Formula calculus

Question

What is the coefficient of correlation for y=586.3x + 9716 ( round to the nearest thousandth as needed).

Answer 1

Aireeyon,

The coefficient of correlation (r) measures the strength and direction of a linear relationship between two variables. If a set of data points measuring the relationship between two variables clearly resembles a straight line (with either a positive or negative relationship), that means there is a direct or indirect relationship between the two and r will measure closer to 1. However if a set of data points forms a shape resembling a paraloba, it would have a very weak value for r (r would be close to zero, as a straight line could not accurately represent the data).

The expression y = 586.3x + 9716 is an equation of a line (in standard form). As we know the slope of this line, m, is the coefficient before the "x" variable, in this case it is 586.3. This information tells us that there is a direct relationship that as x increases by 1, the value for y will increase 586.3 linearly. Since a standard equation for a line by definition has a direct, linear relationship between its two variables, the correlation coefficient "r" must equal exactly 1. In other words, a line of best fit representing the data generated by the original equation y = 586.3x + 9716 would lie perfectly on all points.

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