Answer:
[tex]\hat y(2)=2 +3(2) =8[/tex]
C 8.0
Step-by-step explanation:
Assuming the linear model y=mx+b where m is the slope and b the intercept.
For this case the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
[tex]b=\bar y -m \bar x[/tex]
After the calculations we see that m=3 and b=2 from the info given by the linear model.
For this case we have the equation obtained by least squares given by:
[tex]\hat y =2 +3x[/tex]
Where 2 represent the intercept and 3 the slope. We are interested on the best predicted value of y when x=2.
If we see our linear model we have the equation in terms of y and x. So we can replace directly the value of x=2 into the equation and see what we got:
[tex]\hat y(2)=2 +3(2) =8[/tex]
