It is widely believed that there is a certain connection between the change in the solar rotation rate and solar activity, but the research conclusions of different scholars are contradictory: some believe that the two are positively correlated, while some believe that the two are negatively correlated. Further analysis is needed to reliably establish the actual relationship. This paper uses EEMD (Ensemble Empirical Mode Decomposition) and other methods to calculate and analyze the correlation between the solar rotation rate and sunspot number, as well as the phase relationship, in order to explore the relationship between the change in the solar rotation rate and solar activity. It is found that the long-term trend components of the two are significantly negatively correlated; the observed solar rotation rate lags behind the sunspot variation by about 2 years and shows a significant negative correlation, with a sub-significant positive correlation about 3 years ahead; the analysis of the correlation between sunspots and solar rotation rate within each week of the 12th--23rd weeks of solar activity shows that the relationship between the two is complex, but the negative correlation is more significant. This provides a new basis for further understanding of the causal link between changes in solar activity and changes in solar rotation rate.