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Answer on Statistics and Probability Question for Jon

Question #3871
Use pair data values and the summations given to <br>x:& 1 & & & & 3 & 5 & & 7 & & 9<br>y:& 10& & & 8& & 7& & & 4& & & 2<br><br>Σx= 25;& & & Σy= 31;& & & & & Σxy= 115:& & & & Σx² = 165<br><br>a. Find the equation for the least squares regression line. <br>b. Predict the value of y when x is 6 using your equation
Expert's answer
1. The average x and y are
x = 25/5 = 5
y = 31/5 = 6.2
2. The regression coefficient is

/cgi-bin/mimetex.cgi?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

http://latex.codecogs.com/gif.latex?(x-5) = -1(y - 6.2) \ y = -x + 11.2
When x= 6,
y = -6 + 11.2 = 5.2

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