ES2513 Circle Lab day: Tue, Wed. Thur, Fri Name: Below is a table of data values. The ten data pairs (W. ), were collected from an experiment (-1,2 3, . 10). A plot of the pairs (WZ ) indicates the relationshi linear correlation, possibly an order m-polynomial: z-B.W the relationship between the data points is a polynomial, then a log log-transformation should result in a straight line between the two variables have a non- 1. Compute a log transformation for all the ordered pairs (W.-Zo and fill in the rows W 050 100 150 2.00 2.50 3.00 350 4.00 450 5.00 013 052 113 201 314 4.50 613 801 1014 1251 YalogiZ Scatter Diagram (Wi,Zi) 14.00 10.00 8.00 3.00 4.005.00 60 0.00 2. Compute the arithmetic mean for both Xi and Y: X.Y 3. If the (X, Y.) pairs are on a straight line, then the (X, Z ) data pairs must describe an exponential function. Calculate the slope for these (Xi, Y ) pairs: slope slope slope-3: (Xs, Yo).(x,Y) slope Are all the slopes the same? (Circle: Yes or No) 4, Plot the log 10-transformed data (XiY) pairs. Is the plot a line? ( Circle Yes or No ) Plot of (Xi, Y) 5. The algebra used to solve for the exponential relationship is as follows: logiZ)-log(B) + m logi Wi) Let y- logiz), x log(W) and let b- log/B); and since log( 10) - I, then by substitution. mx+b 6. The computed slope for the line generatcd by the points CKe, Yo) is 7. The vertical intercept for the line, bis b-Y-mX. Compute b- 8. Since b-kg(8), then B s 10". Compute B- 9. The equation-model using coefficients (B, m) for, is most likely (2 significant digits) 10. Using the model, verify the equation for Z is correct using two Wi values from the data table