Question

Find the line y=a+bx which best approximates the data points

(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14)

y=

Answer 1

y = 11.84x - 32.71

Explanation:

Here, the given data points,

(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14),

Let x represents the input value and y represents the output value,

So, the table that represents the given situation is,

x -3 -1 1 2 4

y -70 -42 -21 -9 14

By the above table,

`\sum x=3`

`\sum y=-128`

`\sum xy = 269`

`\sum x^2=31`

`\sum y^2 = 7382`

Let the equation of the line is,

y = bx + a

Where,

`a=(\sum y \sum x^2 - \sum x\sum xy)/(n(\sum x^2)-(sum x)^2)`

`b=(n\sum xy - \sum x \sumy)/(n(\sum x^2)-(\sum x)^2)`

n = number of data points = 5,

By substituting the values we get,

a = - 32.70547945 ≈ - 32.71,

b = 11.84246575 ≈ 11.84,

Hence, the equation of line would be,

y = 11.84x - 32.71