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

Answer:

y = 11.84x - 32.71

Step-by-step 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,

$a=\frac{\sum y \sum x^2 - \sum x\sum xy}{n(\sum x^2)-(sum x)^2}$

$b=\frac{n\sum xy - \sum x \sumy}{n(\sum x^2)-(\sum x)^2}$

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