**Do heavier cars really use more gasoline?**Suppose a car is chosen at random. Let \( x \) be the weight of the car (in hundreds of pounds), and let \( y \) be the miles per gallon (mpg).| \( x \) | 25 | 42 | 29 | 47 | 23 | 40 | 34 | 52 ||--------|----|----|----|----|----|----|----|----|| \( y \) | 30 | 21 | 22 | 13 | 29 | 17 | 21 | 14 |### Tasks1. **Verify the given sums \( \Sigma x, \Sigma y, \Sigma x^2, \Sigma y^2, \Sigma xy \), and the value of the sample correlation coefficient \( r \).** (Round your value for \( r \) to four decimal places.) - \(\Sigma x = \) [Input] - \(\Sigma y = \) [Input] - \(\Sigma x^2 = \) [Input] - \(\Sigma y^2 = \) [Input] - \(\Sigma xy = \) [Input] - \( r = \) [Input]2. **Find \(\bar{x}\), and \(\bar{y}\). Then find the equation of the least-squares line \(\hat{y} = a + bx\).** (Round your answers to four decimal places.) - \(\bar{x} = \) [Input] - \(\bar{y} = \) [Input] - \(\hat{y} =\) [Input] \(+ \) [Input] \( x \)3. **Find the value of the coefficient of determination \( r^2 \).** What percentage of the variation in \( y \) can be explained by the corresponding variation in \( x \) and the least-squares line? What percentage is unexplained? (Round your answer for \( r^2 \) to four decimal places. Round your answers for the percentages to two decimal places.) - \( r^2 = \) [Input] - explained [Input] % - unexplained [Input] %4. **Suppose a car weighs \( x = 31 \) (

x y xy x2 y2 25 30 750 625 900 42 21 882 1764 441 29 22 638 841 484 47 13 611 2209 169 23 29 667 529 841 40 17 680 1600 289 34 21 714 1156 441 52 14 728 2704 196 292 167 5670 11428 3761 Total ======================================== ∑x =292∑y =167∑x2=11428∑y2=3761∑xy =5670 =============================== r = n∑xy-∑x∑yn∑x2-(∑x)2n∑y2-(∑y)2 ; n = 8 r = -0.9249 ================================= x¯ =∑xn=2928=36.5 y¯ = ∑yn = 1678=20.8750 y^ =41.0448 +(-0.5526) x =================================== r2 = (-0.9249)2 = 0.8554 explained = 85.54 % unexplained = 14.46 % ============================ y = 41.0448 - 0.5526*31 =23.91

Math

Statistics

o heavier cars really use more gasolline? Suppose or pounds), and 25 42 29 47 23 40 34 52 30 21 22 13 29 17 21 14 Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex? = Ey? = Exy = Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.) y = Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage unexplained? (Round your answer for to four decimal places. Round your answers for the percentages to two decimal place.) explained % unexplained % Suppose a car weighs x = 31 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) mpg

o heavier cars really use more gasolline? Suppose or pounds), and 25 42 29 47 23 40 34 52 30 21 22 13 29 17 21 14 Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex? = Ey? = Exy = Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.) y = Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage unexplained? (Round your answer for to four decimal places. Round your answers for the percentages to two decimal place.) explained % unexplained % Suppose a car weighs x = 31 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) mpg

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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