Question

Use the table to answer the question.

This table presents a set of x values and their corresponding y values, showing a nonlinear pattern where y increases at varying rates as x increases.
x y
1 5
2 9
3 10
4 10.5
5 11
Use a calculator to determine the equation of the line of best fit for the data in this table. Round to the nearest hundredth, if needed.

(1 point)
Responses

y=5.05x+1.35

y equals 5.05 x plus 1.35

y=x+5

y equals x plus 5

y=5x+11

y equals 5 x plus 11

y=1.35x+5.05

y equals 1.35 x plus 5.05
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Answer 1

Compute the least-squares line. n=5, x̄ = 3, ȳ = 9.1.
Sum(xy)=150, sum(x^2)=55, so
m = [sum(xy) − n x̄ ȳ] / [sum(x^2) − n x̄^2] = (150 − 5·3·9.1) / (55 − 5·3^2) = 13.5 / 10 = 1.35.
b = ȳ − m x̄ = 9.1 − 1.35·3 = 5.05.

Equation: y = 1.35x + 5.05 (the last choice).