Answer:
the equation of the least-squares line for the data is: [tex]\hat Y=9.3+1.3x[/tex]
Step-by-step explanation:
In a simple linear regression model, such as, [tex]\hat Y=b_0+b_1x[/tex], the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:
[tex]b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}[/tex]
For the data provided you have to:
[tex]S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4[/tex], thus:
[tex]b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3[/tex]
the equation of the least-squares line for the data is:
[tex]Y=9.3+1.3x[/tex]
