computing residuals from an equation and table\njohn estimates the value of his car over time. the equation…

computing residuals from an equation and table\njohn estimates the value of his car over time. the equation for the line of best fit is approximated as y = - 2.9x + 17.7, where y represents the value, in thousands of dollars.\nwhat values complete the residual table?\nage (years) given value predicted value residual\n1 15 a 0.2\n2 12 11.9 b\n3 9 c 0\n4 5 6.1 d\n5 4 3.2 0.8

computing residuals from an equation and table\njohn estimates the value of his car over time. the equation for the line of best fit is approximated as y = - 2.9x + 17.7, where y represents the value, in thousands of dollars.\nwhat values complete the residual table?\nage (years) given value predicted value residual\n1 15 a 0.2\n2 12 11.9 b\n3 9 c 0\n4 5 6.1 d\n5 4 3.2 0.8

Answer

Explanation:

Step1: Calculate value of a

Substitute $x = 1$ into $y=-2.9x + 17.7$. $y=-2.9\times1+17.7=14.8$ Since residual = given - predicted and residual is 0.2, given is 15. So predicted $a = 15 - 0.2=14.8$

Step2: Calculate value of b

Residual $b=$ given - predicted. Given is 12 and predicted is 11.9. $b=12 - 11.9 = 0.1$

Step3: Calculate value of c

Since residual is 0, given = predicted. Given is 9, so $c = 9$

Step4: Calculate value of d

Residual $d=$ given - predicted. Given is 5 and predicted is 6.1. $d=5 - 6.1=-1.1$

Answer:

$a = 14.8$ $b = 0.1$ $c = 9$ $d=-1.1$