Answer:
The equation of the linear function that best fits the data is,
y = 18.66x + 66.87.
Step-by-step explanation:
The line of best is of the form: y = mx + b.
Here, m = slope of the line and b = intercept.
The formula to compute the intercept and slope are:
[tex]b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
[tex]m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
Consider the table below for the values of ∑ X, ∑ Y, ∑ X² and ∑ XY.
Compute the value of intercept and slope as follows:
[tex]b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(793\times91)-(21\times3102)}{(6\times91)-(21)^{2}} =66.867[/tex]
[tex]m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(6\times3102)-(21\times793)}{(6\times91)- (21)^{2}} =18.657[/tex]
The line of best fit is:
[tex]y=mx+b\\y=18.657x+66.867\\y=18.66x+66.87[/tex]
Thus, the equation of the linear function that best fits the data is y = 18.66x + 66.87.
