points and their residual values are shown in the table.\n| x | y | residual |\n|----|----|----------|\n| 1…

points and their residual values are shown in the table.\n| x | y | residual |\n|----|----|----------|\n| 1 | 2 | -0.4 |\n| 2 | 3.5 | 0.7 |\n| 3 | 5 | -0.2 |\n| 4 | 6.1 | 0.19 |\n| 5 | 8 | -0.6 |\nwhich residual value is the farthest from the line of best fit?\n○ 0.19\n○ 0.7\n○ 2\n○ 8

points and their residual values are shown in the table.\n| x | y | residual |\n|----|----|----------|\n| 1 | 2 | -0.4 |\n| 2 | 3.5 | 0.7 |\n| 3 | 5 | -0.2 |\n| 4 | 6.1 | 0.19 |\n| 5 | 8 | -0.6 |\nwhich residual value is the farthest from the line of best fit?\n○ 0.19\n○ 0.7\n○ 2\n○ 8

Answer

Explanation:

Step1: Recall residual distance concept

The distance of a residual from the line of best fit is the absolute value of the residual (since residual is ( y - \hat{y} ), and we care about magnitude).

Step2: Calculate absolute values of residuals

  • For residual (-0.4): ( | - 0.4| = 0.4 )
  • For residual (0.7): ( |0.7| = 0.7 )
  • For residual (-0.2): ( | - 0.2| = 0.2 )
  • For residual (0.19): ( |0.19| = 0.19 )
  • For residual (-0.6): ( | - 0.6| = 0.6 )

Step3: Compare with given options

The options are (0.19), (0.7), (2), (8). Wait, but from the table, the residuals are (-0.4), (0.7), (-0.2), (0.19), (-0.6). Wait, maybe the options have a typo? Wait no, the question is which residual value (from the options) is the farthest. Wait, no—wait, the residuals in the table are for the points. Wait, maybe the options are miswritten? Wait no, let's check again. Wait, the residual is ( y - \hat{y} ), so the magnitude (absolute value) tells the distance. Among the options, (0.19) (absolute value (0.19)), (0.7) (absolute value (0.7)), (2) (but there's no residual of (2) in the table? Wait, no—wait, maybe the question is about the options given. Wait, no, the table has residuals: (-0.4), (0.7), (-0.2), (0.19), (-0.6). Wait, the options are (0.19), (0.7), (2), (8). Wait, maybe the options are wrong, but among the residuals in the table, the largest absolute value is (0.7) (wait, no: (|-0.6| = 0.6), (|0.7| = 0.7), (|-0.4| = 0.4), (|-0.2| = 0.2), (|0.19| = 0.19)). Wait, but the options include (0.7), (0.19), (2), (8). But (2) and (8) are not residuals from the table. Wait, maybe the question is misprinted, but assuming the options are as given, but from the table's residuals, the largest absolute residual is (0.7) (since (2) and (8) are not residuals here). Wait, no—wait, maybe the question is about the options, but the table's residuals are for the points. Wait, perhaps the options are supposed to be the absolute values or there's a mistake. But based on the table, the residual (0.7) has absolute value (0.7), which is larger than (0.6), (0.4), (0.2), (0.19). Among the options, (0.7) is a residual (from the table, the second row has residual (0.7)), and its absolute value is (0.7), which is larger than (0.19)'s (0.19), and (2) and (8) are not residuals from the table (so maybe they are incorrect options). So the farthest (largest absolute value) among the valid residuals (from the table) and the options is (0.7).

Answer:

0.7 (the option with residual 0.7, as its absolute value is the largest among the relevant residuals)