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mrs_skeptik [129]
2 years ago
11

WILL GIVE BRAINLIEST IF CORRECT!!

Mathematics
1 answer:
vfiekz [6]2 years ago
5 0

Answer:

\displaystyle y=-0.927x+13.63

Step-by-step explanation:

<u>Simple Linear Regression </u>

It a function that represents the relationship between two or more variables in a given data set. It uses the method of the least-squares regression line which minimizes the error between the estimate function and the real data.

Let's compute the best-fit line for the data

x=\{1,5,6,12,15\}

y=\{14,11,4,2,1\}

First, we find the sums

\displaystyle \sum x=1+5+6+12+15=39

\displaystyle \sum y=14+11+4+2+1=32

Then, we compute the averages values

\displaystyle \bar{x}=\frac{39}{5}=7.8

\displaystyle \bar{y}=\frac{32}{5}=6.4

We will also compute the sums of the cross-products and the sum of the squares

\displaystyle \sum xy=(1)(14)+(5)(11)+(6)(4)+(12)(2)+(15)(1)=137

\displaystyle \sum x^2=1^2+5^2+6^2+12^2+15^2=1+25+36+144+225

\displaystyle \sum x^2=431

We will compute Sxy and Sxx

\displaystyle S_{xy}=\sum xy-\frac{\sum x\ \sum y}{n}

\displaystyle S_{xy}=137-\frac{(39)(32)}{5}

\displaystyle S_{xy}=-117.6

\displaystyle S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}

\displaystyle S_{xx}=431-\frac{39}{5}^2=126.8

The slope of the linear regression function is given by

\displaystyle m=\frac{S_{xy}}{S_{xx}}=\frac{-117.6}{126.8}=-0.927

The y-intercept ot the linear function is

\displaystyle b=\bar{y}-b\bar{x}=6.4-(-0.927)(7.8)

\displaystyle b=13.63

Thus the best-fit line is

\displaystyle y=-0.927x+13.63

The correct option is the last one

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