Magic Case Study

Magic Case Study
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Institution
Magic Case Study
Regression Analysis
The number of sales acted as the response variables while the market potential of the territory, the number of shops, dealers, popular brands and the size of the population as the predictor variables.
The factors that affect sales are the number of dealers and the number of popular brands because they had p values of 0.012 and 0.011 respectively, which are less than 0.05 (Downing and Clark, 2010).
The market potential of each territory, the y intercept, and the number of shops had p values of 0.134, 0.758, and 0.359 (greater than 0.05) respectively hence, are insignificant predictors.
We cannot determine whether the size of the population influences the number of sales because it had a p value of 0.51, which is almost equal to 0.05.
The R squared from the regression summary is 98.13 percent meaning 98 percent of the variation in sales is explained by the response variables used.
Considering the level of significance in the regression model, sales can be predicted by the following equation. Sales = 3.39 + 0.590 No of Dealers - 0.805 No of Popular Brands + 0.1764 Population.
Regression Analysis: sales versus Market Potential, No of Shops, No of Dealer, No of Popular Brands, and Population Size.
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 5 8825.99 1765.20 252.16 0.000
Market Potential of The Territory 1 16.87 16.87 2.41 0.134
No of Shops 1 6.11 6.11 0.87 0.359
No of Dealers 1 51.62 51.62 7.37 0.012
No of Popular Brands 1 53.18 53.18 7.60 0.011
Population 1 29.57 29.57 4.22 0.051
Error 24 168.01 7.00
Total 29 8994.00
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.64583 98.13% 97.74% 96.96%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 2.03 6.50 0.31 0.758
Market Potential of the Territory 0.262 0.169 1.55 0.134 8.90
No of Shops 0.288 0.308 0.93 0.359 10.17
No of Dealers 0.428 0.158 2.72 0.012 19.88
No of Popular Brands -0.808 0.293 -2.76 0.011 6.93
Population 0.1393 0.0678 2.06 0.051 22.90
Regression Equation
Sales = 2.03 + 0.262 Market Potential of the Territory + 0.288 No of Shops
+ 0.428 No of Dealers - 0.808 No of Popular Brands + 0.1393 Population
Fits and Diagnostics for Unusual Observations
Obs sales Fit Resid Std Resid
9 25.00 30.40 -5.40 -2.29 R
23 30.00 35.62 -5.62 -2.25 R
R Large residual
Prediction of the Future Demand
The future demand requires the collection of data with different variables that is time and the number of sales. Otherwise, the available data can only determine the crucial factors required to increase sales, but cannot predict the future demand.
However, the model can predict the number of sales given the size of the population, the number of dealers, and the number of popular brands. Consider the following values, 36 dealers, 6 Popular Brands, and a population of 135. The output below predicts the number of sales.
Results for: Sheet1

Prediction for sales
Regression Equation
sales = 3.39 + 0.590 No of Dealers - 0.805 No of Popular Brands + 0.1764 Population
Variable Setting<...