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# Answer to Question #3871 in Statistics and Probability for Jon

Question #3871
Use pair data values and the summations given to &lt;br&gt;x:& 1 & & & & 3 & 5 & & 7 & & 9&lt;br&gt;y:& 10& & & 8& & 7& & & 4& & & 2&lt;br&gt;&lt;br&gt;&Sigma;x= 25;& & & &Sigma;y= 31;& & & & & &Sigma;xy= 115:& & & & &Sigma;x&sup2; = 165&lt;br&gt;&lt;br&gt;a. Find the equation for the least squares regression line. &lt;br&gt;b. Predict the value of y when x is 6 using your equation
1. The average x and y are
x = 25/5 = 5
y = 31/5 = 6.2
2. The regression coefficient is

$b = frac{frac{sum x_iy_i}{n}- ar{x}ar{y}}{frac{sum x_i^2}{n}-ar{x}^2} = frac{115/5 +5*6.2}{165/5 - 5^2} = -1$
thus the equation of the least squares would be

$(x-5) = -1(y - 6.2) \ y = -x + 11.2$
When x= 6,
y = -6 + 11.2 = 5.2

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