(PDF) A Study on Multiple Linear Regression Analysis
Added on 2021-06-07
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Part 1:Model Description:Multiple OLS is a statistical method that predicts the outcome of a response variable bycombining many explanatory variables. MLR targets to model the linear relationship betweenexplanatory variables accompanied by the response, variable. To predict log salary for the CEO, we used a multiple regression model with the followingvariables: return for assets for the firm; the log of total assets of the company; volatilitymeasured by the daily return; the age of the CEO for the firm, CEO female and extent ofindependent directors.Model Summary:ModelR.R SquareAdj. R SquareStandard error of theEst.1.0.72.52.472566.09Interpretation:The OLS regression model is summarised in the table above. The percentage of variance in theCEO pay (dependent variable) that predicted using explanatory variables is known as R-Square(female CEO, board independence, CEO age, volatility, roa, firm size). The R-squared value is0.526, indicating that the predictors account for 52 percent of the variance in CEO salary.As more predictors are being added to the model, each one will, by chance, explain the presenceof some of the variance among dependent variables. Though some of the increment in R-squarewould be due to chance variation in that specific test, one may proceed to include indicators tothe demonstrate variable, which would help to improve the predictors' ability to explaindependent variable.
Adjusted R-square is attempt to quantify R-squared for the population with a more accuratevalue. In our model, the modified R square value is 0.47. The standard deviation’s value of theerror term is 2566.09, and the standard error of the estimation is 2566.09.ANOVA:ModelsSum of SquaresDfMean SquareFSig.Regression.415884877.326.0069314146.2210.52.00Residual.375335876.6757.006584839.94Total.791220754.0063.00Interpretation:The result of the ANOVA is shown in the table above. In the second column, we are having asource of variation, The total SS is 791220754.00, which is divided into regression and residualparts, the SS for residual is 375335876.67 with 57 degrees of freedom while SS for regression is415884877.32 having 6 degrees of freedom. MS are calculated so that you can test theimportance of the predictors for the model by dividing by the Mean Square Regression withMean Square Residual and computing F ratio.The p-value which is linked with the F value is 0, which is very small. Thus we can assume thatthe independent variables is accurately predicting the dependent variable since the p-value is lessthan alpha 0.05. We would argue that the factors female CEO, board independence, CEO age,volatility, roa, and firm size can be used to predict CEO pay with reasonable accuracy.Parameter Estimates:
CoefficientsModelsUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd. ErrorBeta(Constant)-8735.425029.43-1.73.08Roa13.9056.22.02.247.80Firm size1239.43290.21.484.27.00Volatility-108.8328.16-.38-3.86.00Ceo age53.3574.11.06.72.47Boardindependence40.3740.30.101.00.32Female ceo-3005.911345.06-.20-2.23.02Interpretation:We will get parameter estimates from the table above. Relationship between independentvariables and dependent variable is revealed unstandardized coefficients. The values for theregression equation for forecasting dependent variable by use of independent variable are listedabove. Because they are measured in their natural units, they are referred to as unstandardizedcoefficients. As a result, since the coefficients can be measured on different scales, they cannotbe compared to determine which one is more powerful in the model.Betas are coefficients that are attained if all of the variables in the regression were standardized,it includes the dependent and independent variables, and the regression was run. By comparedsize of coefficients to check which one has more of an effect by institutionalizing factorssometime recently running regression.These estimates show how much of an increase in CEO pay can be expected by a one-unitincrease in the predictor, for example, a one-unit increase in the firm size would result in a
1239.43 increase in CEO pay, similarly, a one-unit increase in the firm's return on assets percentwould result in a 13.90 increase in CEO pay.Statistically important coefficients have p-valuesless than alpha. Firm size, volatility, and female CEO are all important coefficients in our model.Because the p-value is greater than .05, therefore, coefficients for roa, CEO age, and boardindependence are not statistically significant at the 0.05 level.Part 2: From 3/10/2019 to 3/10/2021, we received commodity price data from World Bank’s website.As commodities, we used sugar, wheat, and chicken.Weak form efficiency:Weak shape effectiveness attests that past cost developments, volume, and profit informationhave no bearing on a stock's cost and so cannot be utilized to estimate its future heading. One ofthe three degrees of compelling advertise hypothesis is weak frame effectiveness (EMH). Thearbitrary walk hypothesis, moreover known as frail frame productivity, states that future securitycosts are arbitrary and unaffected by past occasions. Advocates of weak frame effectivenessaccept that stock prices represent all current data, which past data has no bearing on current
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