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To estimate the CEO salaries, a linear regression analysis was carried out. The results are presented in Table 1 below.
Table 1: Regression Model 1
From the outcome:
Salary = 273.81 + 12.76(age) – 0.10(agesq) -40.70(grad) + 11.45(ceoten) + 0.02(mktval) +0.22(profits)
The average age from the results in Table 2 was 56 years.
Table 2: Age Summary
The researcher tested whether the age of 65 years had a statistically significant effect on salaries, starting at the average value of age. The results are presented in Table 3.
Table 3: T-Test – Comparing Salaries for 56 Years and 65 Years
From the findings, t(176) = 18.13; p<0.05. Since the p-value was less than 0.05, this meant that there was a statistically significant difference in the salaries between the average age of 56 and the age of 65.
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Table 4: Correlation and VIFs
Thus, to deal with multicollinearity, it was imperative to remove one of the variables, particularly profits.
Table 5: Regression Results
Forage (t = 0.31; p>0.05) and for agesq (t = -0.29; p>0.05). Since both beta coefficients were not statistically significant, this meant that the relationship between age and CEO salaries was neither linear nor quadratic in nature.
The corresponding model is presented in Table 5.
Table 6: Regression Results – Excl. Age
From the outcome, only the CEO's tenure at the firm had a statistically significant influence on salary.
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Hypothesis testing explained by our Stata tutors
H0: The coefficients for firm profits and market value are jointly equal to zero (βprofits = βmktvalue = 0)
H1: The estimated coefficients for firm profits and market value are not jointly equal to zero
Table 6 presents the results.
Table 7: Joint significance
From the outcome, F(2, 172) = 35.98; p<0.05. This meant that the estimated coefficients for firm profits and market value were not jointly equal to zero
The major reason why profits and market value have joint significance but lack individual statistical significance is that both are confounding variables. The profits influence both the dependent variable, CEO salary, and the independent variable, market value. This causes a spurious association.
. generate lg_salary = log(salary)
. generate lg_mktval = log(mktval)
. regress lg_salary grad ceoten lg_mktval profits, robust
Our Stata tutors summarize the regression results as below.
Table 8: Regression Results
From the outcome, again, the market value was now a statistically significant variable.
The logarithm function log(x) is defined only for values greater than zero. So the logarithm of a negative number would be not defined. The profits variable included negative numbers (loss) and this meant the need to avoid using the natural log for the profits variable.
Market value had a statistically significant impact on the CEO salary (t = 3.83; p<0.05). The profits did not have a statistically significant impact on the CEO salary (t = 0.60; p>0.05).
Yes, we should drop profits from the model because it is highly correlated with market value and this. From Table 8 below, their correlation coefficient was 0.918 and this was a very high correlation. Further, the VIF statistic for both market value and profits was observed to be higher (VIF> 5) than the minimum acceptable threshold range of between 3 and 5.
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