Final Answer:
The effect of this one data point on the value of r and the slope of the regression equation is significant, as it can influence the correlation coefficient (r) and the slope of the regression line.
Step-by-step explanation:
When a single data point is added or removed from a dataset, it can have a notable impact on the value of r and the slope of the regression equation. The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. Adding or removing a data point can alter the overall pattern of the data, potentially changing the correlation coefficient. For instance, if an outlier is added, it can decrease the value of r, indicating a weaker linear relationship.
Similarly, the slope of the regression equation represents the rate of change between the independent and dependent variables. When a single data point significantly deviates from the overall trend, it can influence the slope of the regression line. This is particularly evident in cases where outliers are present, as they can pull the line of best fit towards them, altering the slope of the regression equation.
In summary, a single data point can have a substantial effect on both the correlation coefficient (r) and the slope of the regression equation, potentially altering our understanding of the relationship between variables.