Final answer:
The residuals for the ordered pairs (3,0.42) and (3,0.3) cannot be definitively determined without the equation of the line of best fit. To identify an outlier, the residual is compared to a threshold, commonly two standard deviations from the line of best fit. Without the predicted values, we cannot choose an option from the given choices.
Step-by-step explanation:
To find a residual for a given ordered pair, you subtract the predicted value (usually represented on the line of best fit on a scatter plot) from the observed value. The formula for the residual is:
Residual = Observed value - Predicted value
However, exact residuals cannot be calculated for the ordered pairs (3,0.42) and (3,0.3) without knowing the equation of the line of best fit. This equation would provide the predicted values for when the x-value is 3, which we can then use to find the residuals by plugging into the formula above. Without the equation or the predicted values, one cannot definitively state which residuals are correct.
When identifying an outlier, we calculate the residual for each data point and compare it to a certain threshold, such as two standard deviations from the predicted values on the line of best fit. If a residual is greater than this threshold, the corresponding data point can be classified as an outlier, which can affect the best-fit line significantly.
The method of numerical identification of outliers involves comparing calculated residuals to a value that is twice the standard deviation from the mean of these residuals (often denoted as 2s). If a residual is beyond this range, it indicates an outlier, which may warrant further investigation and could affect the final analysis and interpretation of the data set.