First part
We need to find the linear regression line of the given table.
The linear regression line is given by
[tex]\begin{gathered} y=391.179-0.827x \\ \text{where} \\ b_1=-0.827 \\ \text{and} \\ b_0=391.179 \end{gathered}[/tex]
The Pearson correlation coefficient is -0.7107. This is a moderate negative correlation, which means there is a tendency for high X variable scores to go with low Y variable scores (and vice versa).
Second part.
Now, If the value of the independent variable is increased by one unit, we have that
[tex]x\longrightarrow x+1[/tex]
by substituting this into the linear regression, we get
[tex]y=391.179-0.827(x+1)[/tex]
and we have
[tex]\begin{gathered} y=391.179-0.827x-0.827 \\ y=390.352-0.827x \\ \end{gathered}[/tex]
then, the change in the dependent variable y is
[tex]\begin{gathered} \\ y=390.352-0.827x \end{gathered}[/tex]
