Consider the multiple regression model: Y_(i=) β_1 X_i1+β_2 X_i2+ε_i i=1, …, n. Where the &; are uncorrelated, with E{ε_i} = 0 and o²{ε_i} = 02. a. State the least squares criterion and derive the least squares estimators of β_1 and β_2 b. Assuming that the ε_i are independent normal random variables, state the likelihood function and obtain the maximum likelihood estimators of β_1 and β_2. Are these the same as the least squares estimators?
Answers
Comparing the least squares and maximum likelihood estimators, we find that they are indeed the same.
In the multiple regression model, Y_i = β_1 X_i1 + β_2 X_i2 + ε_i, the least squares criterion aims to minimize the sum of squared residuals (SSR), which represents the difference between the actual and predicted values of the dependent variable Y. Mathematically, it is expressed as:
SSR = Σ(ε_i)² = Σ(Y_i - (β_1 X_i1 + β_2 X_i2))²
To derive the least squares estimators for β_1 and β_2, we differentiate SSR with respect to β_1 and β_2 and set the resulting equations to zero. This yields the normal equations, which we can solve simultaneously to obtain the estimates for β_1 and β_2.
Assuming the ε_i are independent normal random variables with E{ε_i} = 0 and σ²{ε_i} = σ², the likelihood function can be written as:
L(β_1, β_2, σ²) = Π [ (1/(√(2πσ²))) * exp( -(ε_i)^2 / (2σ²) ) ]
Taking the logarithm of L, we obtain the log-likelihood function, which we differentiate with respect to β_1, β_2, and σ². By setting these partial derivatives to zero and solving the resulting equations, we obtain the maximum likelihood estimators (MLE) for β_1 and β_2.
Comparing the least squares and maximum likelihood estimators, we find that they are indeed the same. This is because both approaches minimize the sum of squared errors in the linear regression model, and the normality assumption of the errors implies that the MLE and least squares estimators coincide.
To know more about regression model, refer to the link below:
https://brainly.com/question/29217160#
#SPJ11
Related Questions
WAGES Mark has already earned money for mowing lawns over the summer when he takes a job at the local grocery store, earning $9.50 per hour. After working 16 hours at the grocery store, Mark has earned a total of $292. Write a linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store.
PLEASE HELP!!!
Answers
Answer:
The linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store is:
m = 9.5h + 140Step-by-step explanation:
GivenEarning per hour = $9.50,Worked hours = 16,Total earning = $292,Mark has earned some amount initially for mowing lawns.To findLinear equation of amount of money m after working h hoursSolutionMark has already earned some amount x. Lets find it using the number of hours worked and the total amount after this:
16*9.50 + x = 292152 + x = 292x = 292 - 152x = 140This amount represents an initial value or the y-intercept of the line and the payment per hour represents the slope of same line.
We know the equation of line in slope-intercept form:
y = mx + b, where y- line, m- slope, b - the y-interceptPlug in the values and variables to get the linear equation for the earned amount:
m = 9.5h + 140Mark's m earned this summer after working h hours at the grocery store is represented by the linear equation: m = 9.5h + 140.
What is meant by linear equation?A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y = mx + b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables. Linear equations are degree 1 equations. It is the straight line equation. The standard form of a linear equation is ax + by + c = 0, where a and b are both zeros.Given
Earning per hour = $9.50,
Worked hours = 16,
Total earning = $292,
Mark has earned some amount initially for mowing lawns.
Linear equation of amount of money m after working h hours
Mark has already earned some amount x.
Lets find it using the number of hours worked and the total amount after this:
16 × 9.50 + x = 292
Simplifying the above equation then we get,
152 + x = 292
x = 292 - 152
x = 140
This amount represents the line's initial value or y-intercept, and the payment per hour represents the slope of the same line.
The slope-intercept equation of a line is as follows:
y = mx + b, where y is the line, m is the slope, and b is the y-intercept
To obtain the linear equation for the earned amount, enter the values and variables as follows:
∴ m = 9.5h + 140
To learn more about linear equation, refer to:
https://brainly.com/question/2030026
#SPJ1
Suppose A ABCNA EFG.
Which congruency statement is true?
O AB~ FG
O ABN EG
• AC~ EF
O BC N FG
Answers
Answer:
third one is true ...........
The figure below shows a region that consists of a semi-circle on top of a rectangle. Give the value of x (l) that maximizes the area of the region if the circumference of the region is 4.Semiccircle+Rectangle
Answers
the value of x (l) that maximizes the area of the region is 2.
Let x represent the length of the rectangle, and let y represent the radius of the semi-circle.
The circumference of the region is given as 4, so we have the equation for the circumference: C = 2πy + 2x = 4
We can rewrite the equation as: πy + x = 2
The area of the region can be expressed as the sum of the area of the semi-circle and the rectangle: A = \(\pi y^{2}\)/2 + xy
Now, we can solve the optimization problem by maximizing the area A with respect to x. We can use the equation for the circumference to express y in terms of x: y = (2 - x)/π
Substituting this expression into the area equation, we have:
A = \(\pi (2 - x)^{2}\)/2π + x(2 - x)/π
Simplifying, we get: A = \((2 - x)^{2}\)/2 + x(2 - x)/π
To maximize the area, we differentiate A with respect to x, set it equal to zero, and solve for x: dA/dx = 2 - x - (2 - x)/π = 0
Simplifying further, we find: (π - 1)(2 - x) = 0
This gives two possible solutions: x = 2 and x = π + 2.
However, since we are looking for a value of x that maximizes the area, we take the value within the range of the problem, which is x = 2.
learn more about circumference here:
https://brainly.com/question/28757341
#SPJ11
MARKING BRAINLEIST BUT PLS BE QUICK
Answers
Answer:
A. \(\frac{81m^{4} }{n{4} }\)
Joy drew a scale drawing of an apartment. The scale of the drawing was
4 millimeters = 5 meters. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Answers
The drawing's scale factor is 1 : 1250
Determining Scale factorFrom the question, we are to determine the drawing's scale factor and we are to write our answer as a ratio
From the given information,
The scale of the drawing was 4 millimeters = 5 meter
Convert 5 meters to millimeters
1 meters = 1000 millimeters
∴ 5 meters = 5000 millimeters
Thus,
The scale of the drawing was
4 millimeters = 5000 millimeters
Divide both sides by 4 millimeters
Therefore,
The scale of the drawing was
1 : 1250
Hence, the drawing's scale factor is 1 : 1250
Learn more on Scale factor here: https://brainly.com/question/14440320
#SPJ1
An assembly line has 10 stations with times of 1, 2, 3, 4, …, 10, respectively. What is the bottleneck time?
Answers
The bottleneck time is 10, as this is the longest time for any station in the assembly line.
What is the bottleneck time?In this assembly line, the bottleneck time is 10. This is the amount of time it takes for a product to pass through the longest station, station 10, and is the limiting factor in the line's overall efficiency.This is referred to as the bottleneck time because it is the maximum time that can be achieved, regardless of how efficient the other nine stations are.The bottleneck time is an important concept in assembly line and production management, as it helps to determine the optimal speed of the line and the maximum output that can be achieved.If the bottleneck time is longer than necessary, it can lead to higher costs and slower production.To improve the bottleneck time, managers can look for ways to reduce the time it takes to complete each task, or reduce the number of tasks required.Additionally, managers may need to invest in additional resources, such as robots, to increase the speed of the bottleneck station.To learn more about The bottleneck time refer to:
https://brainly.com/question/29526739
#SPJ1
which of the given lengths make a right triangle?
A: 8, 12, 20
B: 10, 15, 18.03
C: 3.05, 4.05, 7.10
Answers
Answer:
aaaaaaaaaaaaaaaaaaaaa
Plsss help!!
Geometry A
Brainliest
Answers
Answer
Step-by-step explanation:
If x = a sin teta and y = b cos teta
Find the value of b^2x^2+ a^2y^2
Plssss plsss helppp
Answers
\(\\ \sf\longmapsto b^2x^2+a^2y^2\)
\(\\ \sf\longmapsto b^2(asin\Theta)^2+a^2(bcos\Theta)^2\)
\(\\ \sf\longmapsto b^2a^2sin^2\Theta+a^2b^2cos^2\Theta\)
\(\\ \sf\longmapsto a^2b^2(sin^2\Theta+cos^2Theta)\)
\(\\ \sf\longmapsto a^2+b^2(1)\)
\(\\ \sf\longmapsto a^2b^2\)
Use the factors of the numbers to explain why
45 x 56 = 5 x 7 x 8 x 9
Answers
Answer:
45 x 56=
2520 and
5 x 7=35*8=280*9=2520
2520=2520
Hope This Helps!!!
please help me I have to submit it tomorrow I will give brilliant to the one who solves it
Answers
a. Income tax is the amount of money that an individual is required to pay to the government based on their income.
b. Ramesh's total income in 13 months, including the festival expense, is found as Rs 593,857.
c. Ramesh's annual income tax, considering the investment in citizens' investment fund, is Rs 85,000.
How do we calculate?a. Income tax is described as the amount of money that an individual is required to pay to the government based on their income. found using a specific tax rate applied to different income brackets.
b.
Monthly income = Salary + Dearness allowance
= Rs 43,689 + Rs 2,000
= Rs 45,689
Total income for 13 months = Monthly income * 13
= Rs 45,689 * 13
= Rs 593,857
c.
Total income after deducting citizens' investment fund = Total income - Investment amount
= Rs 593,857 - Rs 2000
= Rs 591,857
Hence, the income tax based on the revised total income is:
Tax for income upto 5 lakh which is 1% of the income
= 0.01 * 500000
= Rs 5,000
Tax for income from 5-7 lakh which is the 10% of the income
= 0.1 * 200000
= Rs 20,000
The Tax for income from 7-10 lakh: 20% of the income
= 0.2 * 300000
= Rs 60,000
The Tax for income from 10-20 lakh is 30% of the income
= 0.3 * 0
= Rs 0
The total income tax = Rs 5,000 + Rs 20,000 + Rs 60,000 + Rs 0 + Rs 0
= Rs 85,000
Learn more about income tax at:
https://brainly.com/question/30157668
#SPJ1
an octagon has interior angles of 120°,110°,130°,144°,90°.if the remaining angles are equal what Is the size of each of the equal angles
Answers
The octagon's remaining equal angles are each 121.5 degrees.
The sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n - 2) * 180 °
where n is the number of sides of the polygon.
In the case of an octagon, which has 8 sides, the sum of the interior angles is:
Sum of interior angles = (8 - 2) * 180°
= 6 * 180°
= 1080°
Now, we subtract the known angles from the sum:
1080 ° - (120 ° + 110° + 130 ° + 144° + 90°) = 486°
We are left with 486 °, which is the sum of the equal angles in the octagon. Since there are four equal angles remaining, we divide 486 ° by 4:
486° / 4 = 121.5°
know more about octagons click here;
https://brainly.com/question/17081076
The size of each of the equal angles is 162 degrees. All the remaining three angles are equal to each other and have a value of 162 degrees.
We know that the sum of all interior angles in a polygon = (n-2)180
where n is the number of sides of that polygon.
In this case, we have an octagon,
The sum of all interior angles in an octagon = (8-2) 180
n = 8 ( an octagon has 8 sides)
The sum of all interior angles in an octagon, A = 1080 degrees.
Sum of given angles = 120 + 110 +130 +144 + 90 = 594
We have 3 more angles in the octagon which are all equal, let's say x
A + x + x + x = 1080
594 + 3x = 1080
3x = 486x
x = 162 degrees
Hence, the remaining equal angles are 162 degrees.
To learn more about interior angles :
https://brainly.com/question/12834063
Brainliest for correct answer !! :D
f (x) = 3x - 5 g (x) =2^x find fg(3)
Answers
(fog)(3) = 22
Step-by-step explanation:
f(x + 3x - 5; g(x)=x²9(3)=3²=9
(fog)(3) = f(g(3)) = f(9)=3-9-5=27
-5-22 [Ans]
for any probability distribution, the expected value: group of answer choices cannot be greater than 1. represents the location/center of the distribution. is equal to the random variable. is equal to the variance of the distribution.
Answers
For any probability distribution, the expected value: 1. represents the location/center of the distribution.
What is an expected value?In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.
For instance, in a game of dice, the total number of outcomes (expected values) is generally equal to six (6). This ultimately implies that, the probability of rolling each number is p(x) = 1/6.
In conclusion, the location or center of distribution is represented by the expected value in any probability distribution.
Read more on probability here: https://brainly.com/question/25870256
#SPJ1
Given two variables, num1=0.956786 and num2=7.8345901. Write a R code to display the num1 value in 2 decimal point number, and num2 value in 3 decimal point
number (clue: use function round).
Answers
The provided R code uses the round function to display num1 rounded to two decimal places and num2 rounded to three decimal places.
num1 <- 0.956786
num2 <- 7.8345901
num1_rounded <- round(num1, 2)
num2_rounded <- round(num2, 3)
print(num1_rounded)
print(num2_rounded)
The R code assigns the given values, num1 and num2, to their respective variables. The round function is then applied to num1 with a second argument of 2, which specifies the number of decimal places to round to. Similarly, num2 is rounded using the round function with a second argument of 3. The resulting rounded values are stored in num1_rounded and num2_rounded variables. Finally, the print function is used to display the rounded values on the console. This approach ensures that num1 is displayed with two decimal places and num2 is displayed with three decimal places.
For more information on R code visit: brainly.com/question/33564611
#SPJ11
This scatter plot shows the number of books read and the
number of days passed.
Based on the information in the scatter plot, what is the best prediction for the number of books read in 9 days?
o 5 books
o 9 books
0 12 books
o 15 books
Answers
Answer:
the answer would be 15 books
Step-by-step explanation:
.
Is this answer right?
Answers
Answer:
that is the correct answer.
Step-by-step explanation:
A cylinder has a radius of 17 yards it’s volume is 15,426. 82 yd.³ what is the height of the cylinder
Answers
Two taps running at the same rate can fill a tank in 45 mins. How long will it take one tap to fill the same tank?
Answers
Answer:
90 minutes
Step-by-step explanation:
it will take twice as long therefore 90 minutes
Taylor and MacLaurin Series: Consider the approximation of the exponential by its third degree Taylor Polynomial: e x
≈P 3
(x)=1+x+ 2
x 2
+ 6
x 3
. Compute the error e x
−P 3
(x) for various values of x : e 0
−P 3
(0)=
e 0.1
−P 3
(0.1)=
e 0.5
−P 3
(0.5)=
e 1
−P 3
(1)=
e 2
−P 3
(2)=
e −1
−P 3
(−1)=
.
Answers
The resultant polynomial is: e^(0) - P3(0) = -0.2818e^(0.1) - P3(0.1) = -0.2948e^(0.5) - P3(0.5) = -1.5180e^(1) - P3(1) = -4.2817e^(2) - P3(2) = -7.2776e^(-1) - P3(-1) = 0.0346
Given, Taylor Polynomial P3(x) for the exponential e^(x) = 1 + x + (x²/2!) + (x³/3!) + ...... + (x^n/n!)P3(x) = 1 + x + 2(x²) / 2! + 6(x³) / 3!
Let's compute the error e^(x) - P3(x) for the given values of x, e^(0) - P3(0) = e^(0) - 1
= 0.7182 - 1
= -0.2818e^(0.1) - P3(0.1)
= e^(0.1) - (1 + 0.1 + 0.2 + 0.1)
= 1.1052 - 1.4
= -0.2948e^(0.5) - P3(0.5)
= e^(0.5) - (1 + 0.5 + 1 + 5/6)
= 1.6487 - 3.1667
= -1.5180e^(1) - P3(1)
= e^(1) - (1 + 1 + 2 + 2)
= 1.7183 - 6
= -4.2817e^(2) - P3(2)
= e^(2) - (1 + 2 + 2(2) + 8(2/3))
= 7.3891 - 14.6667
= -7.2776e^(-1) - P3(-1)
= e^(-1) - (1 - 1 + 2/2 - 2/3)
= 0.3679 - (1/3)
= 0.0346
Therefore, e^(0) - P3(0) = -0.2818e^(0.1) - P3(0.1) = -0.2948e^(0.5) - P3(0.5) = -1.5180e^(1) - P3(1) = -4.2817e^(2) - P3(2) = -7.2776e^(-1) - P3(-1) = 0.0346
Know more about Taylor Polynomial here:
https://brainly.com/question/2533683
#SPJ11
If P(B)=0.3,P(A∣B)=0.5,P(B ′ )=0.7, and P(A∣B ′ )=0.8, find P(B∣A).
Answers
If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113
To find the value of P(B|A), follow these steps:
The probability of B given A can be given by the product of the probability of A given B and the probability of B, divided by the total probability of B. So, the formula for P(B|A) = P(A|B) * P(B) / [P(A|B)*P(B)+P(A|B')*P(B')]. Substituting the values, we get P(B|A) = (0.5) (0.3) / [(0.5) (0.3) + (0.8) (0.7)] ⇒P(B|A) = 0.15 / [0.15 + 0.56] ⇒P(B|A) = 0.15 / 0.71 ⇒P(B|A) = 0.2113. Therefore, P(B|A) = 0.2113.Learn more about probability:
brainly.com/question/13604758
#SPJ11
Find the equation to the tangent line to the curve at the specified point:-F(x) = - 2/3(x^3) + x^2 + 6x – 4at the point: (3, 5)
Answers
Given:
\(\begin{gathered} f(x)=-\frac{2}{3}x^3+x^2+6x-4 \\ \text{ Point = (3,5)} \end{gathered}\)The general equation of tangent line is:
\(y-y_1=m(x-x_1)\)Where,
\(\begin{gathered} (x_1,y_1)=\text{ Point} \\ m=\text{ Slope} \end{gathered}\)Solpe of line is:
\(\begin{gathered} m=f^{\prime}(x) \\ \end{gathered}\)\(\begin{gathered} f(x)=-\frac{2}{3}x^3+x^2+6x-4 \\ f^{\prime}(x)=-\frac{2}{3}(3x^2)+2x+6 \\ x=3;y=5 \\ f^{\prime}(x)=-2x^2+2x+6 \\ f^{\prime}(3)=-2(3)^2+2(3)+6 \\ f^{\prime}(3)=-18+6+6 \\ f^{\prime}(3)=-6 \end{gathered}\)slope of tangent line is -6
then equation of tengent line is:
\(\begin{gathered} y-y_1=m(x-x_1) \\ m=-6 \\ (x_1,y_1)=(3,5) \\ so, \\ y-5=-6(x-3) \\ y-5=-6x+18 \\ y+6x=18+5 \\ y+6x=23 \end{gathered}\)
students in the journalist class at o’henry high school conducted a survey. they ask 25 students to monitor their texting for one month. at the end of the month, each report his or her average daily text for the month the results of the survey are shown in the table
Answers
A dot plot that represent this data set is shown in the image attached below.
What is a dot plot?In Mathematics and Statistics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of crosses or dots.
Based on the information provided about this high school survey, we can reasonably infer and logically deduce that the average daily text for the month with the highest frequency is 300.
In this scenario, we would use an online graphing calculator to construct a dot plot with respect to a number line that accurately fit the data set.
Read more on dot plots here: brainly.com/question/30486649
#SPJ1
Subtract
1/13
31
55
62
110
2
3/5
55
7
10
-
3
22. Simplify the answer.
Answers
When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.
To subtract 3 from 22, we can perform the subtraction operation as follows:
22
3
19
We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.
Therefore, the simplified answer is 19.
The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.
By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.
In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.
for such more question on simplified
https://brainly.com/question/11680269
#SPJ8
Help me out with this question!! 50 points
Answers
C
The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C
The correct answer is D) The first inequality should be s + h ≤ 1800.
The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.
The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.
Draw two cards without replacement from a well-shuffled standard deck of 52 cards. find the probability distribution of the number of diamonds drawn. enter exact answers (fractions).
Answers
There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.
P=13/52*12/51=1/4*4/17=1/17.
More problems related to a similar concept are solved in the link below.
https://brainly.com/question/11234923?referrer=searchResults
#SPJ4
A pair of shoes is originally priced at $120.00 It is on sale for 35% off. What is the price that you would pay?
Answers
\(answer = $78 \\ solution \\ marked \: price = $120 \\ discount \: percent = 35 \\ discount \: amount = discount \: percent \: of \: mp \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 35 \: of \: 120 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ = $42 \\ selling \: price = mp - discount \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 120 - 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = $78 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)..
Plz 50 points im desperate
A show pony weighs at least 900 pounds. After a recent weigh in, the owner of a show pony amended the diet of his pony, increasing the animal's caloric intake, with the hope that the pony would gain weight to be shown in a few months. The data shown in the table and scatter plot below represents the pony's additional daily caloric intake and recorded weight gain (in pounds) of the show pony over the last ten weeks.
Additional Daily Calories Consumed Weight Gained
(in pounds)
1,500 3
1,575 7
1,650 3
1,725 4
1,800 8
1,875 9
1,950 13
2,025 7
2,100 17
2,175 15
Part A: Use the data shown in the table and scatter plot to create an approximate equation for the line of best fit.
Part B: In complete sentences, describe the show pony's weight gain in terms of the units used in the data.
Part C: According to the equation for the best fit line for the data, approximately how much weight would you expect the pony to gain in a week if its additional daily caloric intake for that week is 2,300 calories?
Answers
An approximate equation for the line of best fit is y-hat = 0.018x - 24.5111.
How to explain the equation?A linear regression equation for the line of best fit would be y-hat = 0.018x - 24.5111 where
y-hat is the predicted value for the recorded weight gain (in pounds)
x is the additional daily caloric intake.
b) The pony's additional calorie intake increases, the weight gain also increases in pounds
c) Set x equal to 2300 and solve for y-hat:
y-hat = 0.018x - 24.5111
y-hat = 0.018(2300) - 24.5111
y-hat = 41.4 - 24.5111
y-hat = 16.8889
Therefore, the predicted value for the weight gain based on an additional 2300 calorie intake is 16.9 pounds.
Learn more about equation on:
https://brainly.com/question/2972832
#SPJ1
A model for the food-price index (the price of a representative "basket" of foods) between 1984 and 1994 is given by the functionI(t)=0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33Where t is measured in years since midyear 1984, so 0≤t≤10, and I(t) is measured in 1987 dollars and scaled such that I(3)=100. Estimate to two decimal places the times when food was cheapest and most expensive during the 1984-1994 period
Answers
The time when the food price is most and cheapest is obtained from the extremum value of the function.
The time when the food is cheapest is approximately 1 year after 1984The time when the food is most expensive is approximately 5 years after 1984What is an extremum of a function?The extremum of a function is a maximum or minimum value of the function.
The function that models the food-price is I(t) = 0.00009045·t⁵ + 0.001438·t⁴ - 0.0656·t³ + 0.4598·t² - 0.6270·t + 99.33
Where;
t = The number of years since 1984
I(3) = 100
The time when the food is cheapest or most expensive can be obtained by differentiating the function for food-price and equating the result to 0 as follows;
I'(t) = 0.00009045×5·t⁴ + 0.001438×4·t³ - 0.0656×3·t² + 0.4598×2·t - 0.6270 = 0
Factoring the result, using a graphing calculator, we get;
(t - 0.823)·(t - 5.131)·(t - 11.05)·(t + 29.72) = 0
The values of the minimum and maximum values are therefore';
I(0.823) = 0.00009045×0.823⁵ + 0.001438×0.823⁴ - 0.0656×0.823³ + 0.4598×0.823² - 0.6270×0.823 + 99.33 ≈ 99.08
I(5.131) = 0.00009045×5.131⁵ + 0.001438×5.131⁴ - 0.0656×5.131³ + 0.4598×5.131² - 0.6270×5.131 + 99.33 ≈ 100.67
I(11.05) = 0.00009045×11.05⁵ + 0.001438×11.05⁴ - 0.0656×11.05³ + 0.4598×11.05² - 0.6270×11.05 + 99.33 ≈ 96.38
I(-29.72) = 0.00009045×(-29.72)⁵ + 0.001438×(-29.72)⁴ - 0.0656×(-29.72)³ + 0.4598×(-29.72)² - 0.6270×(-29.72) + 99.33 = 1270.8
Therefore, the food price when the food was cheapest is $99.08
The time when the food is most cheapest where 0 ≤ t ≤ 10 is t = 0.823 years ≈ 1 years
Similarly, the food price when the food was most expensive in a 10 year time frame is $100.67
The time when the food is most expensive is t ≈ 5.131 years ≈ 5 years
Learn more about the maximum and minimum value of a function here:
https://brainly.com/question/6787214
#SPJ1
A swimming pool has dimensions of 50.00 m by 25.00 m by 2.00 m. How many gallons of waters of water will it take to fill the pool?
Answers
Answer:
2500
Step-by-step explanation:
brainliest please if its right