A set of data has the following coordinates t 0 1 3 4 7 y 2...

A set of data has the following coordinates

t	0	1	3	4	7
y	2	4	5	7	10

a) Find the least-squares fit to this data by a linear function of t (that is, find constants c1,c0 so that y(t) = c1t + c0 is the best linear fit to this set of data).

b) Find the equation of the best quadratic fit to the same set of data. Then find the equation of the polynomial of smallest degree that fits the data exactly.

Expert Solution

The following data are provided:

X	Y
0	2
1	4
3	5
4	7
7	10

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	0	2	0	0	4
	1	4	4	1	16
	3	5	15	9	25
	4	7	28	16	49
	7	10	70	49	100
Sum =	15	28	117	75	194

Based on the above table, the following is calculated:

b)

I will be using excel and different polynomial graphs that will help decide the best quadratic fit to the same set of data:

Polynomial degree 3

Polynomial degree - 4 which is a perfect fit. Hence the equation becomes:

y = -0.0536x4 + 0.6786x3 - 2.5179x2 + 3.8929x + 2

with
R² = 1

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

orchestra answered 2 years ago

Step 2 Data Set A x 1 2 3 4 5 6 7 y 7 7...

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For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2,...

For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4, 3, 5, 3, 7] please compute the following 1. measures of central tendency (3 points) 2. standard deviation ( 5 points) 3. is 18 an outlier? (5 points) 4. describe the shape of the distribution (2 points)

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1...

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1 , x'(0)=0

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y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t y′ = 5t4y, y(0) = 1, solution: y(t) = et5 y′ = t3/y2, y(0) = 1, solution: y(t) = (3t4/4 + 1)1/3 For the IVPs above, make a log-log plot of the error of Backward Euler and Implicit Trapezoidal Method, at t = 1 as a function of hwithh=0.1×2−k for0≤k≤5.

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0)...

y′ = t, y(0) = 1, solution: y(t) = 1+t2/2 y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2t y′ = 5t4y, y(0) = 1, solution: y(t) = et5 y′ = t3/y2, y(0) = 1, solution: y(t) = (3t4/4 + 1)1/3 For the IVPs above, make a log-log plot of the error of Explicit Trapezoidal Rule at t = 1 as a function ofhwithh=0.1×2−k for0≤k≤5.

Question

A set of data has the following coordinates t 0 1 3 4 7 y 2...

Solutions

Expert Solution

Related Solutions

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