Question 326968
a) Enter the data into two columns in an Excel spreadsheet.
Highlight the columns and hit the Chart Wizard button.
Choose scatterplot.

b) Looking at the scatterplot, you can make a good guess about the correlation. 
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To get an actual {{{r^2}}} value do the following.
Once you finish the chart, right click on a data point. 
Choose "Add trendline".
Under Type tab, choose Linear.
Go to the Options tab.
Click "Display equation on Chart" and "Display R-sqaured value on Chart".
Read the {{{R^2}}} value off of the chart. 


c) X values in column 1, rows 1-9
Y values in column 2, rows 1-9
Find the average of the x values, xave=9.78.
Find the average of the y values, yave=81.22.
Generate a new column (column 3) equal to (x-9.78), in EXCEL the formula would be "=A1-9.78" for column 3, row 1, cell. Copy this formula down the column.

Generate a new column (column 4) equal to (y-81.22), in EXCEL the formula would be "=B1-81.22" for column 4, row 1, cell. Copy this formula down the column..

Generate a new column (column 5) equal to (x-9.78)^2, in EXCEL the formula would be "=C1^2" for column 5, row 1, cell. Copy this formula down the column.

Generate a new column (column 6) equal to (y-81.22)^2, in EXCEL the formula would be "=D1^2." for column 6, row 1, cell. Copy this formula down the column.

Generate a new column (column 7) equal to (x-9.78)(y-81.22), in EXCEL the formula would be "=C1*D1." for column 7, row 1, cell. Copy this formula down the column.

Sum the values for column 5 (SSXX), column 6 (SSYY), and column 7 (SSXY).
Find the value of SSXY/SSXX, that is b the slope of the regression line. 
Find the value of SSXY/SSYY, call that b'.
By definition, r^2=b*b'
So then to find r, take the square root.

It's actually easier than it looks.
As a check, you should get the 
SSXX=159.56
SSYY=1233.56
If not, there's a mistake somewhere.
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For a more technical explanation, check out http://mathworld.wolfram.com/LeastSquaresFitting.html