other hand, Gregor is conservative and tries to minimize the Thus, the strategy chosen by Gregor will be Strategy 3, where the chance of suffering a loss is minimum.

• A market is favourable with a probability of 55 percent. Thus, the expected profit has been found to be maximum for Strategy 2. Hence Strategy 2 must be chosen.

• The expected returns when the probability of the market being favourable is not fixed at 0.55 percent and lies between 0 and 1 from both the strategies are plotted in the following figure:

i) Strategy 1 will be chosen when the probability of market being favourable is given by 0.67 ≤ P ≤ 1

1. ii) Strategy 2 will be chosen when the probability of market being favourable is given by 0.29 ≤ P ≤ 0.66

iii)        Strategy 3 will be chosen when the probability of market being favourable is given by 0 ≤ P ≤ 0.28

Problem 2

            Let “a” TV advertisements, “b” Radio ads, “c” billboard ads and “d” newspaper ads be posted. The objective of the person is to reach the advertisements to maximum number of readers within a budget of $14,000. Thus, the objective function can be stated as:

Minimize Z = (960 * a) + (480 * b) + (600 * c) + (120 * d)

Subject to the constraints:

a, b, c, d ≤ 10

a + b ≥ 6

(960 * a) – (600 * c) – (120 * d) ≥ 0

And the non-negativity constraints a, b, c and d ≥ 0The maximum number of people that can be reached through these advertisements within the budget is:

(6 * 36,000) + (6 * 26,500) = 3,75,000

• The number of advertisements ordered by Jim Daniels will be 6 TV advertisement and 6 Radio advertisement.
• Problem 3

• Max’s policy was to have a re-order point of 5 and the reordering quantity of 5. According to the policy, the least cost incurred for the inventory policy is $50,940, the highest cost incurred is $70,240 and the average cost incurred is $58,828.
• i) If the reorder point was considered to be 3 and reordering quantity was considered to be 3, the least cost incurred for the inventory policy is $31,340, the highest cost incurred is $39,580 and the average cost incurred is $36,106.

1. ii) If the reorder point was considered to be 7 and reordering quantity was considered to be 7, the least cost incurred for the inventory policy is $80,280, the highest cost incurred is $96,100 and the average cost incurred is $87,100.

• It can be understood from the results obtained above that having a reorder point of 3 and a reordering unit of 3, the cost incurred will be minimum. Thus, this can be considered as the best policy.

Problem 4

Part 2

            It can be seen from the results of the analysis that the coefficient of determination is 0.6323 which indicates explanation of 63.23 percent of variability in the selling prices with area.

Considering area = 2000 ft²,

Selling price    = – 34301.5987 + (62.96 * 2000)

                        = $91618.4

            The regression equation to predict the selling price when the independent variable is bedrooms is given by: Selling Price = 648.6487 + (35168.9189 * Number of Bedrooms).

            It can be seen from the results of the analysis that the coefficient of determination is 0.2547 which indicates explanation of 25.47 percent of variability in the selling prices with area.

Considering bedrooms = 3,

Selling price    = 648.6487 + (35168.9189 * 3)

                        = $106155

            The regression equation to predict the selling price when the independent variable is age is given by: Selling Price = 141448.2518 + (- 2256.7296 * Age).

Advertising Budget Optimization

            It can be seen from the results of the analysis that the coefficient of determination is 0.7446 which indicates explanation of 74.46 percent of variability in the selling prices with area.

Considering age = 24 years,

Selling price    = 141448.2518 + (- 2256.7296 * 24)

                        = $87286.7

            Variability in selling price can be explained the most by age of the house. Thus, the third model will be considered as the best model.

Part 2

            The regression equation to predict the selling price when the independent variables are area and bedrooms is given by: Selling Price = -26129.5 + (76.1268 * Area) + (-12403.1 * Bedrooms)

            It can be seen from the results of the analysis that the coefficient of determination is 0.7423 which indicates explanation of 74.23 percent of variability in the selling prices with area and bedrooms.

            The regression equation to predict the selling price when the independent variables are area and age is given by: Selling Price = 69793.9387 + (27.0743 * Area) + (-1554.9387 * Age)

            It can be seen from the results of the analysis that the coefficient of determination is 0.774 which indicates explanation of 77.4 percent of variability in the selling prices with area and age.

            The regression equation to predict the selling price when the independent variables are bedrooms and age is given by: Selling Price = 99495.77 + (12389 * Bedrooms) + (-1985.53 * Age)

            It can be seen from the results of the analysis that the coefficient of determination is 0.8665 which indicates explanation of 86.65 percent of variability in the selling prices with bedrooms and age.

            The regression equation to predict the selling price when the independent variables are area, bedrooms and age is given by: Selling Price = 70181.01 + (25.1505 * Area) + (-1574.39 * Age) + (1389.257 * Bedrooms)

            It can be seen from the results of the analysis that the coefficient of determination is 0.8848 which indicates explanation of 88.48 percent of variability in the selling prices with area, bedrooms and age.

            From all the models discussed above in both parts 1 and 2, it can be seen that the multiple regression model predicting the selling price with all the three independent variables is the best predictor with the highest explanation of variability in the selling prices

Problem 5

            From the multilayer perceptron with one hidden layer, it can be seen that the coefficient of determination is 0.9396, which is better than all the developed regression models. Thus, MLP can be considered as a better prediction model than regression.

            On the other hand, considering two hidden layers, it can be seen that the coefficient of determination has decreased to 0.7756 which indicates that the efficiency of the model decreases when the number of hidden layer is increased.

Table 5.1: MLP Summary (One hidden layer)Problem 6

1. There are 17 attributes in the dataset
2. There are 7 numeric attributes

• There are 10 categorical attributes

1. There are 4521 examples
2. The class variable is considered as the variable “y”
3. “y” can take only two values

• Among the two values, “yes” indicates an account will be opened and “no” indicates account will not be opened.

Task 1

Logistic Regression

• Confusion Matrix
• ROC Curve

Naïve Bayes Model

• Confusion Matrix
• ROC Curve

Task 2

Lift Chart for Logistic Regression Model

Conclusion

            The area under the ROC curve is higher in logistic regression (0.888) than that of the Naïve Bayes Model (0.845). This indicates that the logistic regression classifier is a better predictor than the Naïve Bayes classifier.

            On the other hand, the lift chart for the logistic regression shows a higher lift than that of the Naïve Bayes classifier. Thus, from here also it can be concluded that logistic classifier is a better predictor than the Naïve Bayes classifier.

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