Final answer:
The updated regression analysis shows a stronger correlation and better model for prediction after removing the outlier, indicating the outlier was influential. However, the decision to exclude an outlier should consider its origin and relevance to ensure the resulting model accurately represents the data.
Step-by-step explanation:
When evaluating a new point-of-care (POC) instrument and its corresponding linear regression analysis, it is crucial to consider both the statistical best fit of the data points to the regression line and the influence of outliers on the correlation. In this context, the updated slope of 7.39, which is notably higher compared to the initial slope of 4.83, suggests that the relationship between the variables being studied has strengthened. The increase in the correlation coefficient (r-value) from 0.6631 to 0.9121 denotes a more robust correlation and a better predictive model as r = 0.9121 is closer to the perfect correlation value of 1.
Identifying whether to exclude an outlier relies on the nature of the outlier. If the data point is erroneous or doesn’t reflect the expected trend, removing it can refine the accuracy of the regression model. In the example provided, the removal of the outlier (65, 175) significantly alters the r-value, which indicates that this outlier was influential. Excluding it has led to a more strongly correlated model, as evidenced by the line of best fit.
Nonetheless, the decision to exclude an outlier should be made cautiously. Factors such as the reason behind the outlier's occurrence (measurement error, data entry mistake, etc.) and whether it represents a significant condition relevant to the study should be considered. This careful consideration ensures that the final regression model accurately reflects the true relationship between the variables while maintaining the integrity of the data.