Regression analysis
In the above diagram, the statistical analysis has been done taking the data on the CEO and other variables in the form of is the return on assets % for firm i; is measured by the log of firm i’s total assets; is the volatility measured by the daily return standard deviation (%),is the years as CEO with company I, is a dummy variable, = 1 if CEO is female, = 0 otherwise. The study is aiming in developing the regression among the independent and the dependent variable so that the correlation can be determined. Part I: Regression analysis
SUMMARY OUTPUT 

Regression Statistics 

Multiple R 
0.690194931 

R Square 
0.476369043 

Adjusted R Square 
0.422200324 

Standard Error 
0.263262748 

Observations 
65 

ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
6 
3.657000599 
0.6095 
8.794172 
8.06933E07 

Residual 
58 
4.01982192 
0.069307 

Total 
64 
7.676822519 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 

Intercept 
3.118249454 
0.301057329 
10.35766 
8.3E15 
2.515617735 
3.720881173 
2.515617735 
3.720881173 
roa 
0.00529486 
0.005834777 
0.90747 
0.367916 
0.016974435 
0.006384714 
0.016974435 
0.006384714 
firmsize 
0.095659872 
0.02856035 
3.349394 
0.001428 
0.03849012 
0.152829624 
0.03849012 
0.152829624 
volatility 
0.012699849 
0.002957246 
4.29449 
6.75E05 
0.018619419 
0.006780279 
0.018619419 
0.006780279 
foreignceo 
0.086665076 
0.075472039 
1.148307 
0.255556 
0.064408624 
0.237738777 
0.064408624 
0.237738777 
femaleceo 
0.362752099 
0.139314751 
2.60383 
0.011688 
0.641620871 
0.083883327 
0.641620871 
0.083883327 
ceotenure 
0.00207895 
0.006659246 
0.31219 
0.756016 
0.011250979 
0.015408879 
0.011250979 
0.015408879 
Table 1: Regression analysis
The required regression equation that has been used for this purpose of development of better description of the model where is the log salary for CEO i; is the return on assets % for firm i; is measured by the log of firm i’s total assets; ???????? is the volatility measured by the daily return standard deviation (%); is the years as CEO with company i;is a dummy variable, = 1 if CEO is female, = 0 otherwise. is a dummy variable, = 1 if CEO is foreign, 0 otherwise.
Statistics 

High 
Low 
Close_A 
Adj 
Close 

N 
Valid 
14 
12 
11 
1 
502 
Missing 
488 
490 
491 
501 
0 

Mean 
108.42857143 
105.25000000 
110.36363636 
107.00000000 
7727560.16 

Median 
109.50000000 
105.50000000 
110.00000000 
107.00000000 
6974100.00 

Std. Deviation 
4.815268755 
5.971523332 
4.249064068 
3423024.714 

Range 
14.000000 
15.000000 
15.000000 
.000000 
25660000 

Minimum 
101.000000 
98.000000 
103.000000 
107.000000 
2217600 

Maximum 
115.000000 
113.000000 
118.000000 
107.000000 
27877600 
Table 2: Descriptive statistics for 21st century fox Company
In the above table the stock prices of the company 21st century fox has been considered in order to determine the stock prices and the relationship that this value is going to have on the model that has been determined. The ad close variable has been renamed name of the variable daily stock price of the company over a span of two years. The above table is showing the fact that the variable is having a mean of 105.25 and the median and standard deviation is having huge difference. The huge gap among the median and standard deviation is alerting about the presence of the huge level of outlier. Since the daily stock prices has been considered here, thus it has been assumed that presence of seasonality in the data set is varying the outcome.
Descriptive Statistics 

AdjClose 
Valid N (listwise) 

N 
Statistic 
502 
502 
Range 
Statistic 
23.329 

Minimum 
Statistic 
94.655 

Maximum 
Statistic 
117.985 

Sum 
Statistic 
52882.426 

Mean 
Statistic 
105.343 

Std. Error 
.247 

Std. Deviation 
Statistic 
5.528 

Variance 
Statistic 
30.564 

Skewness 
Statistic 
.092 

Std. Error 
.109 

Kurtosis 
Statistic 
.868 

Std. Error 
.218 
These descriptive statistics are important apart from the Rsquared and adjusted Rsquared in the sense that it will help in understanding the situation in which the adjusted close is standing. The descriptive statistics will be showing the skewness and kurtosis that the variable is having.
The above diagram is showing that the above variable is showing a normal distribution. Through this diagram, it is highly skewed in nature. From the above regression table, the Rsquare is showing the values of 0.476369043 and the adjusted Rsquare is around 0.422200324. More or less, the R square is taking some redundant variables that is not making any kind of impact on the development of model taking the return of assets as the dependent variable and other variables in the form of tenure of the CEO, the growth of the firms and many more.
The above equation of the linear regression is claiming that log salary of the CEO is the dependent variable that is depending entirely on the factors like rate of return of the asset, tenure of the CEO, size of the firms, volatility that is involved in the daily data of the stock prices of the company.
Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.690^{a} 
.476 
.422 
.26326 
a. Predictors: (Constant), femaleceo, foreignceo, roa, ceotenure, volatility, firmsize 
Empirical Discussions
Table 3: Model summary
The Rsquare is showing .476 and adjusted Rsquare is .422. The above is showing that taking the variable log salary as the dependent variable and taking femaleceo, foreignceo, roa, ceotenure, volatility, firmsize as the independent variables. Both the Rsquare and the adjusted Rsquared is very close to each other and the presence of the random or outliers is not affecting the model.
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
3.118 
.301 
10.358 
.000 

roa 
.005 
.006 
.100 
.907 
.368 

firmsize 
.096 
.029 
.381 
3.349 
.001 

volatility 
.013 
.003 
.459 
4.294 
.000 

ceotenure 
.002 
.007 
.031 
.312 
.756 

foreignceo 
.087 
.075 
.125 
1.148 
.256 

femaleceo 
.363 
.139 
.254 
2.604 
.012 

a. Dependent Variable: logCEOPAY 
Table 4: Coefficients of the variables
(Source: Created by Author)
The above table is one of the important deductions in the whole model. In the model, the two factors foreign CEO and the female CEO are two dummy variables that are categorical in nature. The above table is showing the degree and direction of the independent variables that are having on the dependent variables. Through the values of the coefficients, the development of the model is possible. Putting the values of the coefficients, the equation will be quite similar with the given equation.
3.1180.005(????1) ROA+0.096(????2) Size0.013(????3)volatility+0.02(????4)ceoten+0.087(????5)foreign ceo0.363(????6)femaleceo
The above equation is literally claiming that the log ceopay is depending negatively with the variables roa, volatility and female ceo. The return of the assets, volatility measured by the standard deviation and on the female ceo. This means, the development of the payment of the Ceo is not depending on the return of the assets that the firm is investing in the business. The coefficients of the independent variables is very small. From the above generated model, it can be stated that there are some other variables that is actually determining the logarithm of the salary of the CEO that is not included in the model.
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
1.624 
.546 
2.976 
.004 

leverage 
.002 
.003 
.082 
.727 
.470 

ceoage 
.014 
.008 
.186 
1.661 
.102 

boardindependence 
.015 
.004 
.417 
3.594 
.001 

ceoduality 
.487 
.229 
.245 
2.123 
.038 

a. Dependent Variable: logCEOPAY 

Table 5: Coeffient of other variables that could have been included
(Source: Created by Author)
In the above table, all the coefficients except the ceo duality variable is having positive coefficients on the development of the log salary of the ceo variable. Looking into this table, it can be concluded that it may be nature of the given data serries the coefficients of the variables are not having that much level of high coefficient variable. Through the development of these two tables are claiming that in both the tables, the variables are significant in nature. Through the development of the significant variables, the model will be able to ignite the development of the business that will help in prediction of the variables. Through the development of better benefits that the most of the companies will be able to predict the future consequences that will not only improve the development of the model.
The model though is not depicting the dependence among the variables, as the Rsquared values and the adjusted Rsquared values is not going past 0.51. The value of both Rsquared and adjusted Rsquared are well below the standard measure of the correlation coefficient. On the other hand, the development of these two variables are not helping in the development of the better and effective modelling. Through the development of the resource utilisation, it is possible for the development of an unbiased model that will not only increase the development of the model and will be helping in the effective predictions.
Description of the results
In most of the regression, it is assumed that all the variables will be highly significant in nature and the variables will be giving highly
Correlations 

logCEOPAY 
roa 
firmsize 
volatility 
foreignceo 
femaleceo 

logCEOPAY 
Pearson Correlation 
1 
.057 
.493^{**} 
.396^{**} 
.310^{*} 
.249^{*} 
Sig. (2tailed) 
.651 
.000 
.001 
.012 
.045 

N 
65 
65 
65 
65 
65 
65 

roa 
Pearson Correlation 
.057 
1 
.300^{*} 
.364^{**} 
.069 
.070 
Sig. (2tailed) 
.651 
.015 
.003 
.587 
.580 

N 
65 
65 
65 
65 
65 
65 

firmsize 
Pearson Correlation 
.493^{**} 
.300^{*} 
1 
.003 
.412^{**} 
.112 
Sig. (2tailed) 
.000 
.015 
.980 
.001 
.374 

N 
65 
65 
65 
65 
65 
65 

volatility 
Pearson Correlation 
.396^{**} 
.364^{**} 
.003 
1 
.082 
.120 
Sig. (2tailed) 
.001 
.003 
.980 
.518 
.343 

N 
65 
65 
65 
65 
65 
65 

foreignceo 
Pearson Correlation 
.310^{*} 
.069 
.412^{**} 
.082 
1 
.028 
Sig. (2tailed) 
.012 
.587 
.001 
.518 
.826 

N 
65 
65 
65 
65 
65 
65 

femaleceo 
Pearson Correlation 
.249^{*} 
.070 
.112 
.120 
.028 
1 
Sig. (2tailed) 
.045 
.580 
.374 
.343 
.826 

N 
65 
65 
65 
65 
65 
65 

**. Correlation is significant at the 0.01 level (2tailed). 

*. Correlation is significant at the 0.05 level (2tailed). 
Table 6: Correlation matrix of the given dependent and independent variable.
(Source: Created by Author)
The variable volatility and the female Ceo is though having negative correlations but are highly significant in nature that too at 99% of the confidence level. On the other hand, the variables that are having single star is significant at 95% of the confidence level. This is one of the important dedications that is claiming that in spite of having negative correlations, these variables are having high impact on the development of the model. However, the model is having some kind of variables that is not allowing the model to have better Rsquare.
Carroll (2017) opined that in order to determine the development of the model, it is important to consider the variable at first that are going to have significant impact on the mode. It has been opined that making the regression model effective in nature will definitely bring in effective innovations. Through the development of better regression model, it is important to indulge better techniques of sample collection that will increase the probability of having better Rsquared and adjusted Rsquared. Through the development of this regression analysis, it will be possible for the statistical analysis to introduce better model development.
According to Chatterjee and Hadi (2015), the development of the regression analysis will take on the development of variables that will not only lie within the significant values but will also increase the development of the authenticity of the model. The regression analysis will not only induce the development of the eternal strength and will highlight the dependence of the independent variables on the dependent variable. On the other hand, it is important to integrate variables in the model having the identification that will increase the model verification. Through the identification of the variables it is important to increase the resource of the modelling of data.
As opined by Darlington and Hayes (2016), in order to find the regression analysis and linear model is helpful for the development of correlation coefficient is important in the sense that through the development of the correlation coefficient it is important for the statisticians to indulge the development of the business by predicting the variable.
In order to discuss about the CEO compensations, it is important to include some of the important variables in the sense that through the development of better model, it is important to introduce the benefits that the most of the CEO will be taking as part of the individual initiative that will help in the development of the return through the development of the business. In order to increase the model development of ceo salary, it is important to undertake certain variables that will not only increase the development of the model but will also indulge the development of ceo salary. Through the development of better innovation technologies. Through the development of the model, it is important for the involvement of better introduction of regression that will not only increase the resources utilisation but will also indulge the formation of the modules taking the variables that will be indulging the development of variables like education of the CEO, working experience of the CEO, the working technologies that has been invented by the CEO. Through the development of the business, the company is indulging the development of business and these variables will definitely improve the models so that the development of the regression become easy that will be able to define the development of better innovations.
Descriptive Statistics 

N 
Range 
Minimum 
Maximum 
Sum 
Mean 
Std. Deviation 
Variance 
Skewness 
Kurtosis 

Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Std. Error 
Statistic 
Std. Error 

Rt 
501 
10.76 
5.29 
5.46 
9.75 
.0195 
1.15161 
1.326 
.225 
.109 
3.326 
.218 
Valid N (listwise) 
501 
Table 7: Summary Statistics for the Rt variable
(Source: Created by Author)
???????? = ???????? − ????????−1/ ????????−1 × 100 is the required formula that is being used for the development of the Rt variable. The Rt variable is showing the return of the investment. Yt is the adjusted closing stock price at the time period of t and Yt_1 is the adjusted closing stock price in the time period of t_1. Through the development of this kind of model, it is possible to know the return and will be able to predict the future consequences of the time series model. Time series is also a part of the linear regression that takes the time into consideration. Through the development of the time series the determination of the lag variable is possible to calculate so that the seasonal adjustments can be easily made.
 Descriptive Statistics and return distributions
Descriptive Statistics 

N 
Range 
Minimum 
Maximum 
Sum 
Mean 
Std. Deviation 
Variance 
Skewness 
Kurtosis 

Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Std. Error 
Statistic 
Std. Error 

Rt_1 
500 
10.76 
5.29 
5.46 
7.56 
.0151 
1.14865 
1.319 
.229 
.109 
3.376 
.218 
Rt 
501 
10.76 
5.29 
5.46 
9.75 
.0195 
1.15161 
1.326 
.225 
.109 
3.326 
.218 
Valid N (listwise) 
500 
Table 7: Summary Statistics for the Rt and Rt_1 variable
(Source: Created by Author)
2) Autoregressive (AR) Model
Correlations 

Rt 
Rt_1 

Pearson Correlation 
Rt 
1.000 
.070 
Rt_1 
.070 
1.000 

Sig. (1tailed) 
Rt 
. 
.060 
Rt_1 
.060 
. 

N 
Rt 
500 
500 
Rt_1 
500 
500 
Model Summary^{b} 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
Change Statistics 
DurbinWatson 

R Square Change 
F Change 
df1 
df2 
Sig. F Change 

1 
.070^{a} 
.005 
.003 
1.14974 
.005 
2.422 
1 
498 
.120 
2.000 
a. Predictors: (Constant), Rt_1 

b. Dependent Variable: Rt 
ANOVA^{a} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
3.202 
1 
3.202 
2.422 
.120^{b} 
Residual 
658.306 
498 
1.322 

Total 
661.508 
499 

a. Dependent Variable: Rt 

b. Predictors: (Constant), Rt_1 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 
95.0% Confidence Interval for B 

B 
Std. Error 
Beta 
Lower Bound 
Upper Bound 

1 
(Constant) 
.018 
.051 
.350 
.727 
.083 
.119 

Rt_1 
.070 
.045 
.070 
1.556 
.120 
.158 
.018 

a. Dependent Variable: Rt 
Walt Disney
Descriptive Statistics 

Mean 
Std. Deviation 
N 

Rt 
.0169 
1.15138 
500 
Rt_1 
.0151 
1.14865 
500 
Correlations 

Rt 
Rt_1 

Pearson Correlation 
Rt 
1.000 
.070 
Rt_1 
.070 
1.000 

Sig. (1tailed) 
Rt 
. 
.060 
Rt_1 
.060 
. 

N 
Rt 
500 
500 
Rt_1 
500 
500 
Model Summary^{b} 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
Change Statistics 
DurbinWatson 

R Square Change 
F Change 
df1 
df2 
Sig. F Change 

1 
.070^{a} 
.005 
.003 
1.14974 
.005 
2.422 
1 
498 
.120 
2.000 
a. Predictors: (Constant), Rt_1 

b. Dependent Variable: Rt 
ANOVA^{a} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
3.202 
1 
3.202 
2.422 
.120^{b} 
Residual 
658.306 
498 
1.322 

Total 
661.508 
499 

a. Dependent Variable: Rt 

b. Predictors: (Constant), Rt_1 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 
99.0% Confidence Interval for B 
Collinearity Statistics 

B 
Std. Error 
Beta 
Lower Bound 
Upper Bound 
Tolerance 
VIF 

1 
(Constant) 
.018 
.051 
.350 
.727 
.115 
.151 

Rt_1 
.070 
.045 
.070 
1.556 
.120 
.186 
.046 
1.000 
1.000 

a. Dependent Variable: Rt 
Conclusion
The wholes study has seen the development of statistics, using two companies Walt Disney and 21^{st} Century Fox. The study has defined the development of the ARIMA model and the linear model taking the lag variable. On the other hand, the development of better technologies will bring in involvement of better designs that will definitely increase the development of better policy formation. The whole study is important in showing the relationship among the daily stock prices of two companies. Various linear regressions has been done and empirical results has been calculated.
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