# Academic Excellence, Website Quality, SEO Performance: Is there a Correlation?
## 4 Results
First, we need to calculate the Pearson correlation coefficient to see if there is a correlation between them. The Pearson correlation is 0.266 at 0.007 2-sided significance, which shows a weak but statistically significant result. At the model summary in Table 10, we can observe that according to \(\mathbb{R}^{2}\) the 7% of the total variance of website quality is due to ARWU with standard estimation error of 10.35 which is a slightly weak outcome. The variance analysis in Table 11, examines the null hypothesis that there is no linear relationship between website quality and ARWU. The result F (1.98) = 7.04, p = 0.007 \(<\) 0.05 is statistically significant and we reject the null hypothesis. Therefore, our predictive model is considered sufficient to continue the additional evaluation of simple regression. In the following Table 11 it is depicted that the value of B is 0.224 (0.007 \(<\) 0.01). We also find that there is a positive correlation between the two variables, that is, for each unit increasing ARWU we have an increase of 0.22 units of website quality. The regression analysis test between ARWU and website quality is depitcted in the histogram and scatterplot of Figure 1. The histogram shows that the slightly skewed, distribution satisfies the normality assumption. The scatterplot has the predicted values in the x-axis and residuals on the y-axis as shown below. Although it shows a slight \"heteroscedasticity\" (meaning that the residuals get larger as the prediction moves from large to small), the regression coefficients still have a correlation. However, we cannot use this model as a strong and accurate predictive approach. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **R** & **R Square** & **Adjusted R Square** & **Std. Error of the Estimate** \\ \hline
1 &.266 a &.071 &.062 & 10.35 \\ \hline \hline \end{tabular} a. Predictors: (Constant), Shanghai rating.  
\end{table} 
Table 10: Model summary of simple regression analysis. Figure 1: **(a)** The histogram of the standardized residuals shows a normal distribution. **(b)** The scatterplot shows that there are no clear patterns except a slight ”heteroscedasticity” which makes this predictive model uncertain. To investigate the influence of weights on the outcome of the relationship between Shanghai ranking and WQR, SEOPR, and OWR, we repeated the test using flat weights. Table 12 shows that the Spearman correlation coefficient decreases for all variables WQR, SEOPR, an OWR in a similar way. This proves that the correlation between Shanghai ranking, WQR and QWR exists and the use of weights makes this relationship more explicit. We found that ARWU ratings and website quality are correlated. However, investigating the correlation between website quality and SEO performance can reveal further information. The aim of this step is to examine these variables' association in order to draw useful conclusions about their co-variation. The simple regression follows by setting website quality as the independent variable and SEO performance as the dependent variable. First the Pearson correlation is r (100) = 0.40 (Sig. 2-sided 0.000) which means that we have a positive correlation between them. At the model summary in Table 13, the R\({}^{2}\) is 0.165 meaning that 16.5% of the total variance of SEO performance is due to website quality and error estimation is 5.48. The ANOVA examines the null hypothesis that there is no linear relationship between SEO performance and website quality. The result F (1.98) = 19.36 p = 0.000 \(<\) 0.05 is statistically significant so we reject the null hypothesis. In the Table 14 it is depicted that the value of B is 0.22 (0.0000 \(<\) 0.01) which means that variable website quality rating can be a predictor of variable SEO performance. Also, there is a positive correlation between the two variables. These results are visualized in Figure 2.