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Business, Pages: 1

Management and Leadership – Regression Analysis

Management and Leadership – Regression Analysis

  1. The regression was designed to determine the effect of manager tenure on division growth

The data used to generate the regression model represents the data collected from the firm’s 107 division managers containing growth figures for each of the different manager divisions, the manager’s tenures in the firm, and the manager’s test scores. The data was collected from the whole firm.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.330781
R Square 0.109416
Adjusted R Square 0.100934
Standard Error 3.106244
Observations 107
ANOVA
  df SS MS F Significance F
Regression 1 124.4701 124.4701 12.90013 0.000502
Residual 105 1013.119 9.648749
Total 106 1137.589
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 3.54965 0.674681 5.261227 7.61E-07 2.211882 4.887418 2.211882 4.887418
Tenure 0.139368 0.038803 3.591676 0.000502 0.062429 0.216308 0.062429 0.216308

The regression model targeted establishing the effect of the manager’s tenure on the growth of the division. This implies that tenure is the explanatory variable while division growth is the response variable. The regression model is generated using the Excel data analysis tool pack. From the regression output above, tenure is positively related to division growth, which is derived from the correlation coefficient of 0.1394. This indicates a weak positive impact of the manager’s tenure on the division’s growth. The implication from the output is that a unit increase in tenure will lead to a divisional growth of 0.1394. Particularly, if a manager’s tenure is increased by a year, the division is likely to grow by 0.1394. The model is also significant at a 5% level of significance, with a p-value of 0.0005. However, a weakness of the model is that it explains 10% of the relationship between the variables as indicated by the R-Square value (Field, 2018).

  1. What role, if any, can the manager’s leadership test score play in the regression you ran for Part A? Explain.

To include the effect of a test score, we can run the regression model by including the test score as a second independent variable.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.539154
R Square 0.290687
Adjusted R Square 0.277046
Standard Error 2.785448
Observations 107
ANOVA
  df SS MS F Significance F
Regression 2 330.682 165.341 21.31034 1.75E-08
Residual 104 806.9068 7.75872
Total 106 1137.589
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.99619 0.67589 2.953423 0.003886 0.655874 3.336505 0.655874 3.336505
Tenure 0.077204 0.036826 2.096475 0.038466 0.004177 0.150231 0.004177 0.150231
Test Score 0.047339 0.009182 5.155393 1.21E-06 0.02913 0.065548 0.02913 0.065548

Including the test score in the model reduces the correlation between the manager’s tenure and division’s growth to 0.077204. The coefficient value for the test score is also very small at 0.0473. This indicates that manager’s tenure and test score may not provide reliable information about the manager’s leadership impact in the firm. The R-squared value after including the test score in the model is also very small (0.290687), which implies that the model explains 29% of the relationship between the dependent and independent variables. This implies for the firm that to understand the impact of the leader on the division’s growth, it is crucial to explore other variables that have a higher correlation coefficient.

References

Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publishers, California.

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Question 

Management and Leadership - Regression Analysis

Management and Leadership – Regression Analysis

In the seventh phase of the business strategy formulation, you decide to study the effect of employees’ time spent in a managerial role on the growth of the division they manage.

To begin your study, you collected data on each of your 107 division managers (contained in a separate Excel spreadsheet). The data contains growth figures for each of the manager’s divisions, the manager’s tenure with the organization, and the manager’s score on a leadership test. This was all administered throughout the organization.
Provide your answer to the following questions:
1. Run a regression designed to determine the effect of manager tenure on division growth.
2. What role, if any, can the manager’s leadership test score play in the regression you ran for #1? Provide analysis to support your answer.