Question

For the following equation y = ax^{b} derive the
relation of constants i.e. a and b using the least squares
method.

Answer #1

Use the partial-fraction method to solve the following
equation.
dy/dx=(y+8)(y-7), where y(0)=5
The partial fraction constants in the partial fraction method
equation 1/(y+8)(y-7)=A/(y+8)+B/(y-7) are A=-1/15 and B= 1/15.
Solve the equation.
y=?

Find the power series solution for the equation y'' − y = x
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.

Consider the differential equation: y'' = y' + y
a) derive the characteristic polynomial for the differential
equation
b) write the general form of the solution to the differential
equation
c) using the general solution, solve the initial value problem:
y(0) = 0, y'(0) = 1
d) Using only the information provided in the description of the
initial value problem, make an educated guess as to what the value
of y''(0) is and explain how you made your guess

2z=(ax+y)²+b
form the partial differential equation?
where a & b are arbitrary constants.
need solution step by step

Derive a formula for βˆ
1 given that β0 = 0 (i.e. the underlying linear model is Y = β1x
+ . In
others words, we are looking for least squares fit for where Yˆ
= βˆ
1x. Hint: Sxy/Sxx is not the
correct answer. You might have to look at minimizing SSE.
Bonus: Find V (βb1) for you estimate from #10.

A sociologist is interested in the relation between x = number
of job changes and y = annual salary (in thousands of dollars) for
people living in the Nashville area. A random sample of 10 people
employed in Nashville provided the following information. x (number
of job changes) 7 4 5 6 1 5 9 10 10 3 y (Salary in $1000) 38 32 34
32 32 38 43 37 40 33 Σx = 60; Σy = 359; Σx2 =...

(a) Suppose you are given the following (x, y)
data pairs.
x
1
2
5
y
2
1
7
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
2
1
7
y
1
2
5
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did...

a) Suppose you are given the following (x, y)
data pairs.
x
2
3
6
y
4
3
7
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
4
3
7
y
2
3
6
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did...

Suppose you are given the following (x, y)
data pairs.
x
1
2
6
y
4
3
9
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
4
3
9
y
1
2
6
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did we...

he equation for a parabola has the form ?=??2+??+?y=ax2+bx+c,
where ?a, ?b, and ?c are constants and ?≠0a≠0. Find an equation for
the parabola that passes through the points (−1,−10)(−1,−10),
(−2,−1)(−2,−1), and (−3,18)(−3,18).

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