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Given the following data points, calculate the curve of best fit. show all steps.

Sagot :

Lanuel

Based on the calculations, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

How to calculate the curve of best fit?

From the table of data points, we have the following:

  • ∑x = 16
  • ∑y = 50.9
  • ∑xy = 24.6
  • ∑x² = 35

Mathematically, the standard equation of a straight line is given by:

y = ax + b       ....equation 1.

Thus, the equations that can be used to model the given data points are:

∑y = na + b∑x             ....equation 2.

∑xy = a∑x + b∑x²       ....equation 3.

Substituting the parameters into the equations, we have;

50.9 = 6a + 16b             ....equation 4.

24.6 = 16a + 35b       ....equation 5.

Solving eqn. 5 and 6 simultaneously, we have:

  • a = -30.17.
  • b = 14.49.

Substituting the value of a and b into eqn. 1, we have;

y = ax + b

y = -30.17x + 14.49.

Therefore, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

Read more on curve of best fit here: brainly.com/question/9366563

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