Question

Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places.
Write your final answer in a form of an equation y = m x + b

x
1
2
3
4
5
6

y
87
102
119
149
158
178

Answer 1

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:

$b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}$

$m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}$

Consider the table below for the values of ∑ X, ∑ Y, ∑ X² and ∑ XY.

Compute the value of  intercept and slope as follows:

$b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(793\times91)-(21\times3102)}{(6\times91)-(21)^{2}} =66.867$

$m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(6\times3102)-(21\times793)}{(6\times91)- (21)^{2}} =18.657$

The line of best fit is:

$y=mx+b\\y=18.657x+66.867\\y=18.66x+66.87$

Thus, the equation of the linear function that best fits the data is y = 18.66x + 66.87.