1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bezimeni [28]
3 years ago
7

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research de

partment at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices(in hundreds of dollars) of these carsAge 8 3 6 9 2 5 6 3Price 18 94 50 21 145 42 36 99(a) Find the regression line with price as a dependent variable and age as an independent variable.(b) Predict the price of a 7 year old car of this model.(c) Estimate the price of an 18 year old car of this model.
Mathematics
1 answer:
sertanlavr [38]3 years ago
8 0

Answer:

a)

Price=150.414-16.626 Age

b)

$34.032

c)

We can't estimate the price of 18 year old car using the above regression equation because the price of 18 year old car falls outside the scope of the model

Step-by-step explanation:

Age(X)   Price(Y)

8              18

3              94

6              50

9              21

2              145

5              42

6              36

3              99

a)

The regression equation can be written as

y=a+bx

b=\frac{sum(x-xbar)(y-ybar)}{sum(x-xbar)^{2} }

a=ybar-bxbar

xbar=sumx/n

xbar=(8+3+6+9+2+5+6+3)/8=5.25

ybar=sumy/n

ybar=(18+94+50+21+145+42+36+99)/8=63.125

x y x-xbar y-ybar (x-xbar)^2 (x-xbar)(y-ybar)

8 18 2.75  -45.125 7.5625        -124.09375

3 94 -2.25 30.875 5.0625        -69.46875

6 50 0.75 -13.125 0.5625        -9.84375

9 21 3.75  -42.125 14.0625        -157.96875

2 145 -3.25 81.875 10.5625        -266.09375

5 42 -0.25 -21.125 0.0625         5.28125

6 36 0.75 -27.125 0.5625        -20.34375

3 99 -2.25 35.875 5.0625        -80.71875

Total             43.5        -723.25

b=\frac{sum(x-xbar)(y-ybar)}{sum(x-xbar)^{2} }

b=-723.25/43.5

b=-16.626

a=ybar-bxbar

a=63.125-(16.626)*5.25

a=150.414

Thus, the required regression equation is

y=150.414-16.626 x

Price=150.414-16.626 Age

b)

For predicting price of 7 years old car we put x=7 in the estimated regression equation

y=150.414-16.626 x

y=150.414-16.626(7)

y=150.414-116.382

y=34.032

The predicted price of a 7 year old car is $34.032.

c)

We can't estimate the price of 18 year old car using the above regression equation because the price of 18 year old car falls outside the scope of the model. The estimate of price is only valid for 2 to 9 year old car.

You might be interested in
What is the average distance of earth to the sun in km
dybincka [34]
The average distance is 3.23!! I found this question very interesting thanks!
7 0
2 years ago
What is the area of a circle with a radius of 3 meters using 3.14 for pie
Scorpion4ik [409]
Wah..I need to ask my bro to answer this.. Brb
6 0
3 years ago
If the radius of a circle is 14 ft, then the diameter of the circle is _____.
miv72 [106K]

14 \times 2 = 28
its B.) 28ft
6 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bn%5E5%7D%7Bn-6%7D%20%2A%20%5Cfrac%7Bn%5E2-6%7D%7Bn%5E8%7D" id="TexFormula1" title="\
ddd [48]

Step-by-step explanation:

Dod you mean

=  \frac{ {n}^{5} }{ {n}^{ - 2} }  \times  \frac{ {n}^{2 - 6} }{ {n}^{8} }

=  {n}^{5 - ( - 2)}  \times  {n}^{2 - 6 - 8}

=  {n}^{7}  \times  {n}^{ - 12}

=  {n}^{7 + ( - 12)}

=  {n}^{ - 5}  =  \frac{1}{ {n}^{5} }

5 0
2 years ago
5 times the difference between 19 and 13
BaLLatris [955]
5 times 19-13 would equal 30 as 19-13 is 6 times 5 =30
6 0
3 years ago
Other questions:
  • The amount of money in your bank account is $512.18. Is the data type discrete or continuous?
    8·1 answer
  • Which decimal is equivalent to 95
    6·2 answers
  • The total of 36, 78, 198, 475, and 620 is <br> A. 1,187. <br> B. 1,407. <br> C. 2,109. <br> D. 1,731
    7·2 answers
  • Last year Anne invested a total of $6,400. She invested part of it in a certificate of deposit that earned 2% interest for the y
    7·1 answer
  • Can somebody explain this to me when 2du = 16xdx ???
    15·1 answer
  • Solve for s.<br>- 6 – 2s = -6​
    10·1 answer
  • Find the midpoint of A and B has coordinates (2,9) and B has coordinates (7,4)
    6·1 answer
  • Mark the absolute maximum point of the graph
    11·1 answer
  • 2x + y = 3
    5·1 answer
  • Mike hiked to a lake in 5.5 hours at an average rate of 4 1/5 miles per hour. Pedro hiked the same distance at a rate of 4 3/5 m
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!