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Fitting a straight line to a set of paired observations (x1;y1);(x2;y2);:::;(xn;yn). Mathematical expression for the straight line (model) y = a0 +a1x where a0 is the intercept, and a1 is the slope. Define ei = yi;measured ¡yi;model = yi ¡(a0 +a1xi) Criterion for a best fit: minSr = min a0;a1 Xn i=1 e2 i = min a0;a1 Xn i=1 (yi ¡a0 ¡a1xi ...
a. Find the quadratic relationship between the energy and velocity of the object. b. What is the energy of an object with a speed of 5 m/s? c. What is the velocity of the object if the energy is 128 joules? _____________________________ Original content Copyright © by Holt McDougal.
The process of constructing an approximate curve , which fit best to a given discrete set of points is called curve fitting. Curve fitting and interpolation are closely associated procedures. In interpolation, the fitted function should pass through all given data points; whereas curve fitting methodologically
5. Sketch the line of best fit. 6. Find the slope of the line. _____ 7. Write the equation of the line. _____ 8. Would you expect the correlation coefficient for the line of best fit to be between 1 and 0 or between 0 and 1? Why? _____ 9.
Section 2.7 – Curve Fitting with Linear Models Per: ___ The problems on this worksheet come from your book, p.146-148 #2-6, 12, and 14. 1. Driving. Use your graphing calculator to make a scatter plot for this data set using gallons as the independent variable. Identify the correlation and find the equation of the line of best fit.
Yields a unique best-fit line for a given set of data. The sum of the squares of the residuals is a function of the two fitting parameters, 0 and. 1, 0, 1. Minimize by setting its partial derivatives to zero and solving for 0 and 1.
Practice A. Curve Fitting with Linear Models. Sketch the line of best fit for each scatter plot. Name the type of correlation. 1. X. 2. X. Positive. Negative. 3. X. Positive. As a science experiment, Keith recorded the percent humidity and the number of stars he could see at 10:00 P.M. each evening. Use the data in the table for Exercises 4 – 9. 4.
