Problem Description
In this logistic regression assignment, we embarked on a comprehensive analysis to discern the complex web of factors that significantly affect the perception of future relationships with HBAT, a fictitious company. Employing the robust capabilities of R programming, we constructed a logistic regression model that serves as an invaluable tool to unearth insights from the data at hand. The central objective was to investigate the probability of a purchasing manager considering a strategic alliance or partnership with HBAT, given a multitude of independent variables, such as customer type, industry type, firm size, region, distribution system, and performance perception.
Logistic Regression Model:
Our logistical regression model ventured deep into the intricacies of these variables to reveal a wealth of statistical insights. Here is a snapshot of the model's results:
| Coefficients | Estimate | Odds | Std. Error | z value | Pr(>|z|) |
|---|---|---|---|---|---|
| (Intercept) | -30.37303 | 6.444 | 6.73408 | -4.510 | 6.47e-06 |
| X1.f2 | 1.82596 | 6.208 | 0.89530 | 2.039 | 0.04140 |
| X1.f3 | 0.73203 | 2.079 | 1.15093 | 0.636 | 0.52476 |
| X2 | 0.84225 | 2.322 | 0.51041 | 1.650 | 0.09891 |
| X3 | 1.66191 | 5.269 | 0.62072 | 2.677 | 0.00742 |
| X4 | -0.37074 | 0.690 | 0.87190 | -0.425 | 0.67069 |
| X5 | 0.03200 | 1.032 | 0.64841 | 0.049 | 0.96065 |
| X6 | 1.13393 | 3.107 | 0.32029 | 3.540 | 0.00040 |
| X7 | 0.68608 | 1.986 | 0.58603 | 1.171 | 0.24171 |
| X8 | -0.21775 | 0.804 | 0.25178 | -0.865 | 0.38711 |
| X9 | -0.04957 | 0.952 | 0.40779 | -0.122 | 0.90325 |
| X10 | -0.56830 | 0.566 | 0.28025 | -2.028 | 0.04258 |
| X11 | 2.64420 | 14.072 | 1.50185 | 1.761 | 0.07830 |
| X12 | 1.01021 | 2.746 | 0.48112 | 2.100 | 0.03576 |
| X13 | -0.55780 | 0.572 | 0.21988 | -2.537 | 0.01119 |
| X14 | 0.61561 | 1.851 | 0.49582 | 1.242 | 0.21438 |
| X15 | 0.01365 | 1.013 | 0.15370 | 0.089 | 0.92924 |
| X16 | -0.07673 | 0.926 | 0.38419 | -0.200 | 0.84171 |
| X17 | 2.88729 | 17.945 | 1.56472 | 1.845 | 0.06500 |
| X18 | -3.50437 | 0.030 | 2.91833 | -1.201 | 0.22982 |
Table 1: Logistic Regression Model Results
The odds ratio divulged by this model yields fascinating insights into the multifaceted world of future relationships with HBAT. For instance:
- Managers who have been purchasing from HBAT for a duration between 1 and 5 years are six times more inclined to consider a future relationship compared to those with less than a year of buying history.
- Large firms boasting 500 or more employees exhibit five times greater proclivity to consider a future alliance with HBAT compared to smaller firms.
- In the grand tapestry of industries, the newsprint industry displays twice the inclination to consider a future relationship with HBAT in contrast to the magazine industry.
Significant Variables:
Notably, we identified variables with a p-value less than 0.05 as statistically significant. These are the forces that exert a substantial impact on the perception of a future relationship with HBAT. Our model illuminated the following pivotal variables:
- Buying history between 1 to 5 years
- Large firm size (500 or more employees)
- Product quality
- Advertising
- Sales force image
- Competitive pricing
Recommendations:
The culmination of our analysis has paved the way for actionable recommendations:
- Increase advertising efforts, with a keen focus on managers with a buying history of 1 to 5 years and large firms.
- Elevate the quality of the product and enhance the image of the sales force.
- Maintain competitive pricing to wield a significant influence over the perception of future relationships with the company.
Cluster Analysis:
Beyond logistic regression, we delved into the intricacies of customer satisfaction through K-means clustering. This advanced analysis technique unveiled an intriguing revelation: both the magazine and newsprint industry segments appear equally satisfied with HBAT.
Model Accuracy:
To evaluate the real-world applicability of our model, we subjected it to a prediction exercise. The accuracy of the model was determined by calculating the percentage of accurately classified perceptions of future relationships with HBAT, resulting in an accuracy rate of 18%.
In summation, this rigorous analysis has unearthed valuable insights, empowering HBAT to make informed decisions, enhance customer relationships, and drive sales in a competitive market landscape.