Scatter plot correlation coefficient

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The condition "if sum of (xi-x_bar)^2(yj-y_bar)^2=0 when i=/=j" indicates that for the sum to equal zero, each term must also be zero, implying that all data points must lie on a straight line. This results in a perfect linear correlation, as the squared terms being positive definite means that any deviation from the mean would contribute positively to the sum. Thus, the only way for the entire sum to be zero is if there is no deviation, confirming linearity. Understanding this condition is crucial for interpreting scatter plot correlation coefficients accurately. The discussion emphasizes the mathematical foundation behind linear relationships in data analysis.
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how can I interpret the condition "if sum of (xi-x_bar)^2(yj-y_bar)^2=0 when i=/=j?"

why does this make the line linear?
 
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Since each term is squared, it is positive definite. So for the entire sum to be equal to 0, each individual term has to be 0. Does that help?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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