1) You are estimating the cost ($K) of optical sensors based on the power output of the sensor. Using the preliminary calculations from a data set of 8 sensors, determine the equation of the line. (Round your intermediate calculations to 3 decimal places) ΣY = 2575 ΣX=680 ΣXY=241400 ΣX2=62600 Cost = -77.005 + 4.693 (Power) Cost = 3.786 + 6.763 (Power) Cost = 6.763 + 3.786 (Power) Cost = 4.693 + (-77.005) (Power)
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

It seems we're trying to calculate the linear regression equation y=mx+b.

The given summations enable us to calculate what we need to find m and b. And we're given that the dataset has 8 pairs of (X,Y) elements. We use this number to find mean values. ∑X/8 = Xm the mean or average of the X's. ∑Y/8 = Ym the mean of the Y's. ∑X^2/8 = Xms the mean of the squares of X. ∑XY/8 = XYm the mean of the products of X and Y.

m=(XmYm-XYm)/((Xm)^2-Xms). Xm=680/8=85; Ym=2575/8=321.875; XYm=241400/8=30175; Xms=62600/8=7825. So m=(85*321.875-30175)/(7225-7825)=4.693 approx.

b=Ym-mXm=321.875-4.693*85=-77.03; y=4.693x-77.03 is the linear regression equation, in which y is the cost and x is the power.

We can write this Cost=4.693*Power-77.03 so that it's clear what the variables are. From this it seems the first answer in the list of possible answers is the right one: Cost=-77.005+4.693(Power).  (The small discrepancy in the constant is due to rounding. A more accurate estimate of m is 4.6927. This value gives b=-77.0045.)

answered Jul 18, 2016 by Rod Top Rated User (487,620 points)

Related questions

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!
79,849 questions
83,687 answers
66,612 users