Question

Find the best linear fit to the following data points:
x 1 2 3 4 5
y 3 4 5 6 8

Answer 1

Answer:

y = 1.2x + 1.6

Step-by-step explanation:

$\displaystyle\mbox{Line: {}}y=ax+b\\\mbox{where: {}}a=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}\ \mbox{and}\ b=\bar y-a\bar x\\ \\\bar x=(1+2+3+4+5)/5=3\\\bar y=(3+4+5+6+8)/5=5.2\\x_i-\bar x:\ -2,-1,0,1,2\\y_i-\bar y:\ -2.2,-1.2,-0.2,0.8,2.8\\\textstyle\sum(x_i-\bar x)(y_i-\bar y)=4.4+1.2+0+0.8+5.6=12\\\sum(x_i-\bar x)^2=4+1+0+1+4=10\\a=12/10=1.2\\b=5.2-1.2\times3=1.6$