Assumptions tests for regression analysis APPENDIX

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APPENDIX

Assumptions tests for regression analysis

Conceptual framework related to board gender diversity, social shareholder activism and CSP. Assumptions tests for hypothesis 1a and 2a.

I tested the first assumption for normality of residuals by using a Shapiro-Wilk test and I found a statistically significant result (p<0.01) for both the dependent variable and the residuals of that variable, which indicate that they are not normally distributed. In accordance to Field (2013), this is not a concern as the Shapiro-Wilk can demonstrate significant results with deviations from normality when there is a large sample size. As the normality is not a necessary requirement in order to run a linear regression analysis and, also, the nature of the data does not favour expectations for normality, this result is not considered as an issue and, thus, I can proceed (Lumley, Diehr, Emerson, & Chen, 2002). However, by observing the histogram it is apparent that the standardized residuals are almost normally distributed as they appear to form a bell-shaped curve. From the P-P plot it is apparent that there are not drastic deviations and from the scatterplot an almost rectangular shape can be observed and, hence, it can be further supported that I can indeed proceed with the interpretation of the results of the regression analysis.

Additionally, the second assumption of homoscedasticity has been also checked from the scatterplot and it is not violated as it has a rectangular shape.

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

CSP 0.2 491 0.00 0,781 491 0.00

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Also, the assumption of multicollinearity is not an issue as from the table of correlations (Table 2) presented in the results section, there is not any value between the independent variables that exceed 0.7. Also, multicollinearity was checked by using Variation Inflation Factors (VIF). As there is not any value of VIF above 10.00 (Marano & Kostova, 2016), multicollinearity is not an issue.

Test for Multicollinearity

Model 1 Model 2 Model 3 Model 4 Variables Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF

Control Board Size 0,768 1,303 0,768 1,303 0,765 1,308 0,761 1,315 Log Number of employees 0,672 1,488 0,660 1,516 0,645 1,550 0,645 1,550 ROA 0,818 1,223 0,811 1,234 0,809 1,236 0,807 1,238

Log Firm age 0,912 1,097 0,888 1,126 0,887 1,127 0,886 1,128

mining 0,810 1,235 0,810 1,235 0,809 1,236 0,805 1,242 construction 0,980 1,020 0,977 1,024 0,977 1,024 0,976 1,024 transportation public utilities 0,819 1,221 0,818 1,222 0,817 1,223 0,816 1,226 wholesale trade 0,953 1,050 0,951 1,051 0,946 1,058 0,945 1,058 retail_trade 0,804 1,244 0,803 1,246 0,797 1,254 0,797 1,255 finance insurance real estate 0,705 1,419 0,704 1,421 0,701 1,427 0,701 1,427 services 0,835 1,197 0,835 1,197 0,830 1,205 0,830 1,205 Independent Board Gender Diversity 0,916 1,092 0,916 1,092 0,910 1,099 Moderator 0,913 1,095 0,716 1,397 Social shareholder activism Interaction 0,771 1,297 Board Gender diversity x Social shareholder activism

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Regarding the assumption for the independence of errors, as the value of Durbin-Watson test for each model is in the range between 1.5 and 2.5 (Field, 2013), this assumption is satisfied.

Test for Independence of

Errors

Model 1 Model 2 Model 3 Model 4

Durbin-Watson

Test 1,947 1,942 1,947 1,951

Conceptual framework related to board gender diversity, social shareholder proposals and Social CSP. Assumptions tests for hypothesis 1a and 2b.

I tested the first assumption for normality of residuals by using a Shapiro-Wilk test and I found a statistically significant result (p<0.01) for both the dependent variable and the residuals of that variable which indicate that they are not normally distributed. In accordance to Field (2013), this is not a concern as the Shapiro-Wilk can demonstrate significant results with deviations from normality when there is a large sample size. As the normality is not a necessary requirement in order to run a linear regression analysis and the nature of the data do not favour expectations for normality, this result is not considered as an issue and thus I can proceed (Lumley et al., 2002). However, by observing the histogram it is apparent that the standardized residuals are almost normally distributed as they appear to form a bell-shaped curve. From the P-P plot it is apparent that there are not drastic deviations and from the scatterplot an almost rectangular shape can be observed and, hence, it can be further supported that I can indeed proceed with the interpretation of the results of the regression analysis.

Additionally, the second assumption of homoscedasticity has been also checked from the scatterplot and it is not violated as it has a rectangular shape.

Social CSP 0,139 491 0,000 0,879 491 0,000

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Also, the assumption of multicollinearity is not an issue as from the correlations table (Table 2) presented in the results section, there is not any value between the independent variables that exceed 0.7. Also, multicollinearity was checked by using Variation Inflation Factors (VIF). As there is not any value of VIF above 10.00 (Marano & Kostova, 2016), multicollinearity is not an issue.

Test for

Multicollinearity

Log Firm age 0,912 1,097 0,888 1,126 0,888 1,126 0,888 1,126

mining 0,810 1,235 0,810 1,235 0,810 1,235 0,810 1,235 construction 0,980 1,020 0,977 1,024 0,977 1,024 0,977 1,024 transportation public utilities 0,819 1,221 0,818 1,222 0,813 1,230 0,812 1,231 wholesale trade 0,953 1,050 0,951 1,051 0,949 1,054 0,949 1,054 retail trade 0,804 1,244 0,803 1,246 0,802 1,246 0,801 1,248 finance insurance real estate 0,705 1,419 0,704 1,421 0,703 1,423 0,702 1,424 services 0,835 1,197 0,835 1,197 0,835 1,198 0,834 1,199 Independent Board Gender Diversity 0,916 1,092 0,914 1,094 0,913 1,095 Moderator 0,936 1,069 0,764 1,309 Social shareholder proposals Interaction 0,805 1,242 Board Gender diversity x Social shareholder proposals

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linear relationship between the independent (board gender diversity) and the dependent variable (CSP) as it is significant (p<0.01).

Test for Independence of

Errors

Durbin-Watson Test 2,07 2,07 2,072 2,076

Conceptual framework related to board gender diversity, environmental shareholder proposals and environmental CSP. Assumptions tests for hypothesis 1c and 2c.

I tested the first assumption for normality of residuals by using a Shapiro-Wilk test and I found a statistically significant result (p<0.01) for both the dependent variable and the residuals of that variable which indicate that they are not normally distributed. In accordance to Field (2013) this is not a concern as the Shapiro-Wilk can demonstrate significant results with deviations from normality when there is a large sample size. As the normality is not necessary requirement in order to run a linear regression analysis and the nature of the data do not favour expectations for normality, this result is not considered as an issue and thus I can proceed (Lumley et al., 2002). However, by observing the histogram it is apparent that the standardized residuals are almost normally distributed as they appear to form a bell-shaped curve. From the P-P plot it is apparent that there are not drastic deviations and from the scatterplot an almost rectangular shape can be observed and, hence, it can be further supported that I can indeed proceed with the interpretation of the results of the regression analysis.

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The assumption of linearity was checked as well. By observing the table of correlations (Table 2) presented in the results section, it is obvious that there is a linear relationship between the independent (board gender diversity) and the dependent variable (CSP) as it is significant (p<0.01).

Test for

Multicollinearity

Log Firm age 0,912 1,097 0,888 1,126 0,888 1,126 0,888 1,126

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Test for Independence

of Errors

Durbin-Watson Test 1,69 1,7 1,706 1,707

REFERENCES

Field, A. 2013. Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications. https://books.google.nl/books?id=c0Wk9IuBmAoC.

Lumley, T., Diehr, P., Emerson, S., & Chen, L. 2002. The importance of the normality assumption in large public health data sets. Annual Review of Public Health, 23: 151– 169.