Answer:
Step-by-step explanation:
Hello!
Given the data sets for the variables:
Yi: 7; 18; 9; 26; 23
Xi: 2; 6; 9; 13; 20
You have to estimate the regression equation: ^Y= a + bXi
For this you need the auxiliary calculations:
∑X= 50
∑X²= 690
∑Y= 83
∑Y²= 1659
∑XY= 1001
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
[tex]b= \frac{1001-\frac{50*83}{5} }{690-\frac{50^2}{5} } = 0.9[/tex]
X[bar]= ∑X/n= 50/5= 10
Y[bar]= ∑Y/n= 83/5= 16.6
a= Y[bar]-bX[bar]= 16.6-(0.9*10)
a= 7.6
The estimated regression equation is ^Y= 7.6 + 0.9Xi
I hope it helps!
The estimated regression equation of the observations is [tex]\mathbf{\^y = 0.9x + 7.5}[/tex]
The points are given as:
Xi: 2; 6; 9; 13; 20
Yi: 7; 18; 9; 26; 23
From the table of values, we have:
[tex]\mathbf{\sum x = 2 + 6 + 9 + 13 + 20 = 50}[/tex]
[tex]\mathbf{\sum y = 7 + 18 + 9 + 26 + 23 = 83}[/tex]
Also, we have:
[tex]\mathbf{\sum xy = 2 \times 7 + 6 \times 18+ 9 \times 9+ 13\times 26 + 20\times 23 = 1001}[/tex]
[tex]\mathbf{\sum x^2 = 2^2 + 6^2 + 9^2 + 13^2 + 20^2 = 690}[/tex]
[tex]\mathbf{\sum y^2 = 7^2 + 18^2 + 9^2 + 26^2 + 23^2 = 1659}[/tex]
The slope (b) is calculated as:
[tex]\mathbf{b = \frac{\sum xy - \frac{\sum x \times \sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}n}}[/tex]
So, we have:
[tex]\mathbf{b = \frac{1001 - \frac{50\times 83}{5}}{690 - \frac{50^2}5}}[/tex]
[tex]\mathbf{b = \frac{1001 - 830}{690 - 500}}[/tex]
[tex]\mathbf{b = 0.9}[/tex]
The y-intercept (a) is calculated as:
[tex]\mathbf{a = \bar y -b\bar x}[/tex]
Where:
[tex]\mathbf{\bar y = \frac{\sum y}n = \frac{83}{5} = 16.6}[/tex]
[tex]\mathbf{\bar x = \frac{\sum x}n = \frac{50}{5} = 10}[/tex]
So, we have:
[tex]\mathbf{a = 16.5 - 0.9 \times 10}[/tex]
[tex]\mathbf{a = 7.5}[/tex]
The regression equation is represented as:
[tex]\mathbf{\^y = bx + a}[/tex]
So, we have:
[tex]\mathbf{\^y = 0.9x + 7.5}[/tex]
Read more about regression equations at:
https://brainly.com/question/7656407
