1) Since the question here is to predict a player's salary, then we'll need two columns from that: HR and Salary to begin with:
2) Now we need to expand this table to get the values we need to write out the equation, to begin answering those questions:
a) Examining the data, we can infer that:
No, it does not seem likely that there is a strong correlation
Analyzing Home Runs (x) and Salaries (y) on the table above, since there is one player with 47 HR earning a lot less than another one who made 15 Home Runs.
b) Let's calculate the value of this correlation coefficient using this formula:
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\lbrack n\Sigma x^2-(\Sigma x)^2\rbrack\lbrack n\Sigma y^2-(\Sigma y)^2\rbrack}}[/tex]
Plugging into that the values or our table we have:
[tex]\begin{gathered} r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\lbrack n\Sigma x^2-(\Sigma x)^2\rbrack\lbrack n\Sigma y^2-(\Sigma y)^2\rbrack}} \\ r\approx0.137 \end{gathered}[/tex]
So we have a correlation (r) of r= 0.137 a weak positive correlation
c)
d) To find the equation of the line, we need to find the slope first and then the linear coefficient:
[tex]\hat{y}=mx+b[/tex]
So let's find out the slope, and then plugging into that the values of that table for Σ the last row of each column: Σx, Σy, Σxy, Σx² and Σy² and n=15
[tex]\begin{gathered} m=\frac{n\Sigma xy-\Sigma x\Sigma y}{n\Sigma x^2-(\Sigma x)^2} \\ m=98257 \end{gathered}[/tex]
For the "b" term, i.e. the linear coefficient:
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