Question

Use technology to find an equation of the line of best fit for the data. round the slope and the y intercept to the nearest hundredth -15 -10 ,-5 0 5 ,10 15 ,20 -4 ,2 7 ,16 22, 30 37 ,4

A) y=2.29x+15.71
B) y=2.29x−15.71
C) y=−2.29x+15.71
D) y=−2.29x−15.71

Answer 1

The line of best fit for the data, obtained using the least squares equation is; y ≈ 1.38·x + 15.68

The option that most closely corresponds to the line of best it is option A

The equation of the line of best can be found as follows;

The possible points on the line obtained from a similar question on the website, presented in tabular form are;

x; -15, -10, -5, 0, 5, 10, 15, 20

y; -4, 2, 7, 16, 22, 30, 37, 43

The line of best fit can be obtained using the least squares regression equation as follows;

y = a + b·x

The formula for the coefficient, b is;
`b = \frac{\sum (x - \bar{x})*(y-\bar{y})}{\sum (x-\bar{x})^2}`

The mean of the x-values,
`\bar{x}` = 2.5

Mean of the y-values,
`\bar{y}` = 19.125

`\sum (x - \bar{x})*(y-\bar{y})` = 1447.5

`{\sum (x-\bar{x})^2}` = 1050

Therefore, b is; 1447.5/1050 ≈ 1.38

`\bar{y}` = a + b·
`\bar{x}`

19.125 = a + 1.3786 × 2.5

a = 19.125 - 1.3786 × 2.5

a ≈ 15.68

Therefore, the line of best fit is; y ≈ 1.38·x + 15.68