Final answer:
Finding a linear equation using a single data point (8, $56) is not possible; you need at least two points to create a line. You enter the complete data into a calculator, create a scatter plot, and use a regression function to find the least-squares regression line. If an outlier affects the data significantly, recalculating without it can yield a more accurate line and correlation coefficient.
Step-by-step explanation:
To find a linear equation using the data point (8, $56), you need more than one data point to create a scatter plot and determine a line of best fit. However, if we refer to an example with more data points, the process would include the following steps:
- Enter the data into a calculator and make a scatter plot.
- Use the calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot from Part A.
When outliers are present, as in the point (65, 175), it's essential to determine whether they are influential points by deleting the outlier from the dataset and recalculating the regression line and correlation coefficient. Doing so can significantly change the slope and the correlation coefficient (r-value) indicating the strength of the linear relationship.
For example, after recalculating without the outlier, you might find that the new best-fit line is ŷ = 355.19 + 7.39x and the correlation coefficient improves to r = 0.9121. This suggests that the outlier was indeed influential in the original dataset.