Final answer:
Without the specific prediction equation for the given data point (200, 978), we cannot calculate the approximate value of the residual. Residuals are the difference between observed values and their predicted values from the regression line. A prediction equation or full data set is needed to compute the residual for any observed data point.
Step-by-step explanation:
To calculate the approximate value of the residual for the observed data value (200, 978), you need the predicted value (ŷ) from the line of best fit. The residual is the difference between the observed value (y) and the predicted value (ŷ), which is calculated as y - ŷ. The information provided does not include a direct formula or predicted value for the specific data point in question, so with the given information, we cannot provide an exact answer for the residuals associated with (200, 978).
To provide an accurate residual value, we would need the equation of the linear regression line and use it to calculate the predicted value when x = 200. Once we have the predicted value, ŷ, we would subtract it from the actual observed value, 978, to obtain the residual. However, one such calculation is shown previously as:
ŷ = 173.51 + 4.83(73) = 179.08.
That formula suggests that if for example, a predicted value for x = 73 is given, we can calculate the predicted final exam score for a statistics student. But to apply this to the given data point (200, 978), we would need to adjust the formula for x = 200 or be given the specific formula that applies to this data set.