~~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]
  
 
L7_e1q6.jpg
 
   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.
asked Jul 18, 2016 in Statistics Answers by bb

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

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).

answered Jul 19, 2016 by Rod Top Rated User (424,900 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
77,972 questions
81,716 answers
1,795 comments
60,909 users