Respuesta :
Answer:
Option B.
Step-by-step explanation:
Given information: [tex]\overline{x}=2,s_x=2.3,\overline{y}=22,s_y=4.1,r=-0.94[/tex]
The general equation of least squares regression line is
[tex]\hat y=a+bx[/tex] .... (1)
where,
[tex]b=r\dfrac{s_y}{s_x}[/tex]
[tex]a=\overline{y}-b\overline{x}[/tex]
Substitute the given values in the above formulas to find the values of a and b.
[tex]b=(-0.94)\dfrac{4.1}{2.3}-1.67565\approx -1.68[/tex]
[tex]a=22-( -1.68)(2)=22+3.36=25.36[/tex]
Substitute a=25.36 and b=-1.68 in equation (1).
[tex]\hat y=25.36-1.68x[/tex]
Therefore, the correct option is B.
Following are the calculation to the least-squares regression line:
Given:
[tex]\bar{x} = 2\\\\s_x= 2.3\\\\\bar{y} = 22\\\\s_y = 4.1\\\\r = -0.94[/tex]
To find:
solve =?
Solution:
Calculating the slope:
[tex]\to b_1 = r\times (\frac{s_y}{s_x})\\\\[/tex]
[tex]=- 0.94 \times (\frac{4.1}{2.3})\\\\= -0.94\times 0.17826087\\\\= -0.167565218\approx -0.168\\\\[/tex]
Calculating the intercept:
[tex]\to b_0 = \bar{y}- (b_1\times \bar{x})\\\\[/tex]
[tex]= 22- ( -0.168 \times 2)\\\\ = 22- ( -0.336)\\\\= 22+0.336\\\\= 22.336[/tex]
[tex]\to \hat{y}= b_0 + b_1x\\\\\to \hat{y}= 22.336+0.168x[/tex]
So, the final answer is "[tex]\hat{y}= 22.336+0.168x[/tex]".
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