Answer:
b= - 1.26317
a = 17.237
b. The selling price (in dollars) of a 7-year-old car
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1263.17 $ decreases per year
Step-by-step explanation:
Let y be the selling price in thousands and x be the age in years
Car Age Selling Price
(years) ($000) XY X²
X Y
1 9 11.1 99.9 81
2 5 9.5 47.5 25
3 13 4.4 57.2 169
4 17 4.4 74.8 289
5 7 8.06 56.42 49
6 1 2.07 2.07 1
7 1 0.6 0.6 1
8 14 8.1 113.4 196
9 12 8.1 97.2 144
10 17 4.8 81.6 289
11 4 12.5 50 16
<u>12 4 10.7 42.8 16 </u>
<u>∑ 97 84.33 723.49 1276 </u>
The estimated regression line of Y on X is
Y= a +bX
and the two normal equations are
∑ y= na + b∑X
∑XY= a∑X + b∑X²
Now
X`= ∑X/n = 97/12= 8.083
b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²
b= 723.49 - (97)(84.33)/ 12(1276) - (97)²
b= -7456.52/ 5903
b= - 1.26317
a= Y`- b X`
a= 7.0275 - (-- 1.26317)8.083
a = 17.237
Y = 17.237 - 1.26317 X
y= - 1.26317 X + 17.237
b. The selling price (in dollars) of a 7-year-old car
y = - 1.26317 (7) + 17.237
y= 8.39481
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1.26317 *1000= 1263.17 $ decreases per year
