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consider the following four non-linear points: (1, 3), (2, 5), (3, 7), and (4, 9). find the best fitting line using the least squares method.

User Zhujik
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Answer:

The best fitting line is y = 2x + 3.

User MigRome
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The best-fitting line using the least squares method for the given points is y = 2x + 1

To find the best-fitting line using the least squares method for these points, use linear regression.

The equation for a line is y = mx + b

where; (m) is the slope

(b) is the y-intercept.

Calculate the slope (m) and y-intercept (b):

m = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²

b = (∑y) - m(∑x) / n

Where;

(n) is the number of data points

(∑xy) is the sum of the product of each x and y

(∑x) is the sum of x values

(∑y) is the sum of y values

(∑x²) is the sum of x squared.

Calculating the values:

∑x = 1 + 2 + 3 + 4 = 10

∑y = 3 + 5 + 7 + 9 = 24

∑xy = (1 x 3) + (2 x 5) + (3 x 7) + (4 x 9) = 3 + 10 + 21 + 36 = 70

∑x² = (1²) + (2²) + (3²) + (4²) = 1 + 4 + 9 + 16 = 30

Using these values:

m = (4 x 70) - (10 x 24) / (4 x 30) - 10²

m = 280 - 240 / 120 - 100

m = 40 / 20 = 2

b = 24 - m x 10 / 4

b = 24 - (2 x 10) / 4

m = 4 / 4} = 1

Therefore, the best-fitting line using the least squares method for these points is y = 2x + 1

User Johannes Ferner
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