Find the line y=a+bx which best approximates the data points(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14)y=

Answer:y = 11.84x - 32.71Step-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             4y       -70          -42         -21         -9             14By the above table,[tex]\sum x=3[/tex][tex]\sum y=-128[/tex][tex]\sum xy = 269[/tex][tex]\sum x^2=31[/tex][tex]\sum y^2 = 7382[/tex]Let the equation of the line is,y = bx + aWhere,[tex]a=\frac{\sum y \sum x^2 - \sum x\sum xy}{n(\sum x^2)-(sum x)^2}[/tex][tex]b=\frac{n\sum xy - \sum x \sumy}{n(\sum x^2)-(\sum x)^2}[/tex]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