For the data in the table below, find the sum of the absolute deviations for the predicted values given by the median-median line, y equals 3.6 x minus 0.4.
x y
1 3
2 7
3 9
4 14
5 15
6 21
7 25
(1 point)
Responses
5.7145
5.7145
4.8
4.8
4
4
0.0005
To find the sum of the absolute deviations for the predicted values given by the median-median line, we first need to calculate the predicted y values using the formula y = 3.6x - 0.4.
Predicted y values:
1. y = 3.6(1) - 0.4 = 3.2
2. y = 3.6(2) - 0.4 = 6.8
3. y = 3.6(3) - 0.4 = 10.4
4. y = 3.6(4) - 0.4 = 14.0
5. y = 3.6(5) - 0.4 = 17.6
6. y = 3.6(6) - 0.4 = 21.2
7. y = 3.6(7) - 0.4 = 24.8
Now calculate the absolute deviations for each predicted y value:
1. |3 - 3.2| = 0.2
2. |7 - 6.8| = 0.2
3. |9 - 10.4| = 1.4
4. |14 - 14.0| = 0.0
5. |15 - 17.6| = 2.6
6. |21 - 21.2| = 0.2
7. |25 - 24.8| = 0.2
Sum of absolute deviations = 0.2 + 0.2 + 1.4 + 0.0 + 2.6 + 0.2 + 0.2 = 5.8
Therefore, the sum of the absolute deviations for the predicted values given by the median-median line is 5.8.