Answer:
[tex]\hat y=3(2) +2=8[/tex]
Step-by-step explanation:
Data given
r=0.003 represent the correlation coefficient
[tex]bar y =5[/tex] represent the sample mean for the y observations
Solution to the problem
We assume that they use least squares in order to find the best regression model. The slope is given by 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]
And the slope on this case is:
[tex]m=3[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=5[/tex]
[tex]\bar y= \frac{\sum y_i}{n}[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=5-(3*\bar x)=2[/tex]
So the line would be given by:
[tex]\hat y=3x +2[/tex]
And the best predicted value for x=2 would be:
[tex]\hat y=3(2) +2=8[/tex]
