Question

Citations are "speeding tickets." You may fill in the table to help you answer the question.Approximate the data using the line y = 0.25x + 3. Find the data point that has the residual with the greatest absolute value. Give that data point and its associated residual.A.) Data point: (10, 10); Residual = 4.50B.) Data point: (15, 5); Residual = 6.75C.) Data point: (20, 6); Residual = -2.00D.) Data point: (5, 3); Residual = -1.25

Answer 1

Data point (10, 10) has the greatest absolute residual value of 4.5 when compared with the predicted value using the line of best fit y = 0.25x + 3.

Step-by-step explanation:

The student is asking about determining which data point has the greatest absolute residual value, considering the provided line of best fit, y = 0.25x + 3. The residual for a data point is calculated by taking the actual y value from the data and subtracting the predicted y value (ŷ) from the regression line equation. To find the data point with the greatest absolute residual, you compare the actual y value with its corresponding predicted y (ŷ) value.

For example, from the options:

• A) For (10, 10), the predicted y is 0.25(10) + 3 = 5.5, so the residual is 10 - 5.5 = 4.5
• B) For (15, 5), the predicted y is 0.25(15) + 3 = 6.75, so the residual is 5 - 6.75 = -1.75 (the absolute value is 1.75, not 6.75 as mistakenly written)
• C) For (20, 6), the predicted y is 0.25(20) + 3 = 8, so the residual is 6 - 8 = -2
• D) For (5, 3), the predicted y is 0.25(5) + 3 = 4.25, so the residual is 3 - 4.25 = -1.25

Considering all options, data point (10, 10) with a residual of 4.5 has the greatest absolute residual value.