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mixas84 [53]
3 years ago
7

Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal p

laces.
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

Mathematics
1 answer:
natta225 [31]3 years ago
3 0

Answer:

The equation of the linear function that best fits the data is,

<em>y</em> = 18.66<em>x</em> + 66.87.

Step-by-step explanation:

The line of best is of the form: <em>y</em> = <em>mx</em> + <em>b</em>.

Here, <em>m</em> = slope of the line and <em>b</em> = 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 <em>∑ X, ∑ Y, ∑ X² </em>and <em>∑ XY</em>.

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 <em>y</em> = 18.66<em>x</em> + 66.87.

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