Question

the table and scatter plot show the average monthly temperature, ( x ), and a familys monthly heating cost, ( y ), for 10 different months. the equation of the line of best fit is ( y = -0.9x + 79.84 ).

average monthly temperature, ( x ) (in ( ^circ )f)	monthly heating cost, ( y ) (in dollars)
34.4	67.00
36.5	41.53
40.8	30.04
45.5	52.02
49.8	30.45
50.1	15.20
50.7	50.92
56.7	23.72
60.6	30.50

(scatter plot: x - axis: average monthly temperature (in ( ^circ )f), y - axis: monthly heating cost (in dollars))
use the equation of the line of best fit to fill in the blanks below. give exact answers, not rounded approximations.

average monthly temperature (in ( ^circ )f)	observed monthly heating cost (in dollars)	predicted monthly heating cost (in dollars)	residual (in dollars)
34.4

Explanation:

Step1: Get observed cost from table

For $x=26.6$, observed $y=51.00$; for $x=34.4$, observed $y=67.00$.

Step2: Calculate predicted cost for $x=26.6$

Substitute $x=26.6$ into $y=-0.9x+79.84$:
$y=-0.9(26.6)+79.84 = -23.94 + 79.84 = 55.90$

Step3: Calculate residual for $x=26.6$

Residual = Observed - Predicted:
$51.00 - 55.90 = -4.90$

Step4: Calculate predicted cost for $x=34.4$

Substitute $x=34.4$ into $y=-0.9x+79.84$:
$y=-0.9(34.4)+79.84 = -30.96 + 79.84 = 48.88$

Step5: Calculate residual for $x=34.4$

Residual = Observed - Predicted:
$67.00 - 48.88 = 18.12$

Answer:

Average monthly temperature (in °F)	Observed monthly heating cost (in dollars)	Predicted monthly heating cost (in dollars)	Residual (in dollars)
34.4	67.00	48.88	18.12