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
Rom4ik [11]
3 years ago
10

Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel align

ment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
Weekly Usage
(hours) Annual Maintenance
Expense ($100s)
13 17.0
10 22.0
20 30.0
28 37.0
32 47.0
17 30.5
24 32.5
31 39.0
40 51.5
38
40.0
(a) Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage. What is the estimated regression model?
Let x represent the number of hours of weekly usage.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
(b) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(c) How much of the variation in the sample values of annual maintenance cost does the model you estimated in part (b) explain?
If required, round your answer to two decimal places.
(d) If the maintenance contract costs $3000 per year, would you recommend purchasing it? Explain.
Mathematics
1 answer:
sasho [114]3 years ago
4 0

Answer:

Step-by-step explanation:

Hello!

The given data corresponds to the variables

Y:  Annual Maintenance  Expense ($100s)

X: Weekly Usage  (hours)

n= 10

∑X= 253; ∑X²= 7347; \frac{}{X}= ∑X/n= 253/10= 25.3 Hours

∑Y= 346.50; ∑Y²= 13010.75; \frac{}{Y}= ∑Y/n= 346.50/10= 34.65 $100s

∑XY= 9668.5

a)

To estimate the slope and y-intercept you have to apply the following formulas:

b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95

a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53

^Y= a + bX

^Y= 10.53 + 0.95X

b)

H₀: β = 0

H₁: β ≠ 0

α:0.05

F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}

F= 47.62

p-value: 0.0001

To decide using the p-value you have to compare it against the level of significance:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The decision is to reject the null hypothesis.

At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.

c)

The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:

R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86

This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X

d)

Without usage, you'd expect the annual maintenance expense to be $1053

If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553

If used 1000 hours weekly the expected maintenance expense will be $96053

It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.

You might be interested in
I need help with number 33!!!
sveta [45]

Area of Big Rectangle                                     Area of Small Rectangle

A = L x w                                                           A = L x w

 = (25 + 2w)(10 + 2w)                                           = 25 x 10

 =   250 + 50w + 20w + 4w²                               = 250

       Big - Small  

74 = 250 + 70w + 4w² - 250

74 = 4w² + 70w

0 = 4w² + 70w - 74

   = 2(2w² + 35w - 37)

  = 2[2w² -2w  |  +37w - 37]

  = 2[2w(w - 1) |  +1(w - 1)]

  = 2(2w + 1)(w - 1)

0 = 2                                   0 = 2w + 1                                     0 = w - 1

FALSE so disregard          w = -1/2                                         w = 1

                                         NEGATIVE so disregard

Answer: 1 meter

5 0
3 years ago
Tina wants to save money for school.Tina invests $1,000 in an account that pays an interest rate of 6.75%. How many years will i
shepuryov [24]
It take 2.75 years
Step by step explanation:
18600$ / 1000$x6.75%=2.75
5 0
3 years ago
Write an equation for the vertical line that contains point E(-12, 7). Is anybody able to help?
BigorU [14]

Answer:

x = -12

Step-by-step explanation:

Vertical lines take the form of x = something and horizontal lines take the form of y = something

Why is this? Notice that whenever you make a horizontal line on a graph and select virtually any point that's on that line, all of the points you pick will have the same y value. Try to imagine the same thing with a vertical line, are the results the same?

So the line x = -12 (we got -12 from the coordinate that was given to us on the question prompt) is a vertical line that passes through virtually all possible y values (from positive infinity to negative infinity, or vice-versa) which means that the question prompt having given us the y value was negligible.

Good luck!

5 0
3 years ago
Darlene has 59 pages to type. so far she gas type 23 pages. what fraction of the job is finished ​
coldgirl [10]

Answer:

\frac{23}{59}

Step-by-step explanation:

A fraction can be found be taking the current amount over the total amount:

\frac{current}{total}=\frac{23}{59}

Since Darlene has only typed 23 pages out of 59, her fraction is 23 over 59.  Fractions must always be in simplest form, which means that both the numerator and denominator can no longer be divided by the same factor.  Since the numbers 23 and 59 are both prime and have no other factors other than 1 and themselves, the fraction 23/59 is in simplest form.

4 0
3 years ago
Witch set of orderd pairs contains only points that are on the graph of the function y=12-3x
anygoal [31]
You can try then by plotting the points in. 
The answer is C

Make sure by plotting in the points, lets take (-5,27)
y = 12 -3(-5)
y = 12 + 15
y = 27
27 = 27
This is correct 

Lets try (-1,15)
y = 12 -3(-1)
y = 12 + 3 
y = 15 
15 = 15
This is correct 

Lets try (8,-12)
y = 12 -3(8)
y = 12 - 24 
y = -12 
-12 = -12
This is correct too. 

The correct ordered pairs are <span>C(-5,27),(-1,15),(8,-12)</span>
5 0
3 years ago
Other questions:
  • Expand the expression log (xy/4)<br><br> please show your work trying to lean it
    10·1 answer
  • What is the slope of this line??
    5·2 answers
  • For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the so
    13·1 answer
  • Help please I don’t understand this! Giving brainliest!
    15·2 answers
  • PLEASE ANSWER!!! How many lines can be drawn through point C that are parallel to line L
    8·1 answer
  • A triangle has a base of 15 feet and a height of 9 feet. What is the area of the triangle? Label the figure. Write the formula,
    5·1 answer
  • A circular sector has a central angle of π9 radians and a radius of 13 cm. What is the area of the sector? Use 3.14 for pi. Roun
    8·1 answer
  • Can u pls help me with this question asap ​
    12·1 answer
  • Help due tn
    11·1 answer
  • I NEED THE RIGHT ANSWER ASAP.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!