3. Consider the following table.1.62.12.43.654.254.7X₂Yi6.841 8.794 9.9213.012.1475.620.41614.43616.318 17.743a) Construct the least squares polynomial of degree 4 and compute the error.b) Construct the least squares approximation of the form beax, and compute theerror.

We will use the basic knowledge of numerical analysis to answer both the parts of this question…

Answered: 3. Consider the following table. 1.6…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follovw. Advertising Expenditures Revenue 20 2. 32 45 40 10 53 14 54 20 55 a. Let a equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables (to 2 decimals). = b. Test whether revenue and advertising expenditures are related at a 0.05 level of significance. Compute the following (to 2 decimals). SSE SST SSR MSR MSE Compute the F test statistic (to 2 decimals). What is the p-value? Use Table 4 from Appendix B. |- Select your answer - What is your conclusion? |- Select your answer - c. Prepare a residual plot of y-y versus y. Use the result from part (a) to obtain the values of g. Choose the correct residual plot below.
Find the least squares regression line for temperature (x) and number of ice cream cones sold per hour (y). 65 70 75 80 85 90 95 100 105 y 8 10 11 13 12 16 19 22 23 Oŷ = 2.469x+48.240 ý = 0.383x-17.694 Oŷ = -125.376x+31.656 Oŷ = 0.4x-18
Use the method of least squares to fit the model to the data. Y hat= _+_x
The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming). Year Time (seconds) 1912 82.2 1924 72.4 1932 66.8 1952 66.8 1960 61.2 1968 60.0 1976 55.65 1984 55.92 1992 54.64 2000 53.8 2008 53.1 Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) Find the correlation coefficient r. (Round your answer to four decimal places.)r = Find the estimated gold medal time for 1924. (Use your equation from part (d). Round your answer to two decimal places.) Find the estimated gold medal time for 1992. (Use your equation from part (d). Round your answer to two decimal places.) Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.) ch12#1
Suppose that the following table shows the annual sales, in millions of dollars, for Advanced Auto Parts and Auto Zone for 2000 through 2007. Find the least squares quadratic model for Advanced Auto Parts. Lett represents the year, with = 0 corresponding to 2000. Round all coefficients to two decimal places. Year 2000 2001 2002 2003 2004 2005 2006 2007 Advanced Auto Parts 2744 1789 1125 1037 1531 2847 3198 6250 OS=257.082-1356.11+2812.7 S=263.31²-1379.73t+2824.58 OS=259.31²-1396.29t+2767.18 OS=257.08² +1356.11+28127 OS=259.31²+1396.29t+2767.18
5) Suppose a path C is defined by r(t), 2 and r(8)= . If f is a differentiable function satisfying f(3,9) = 6 and f(6, 10) = 14, what is the value of Vf dr?

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3. Consider the following table. 1.6 2.4 3.0 4.7 2.1 6.841 8.794 9.921 12.147 3.65 4.25 14.436 16.318 17.743 Y 5.6 20.416 a) Construct the least squares polynomial of degree 4 and compute the error. b) Construct the least squares approximation of the form beax, and compute the error.