coefficient of determination (R2)

Question

~~4)  You are estimating the cost of optical sensors based on the power output of the sensor. You decide to calculate the coefficient of determination (R2) as part of determining the goodness of fit of an equation. Using the preliminary calculations below, calculate the R2 and determine its meaning.

[Image Description: Summation of (Yi – Ybar)2 = 189671 Summation of (Yhat – Ybar)2 = 164065 Summation of (Y– Yhat)2 = 25606]
  
 
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   13.50% of the variation in the cost is being explained by the power.
 
   13.50% of the variation in the power is being explained by the cost.
 
   86.50% of the variation in the cost is being explained by the power.
 
   86.50% of the variation in the power is being explained by the cost.

Answer 1

year is the mean, yhat is the fitted value (from the linear regression equation) and y is the observed value. R2 measures the ratio of the variances of the fitted values over the observed values. The variance is the sum of the squares of the difference between each value and the mean.

The picture doesn't appear so I'm guessing what it contains. R2=164065/189671=0.8650 approx.

This means that 86.50% of the variation in cost is explained by the correlation of cost and power (answer 3).