Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.
Repair Time in Hours Months Since Last Service Type of Repair Repairperson
2.9 2 Electrical Dave Newton
3 6 Mechanical Dave Newton
4.8 8 Electrical Bob Jones
1.8 3 Mechanical Dave Newton
2.9 2 Electrical Dave Newton
4.9 7 Electrical Bob Jones
4.2 9 Mechanical Bob Jones
4.8 8 Mechanical Bob Jones
4.4 4 Electrical Bob Jones
4.5 6 Electrical Dave Newton
a) Ignore for now the months since the last maintenance service (x1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x2). Recall that x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical.
b) Does the equation that you developed in part (a) provide a good fit for the observed data? Explain.
c) Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
d) Does the equation that you developed in part (c) provide a good fit for the observed data? Explain.
e) Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service.
f) At the .05 level of significance, test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable.
g) Is the addition of the independent variable x3, the repairperson who performed the service, statistically significant? Use α = .05. What explanation can you give for the results observed?
Answers
a. We can use the following equation y = b₀ + b₁ * x₂
b. The p-value indicates the significance of the relationship.
c. We can use the following equation y = b₀ + b₁ * x₃
d. Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.
e. We can use the following equation y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃
f. A p-value below the significance level (0.05) would indicate a significant relationship.
g. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.
What is linear regression?The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.
a) To develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x₂), we can use the following equation:
y = b₀ + b₁ * x₂
where y represents the repair time and x₂ is the type of repair (0 for mechanical, 1 for electrical).
b) To determine if the equation developed in part (a) provides a good fit for the observed data, we need to analyze the statistical measures such as R-squared and p-value. R-squared measures the proportion of variance in the dependent variable (repair time) explained by the independent variable (type of repair). The p-value indicates the significance of the relationship.
c) To develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service (x₃), we can use the following equation:
y = b₀ + b₁ * x₃
where y represents the repair time and x₃ is the repairperson (0 for Bob Jones, 1 for Dave Newton).
d) Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.
e) To develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service (x₁), the type of repair (x₂), and the repairperson (x₃), we can use the following equation:
y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃
where y represents the repair time, x₁ is the number of months since the last maintenance service, x₂ is the type of repair, and x₃ is the repairperson.
f) To test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable, we can perform a hypothesis test using the F-test or t-test and examine the p-value associated with the test. A p-value below the significance level (0.05) would indicate a significant relationship.
g) To determine if the addition of the independent variable x₃ (repairperson) is statistically significant, we can perform a hypothesis test specifically for the coefficient associated with x₃. The p-value associated with this coefficient will indicate its significance. A p-value below the significance level (0.05) would suggest that the repairperson variable has a statistically significant effect on the repair time. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.
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Related Questions
The largest number which divides 70and 125,leaving reminders 5 and 8 respectivly is
Answers
The largest number which divides 70 and 125 , leaving remainders of 5 and 8 is 13.
To find the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, we can follow these steps:
Subtract the remainders from their respective numbers:
70 - 5 = 65 and
125 - 8 = 117.
Find the factors of each resulting number:
Factor of 65 = 5 and 13
factor of 117 = 3 and 13
Determine the highest common factor (HCF) of the resulting factors:
The HCF of 5 = 1
the HCF of 13 = 1
the HCF of 3 = 3
the HCF of 13 = 13
Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, is 13.
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What is the nearest degree of a base angle of an isosceles triangle if each leg is 30 and the altitude to the base is 20?
Answers
In an isosceles triangle, the base angles are congruent. Let's denote the base angle as θ. We can use the trigonometric relationship between the sides and angles of a right triangle to find the value of θ.
In this case, we have an isosceles triangle with legs of length 30 and an altitude to the base of length 20. The altitude forms a right triangle with one leg equal to half the base (15) and the hypotenuse equal to one of the legs (30).
Using the trigonometric relationship sine (sin), we can write:
sin(θ) = opposite/hypotenuse
sin(θ) = 20/30
sin(θ) = 2/3
To find the value of θ, we can take the inverse sine (sin^(-1)) of both sides:
θ = sin^(-1)(2/3)
Using a calculator, we find:
θ ≈ 41.81 degrees
Therefore, the nearest degree of a base angle of the isosceles triangle is 42 degrees.
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If school starts at 8:30 a.m. and ends at 3:20 p.m., how long is the school day?
6 hours and 10 minutes
11 hours and 50 minutes
5 hours and 10 minutes
6 hours and 50 minutes
Answers
Answer:
50 min 5 hours
Step-by-step explanation:
Answer: 6 hours and 50mins
Step-by-step explanation:
What is the right translation of these expressions and equations? (with solution)
1. 7 - 2m
2. 3( m + 2) = 15
3. 5m - m(2 - m)
Answers
Answer:
7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".
3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".
To solve the equation, we can start by distributing the 3 on the left side:
3(m + 2) = 15
3m + 6 = 15
Then, we can subtract 6 from both sides:
3m + 6 - 6 = 15 - 6
3m = 9
Finally, we can divide both sides by 3:
3m/3 = 9/3
m = 3
Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.
5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".
To simplify the expression, we can use the distributive property to expand the second term:
5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m
Therefore, the simplified expression is m^2 + 3m.
-4x - 12 = -14 can you help me solve this equation
Answers
Answer:
-4x - 12 = -14
-4x - 12+12 = -14+12
-4x = -2
we divide both sides by -4
-4x/-4 = -2/-4
we council the negatives
x = 1/2
Step-by-step explanation:
hope that will help you
Answer:
1/2 or .5
Step-by-step explanation:
-4x - 12 = -14
-4x - 12+12 = -14+12
-4x = -2
\(\frac{-4x}{4}\) = \(\frac{-2}{-4}\)
AC=A, C, equals
Round your answer to the nearest hundredth.
Answers
Answer:
We have the equation A*C = A
Now, as both sides of the equality are the same thing, we can do the same operation to both sides and the equality will remain true.
We can divide both sides by A and get:
(A*C)/A = A/A
C = 1
So here we finded the value of A.
If A and C are matrices, then C is the identity matrix.
Please help me if you can..
Answers
Where dose - 11/10 go on a number line
Answers
Well, -11/10 is also -1.1. So, it goes right next to -1 on a number line.
The manager of a music store surveyed a random sample of customers who shop in the store
about their favorite type of music. The table shows the number of customers who selected
each type of music.
Favorite Type of Music
Rock
Country
Jazz
Classical
Rap
Pop
37
27
5
9
12
35
Based on the information in the table, which Inference about the favorite type of music of all
the customers who shop in the music store appears to be valid?
F They are certain to select rock or pop music.
G They are less likely to select country or rap music than rock music.
music
H They are more likely to select country music than jazz, classical, or rap music,
J They are certain to select any type of music other than Jazz music,
Answers
Answer:
Its H
Step-by-step explanation:
Because Country has more than the others.
Write a fraction to represent the probability of rolling a two.
Answers
Answer:
1/6
Step-by-step explanation:
if you want to roll a 2 from a six sided dice then you have six different outcomes. If you want a two then you have a 1 out of six chance of getting the two
Answer:
thats id correct 1/6
Step-by-step explanation:
the possible out come of rolling a 2 out of six is 1/6
a jar contains 22 red marbles number 1 to 22 and 52 blue marbles number 1 to 50 to a marble is drawn at random from the drawer find the probability of the given event around solution to three decimal places
Answers
We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
\(P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}\)This gives,
\(\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}\)Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
\(P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}\)We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
\(\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}\)The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
\(P(r\cup o)=P(r)+p(o)-p(r\cap o)\)Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
\(\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}\)This implies that,
\(\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}\)Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
\(P(b\cup e)=p(b)+p(e)-p(b\cap e)\)From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
\(\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}\)p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
\(\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}\)p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
\(\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}\)Therefore,
\(\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}\)Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
In the first 3 months of the year,
an electronics store sold 1,446 cameras.
How many cameras did the store sell in March?
Write and solve an equation.
Answers
I need help with this math question please
Answers
Answer:
it is 8cm
Step-by-step explanation:
i forgot how to do the explanation but I know the answer is 8cm
6x - 10 - - 8 + 3
3x
What’s the answer?
Answers
Answer:
Step-by-step explanation:
-2+39x
In two or more complete sentences write and solve an inequality for the situation and explain how you will solve the inequality. The doctor tells Jerry that he will be at most 72 inches tall. He is already 48 inches tall. How many more inches will Jerry grow? NEED HELP ASAP!
Answers
Answer: Jerry will have to grow 24 more inches to reach his max Height of 72 inches. If you put this into an inequality it would be 48 plus a number that is more significant than or equal to 72
Step-by-step explanation:
48+X_>72
please help me! <3 :(
Answers
Answer:
ill help
Step-by-step explanation:
Answer:
Slope = 2 (i think)
Step-by-step explanation:
Seat belt use in a state was estimated at %, which means % of people use their seat belts. Suppose two independent drivers have been randomly selected. a. What is the probability that both of them are using a seatbelt? b. What is the probability that neither of them is using a seatbelt? c. What is the probability that at least one is using a seatbelt? a. The probability that both of them are using a seatbelt is 0.3. (Type an integer or a decimal. Do not round.)
Answers
Question
Seat belt use in a state was estimated at 89%,
which means 89 % of people use their seat belts. Suppose two independent drivers have been randomly selected.
a. What is the probability that both of them are using aseatbelt?
b. What is the probability that neither of them is using aseatbelt?
c. What is the probability that at least one is using aseatbelt?
The probability that both of them are using a seatbelt is ?
Answer:
a
\(P(B) = 0.7921\)
b
\(P(B)' = 0.0121\)
c
\(P(K) = 0.9879\)
Step-by-step explanation:
From the question we are told that
The proportion of seat belt use is p = 0.89
The sample size n = 2
Generally the probability that both drivers are wearing seat belt is mathematically represented as
\(P(B) = (p)^n\)
=> \(P(B) = (0.89 )^2\)
=> \(P(B) = 0.7921\)
Generally the probability that neither of the two drivers are wearing seat belt is
\(P(B)' = (1 - p)^2\)
=> \(P(B)' = (1 - 0.89)^2\)
=> \(P(B)' = 0.0121\)
Generally the probability that at least one of the drivers is wearing a seat belt is
\(P(K) = 1 - P(B)'\)
=> \(P(K) = 1 - 0.0121\)
=> \(P(K) = 0.9879\)
Find the two square roots of 1/16
Answers
Step-by-step explanation:
The square root of a fraction is the square root of the numerator over the square root of the denominator. In this case, 1/4. The square root of 1/16 = 1/4 Ans.
The square root of 1/16 is 1/4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
√(1/16)
This can be written as,
= √1 / √16
= 1 / 4
Thus,
1/4 is the square root of 1/16.
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220 miles on 8 gallons. How many miles in one gallon?
Answers
Answer:
Tune answer is 27. 5
Step-by-step explanation:
220/8=27. 5
can someone help me plz
Answers
Answer:
biuwrou cb irebcjhdhi qiiqbc uof hwtgapkvbzoire oicsboeoubdqubvugfh vxjcwdhwocddjhcqwugcgwcidcdbvubirjgcuiscidvibszj uschosclhsihfhrvghsuviefytcurdyg/cvadhrhegvtxj hachjcskpkevjkgrjtbwfn. crjcbejcbjthrhs d .
Mr. Lambert pours 2 cups of blue paint into a jar for each art station. How many jars can he fill with 1 gallon of blue paint?
WORTH 65 POINTS HURRY
Answers
Answer:
8
Step-by-step explanation:
v A t-shirt originally costs $18.50. It is on sale for 10% off. What is the sale price of the t-shirt?
Answers
Answer:
16.65
Step-by-step explanation:
10% of 18.50 is 1.85, so you just subtract that.
Find the value of x. 3x(5+2)=16
Answers
Answer:
16/21
Step-by-step explanation:
We are given the equation 3x(5 + 2) = 16.
By order of operations, let's add the two numbers in the parentheses first:
3x(5 + 2) = 16
3x(7) = 16
Now, we must multiply 3x by 7:
3x * 7 = 16
21x = 16
Divide both sides by 21:
x = 16/21
The answer is thus 16/21.
~ an aesthetics lover
Answer: x=0.8
Step-by-step explanation:
Distribute
\(3x*5=15x\)
\(3x*2=6x\)
\(15x+6x=21x\)
\(21x=16\)
divide 21 on both sides
\(x=0.76\)
round
\(x=0.8\)
The base of a right triangular prism is right angle triangle if the height of the prism is 12 cm and the longer side of the base is 5 cm while the shortest side is 3 cm then find A)The lateral surface area B)The total surface area
Answers
Answer:
A) 144 cm²;B) 156 cm².-------------------------------
The base is a right triangle with shortest side of 3 cm and hypotenuse of 5 cm.
Then, according to Pythagorean Theorem, its longer leg is:
\(\sqrt{5^2-3^2} =\sqrt{25-9} =\sqrt{16}=4 \cm\) Part AFind the lateral surface area:
LSR = Ph = (3 + 4 + 5)*12 = 12*12 = 144 cm²Part BFind the area of two triangle bases:
A = 2*(1/2)bh = 3*4 = 12 cm²Find the total surface area by adding up base area and lateral surface area:
TSA = 12 + 144 = 156 cm²Which proportion can you use to find the value of a?
Answers
The proportion used to find the value of a is a/18 = 16/a
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given are three similar triangles, (refer to attached figure to separately see the similar triangles)
We know that, similar triangle have corresponding sides in equal ratio,
Therefore,
a/18 = 16/a
Hence, the proportion used to find the value of a is a/18 = 16/a
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2. MODELING REAL LIFE A dumpster rental fee is $350 for
the first week and $10 for each additional day or any portion
of a day. Write and graph a step function that represents the
cost y (in dollars) to rent the dumpster for x days.
Answers
The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.
What is the Graph?
The graph of the step function that represents the cost of renting a dumpster for x days is a graph that shows how the cost of the rental changes based on the number of days. The x-axis represents the number of days, and the y-axis represents the cost in dollars.
To write the step function that represents the cost of renting a dumpster for x days, we can use the information provided in the problem statement. The cost for the first week is $350, and the cost for each additional day is $10.
We can write the step function as:
y = 350, if x <= 7
y = 350 + 10(x-7), if x > 7
In the first case, if x is less than or equal to 7 (i.e. within the first week), the cost is $350. In the second case, if x is greater than 7 (i.e. more than one week), the cost is $350 for the first week plus $10 for each additional day.
To graph the step function, we can start by plotting the two points on the graph:
(7,350) represents the point at which the cost changes from $350 to $10 per day
(x,y) = (7,350) + (x-7,10x-70)
The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.
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A credit card company charges the retail stores a 1.5% fee for each transaction. If a store receives $2,400 in credit card charges one day, how much will it have to pay in fees?
Answers
Answer: It will have to pay $36 in fees.
Step-by-step explanation: Hope this helps:) please mark me brainliest.
Please help doing a Test
Does the number of sides matter when determining the sum of the exterior angles?
Answers
Answer:
YES
Step-by-step explanation:
Which letters from the table represent like terms?
O A and B
O B and C
O A and D
O Band D
Answers
which letter from table represent like terms asnwer A
The binomial letters from the table represent like terms are 'B' and 'C'.
What are binomials?A mathematical expression made up of two terms joined together with a plus or minus sign.
Step 1: Multiplication of binomials:It is necessary to multiply each phrase of the first binomial by each term of the second binomial when multiplying two binomials. Then, like terms are put together.
Step 2: Calculation for the given binomials:A = (-2x)×(4x) = -8x²
B = (4x)×3 = 12x
C = 1×(-2x) = -2x
D = 1×3 = 3
As, it is shown from the given expressions that the values for B and C are alike.
Thus, B and C are the letters from the table represent like terms.
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What is12.869 x 5.847?.z
Answers
Answer:
75.245 or 75.25
Step-by-step explanation: