**Table and Regression Analysis**The table displays data on the number of initial public offerings (IPOs) of stock issued over a 10-year period, alongside the total proceeds from these offerings (in millions):| Issues, x | 415 | 454 | 684 | 485 | 475 | 375 | 56 | 73 | 198 | 165 ||-----------|-----|-----|-----|-----|-----|-----|----|----|-----|-----|| Proceeds, y (in millions) | 18,867 | 28,926 | 43,827 | 30,645 | 26,671 | 16,660 | 21,396 | 11,986 | 30,443 | 27,958 |The regression line is given by the equation: \[ \hat{y} = 47.323x + 18,552.22 \]### (a) Coefficient of Determination*Task*: Find the coefficient of determination and interpret the result.- **Options for Interpretation**: - The coefficient of determination represents the fraction of the variation in proceeds that is unexplained and due to other factors or sampling error; the remaining fraction is explained by variation in the number of issues. - The coefficient of determination represents the fraction of the variation in proceeds explained by variation in the number of issues; the remaining fraction is unexplained due to other factors or sampling error.### (b) Standard Error of Estimate \( s_e \)*Task*: Find the standard error of estimate \( s_e \) and interpret the result.- **Options for Interpretation**: - The standard error of estimate for the proceeds for a specific number of issues is about \( s_e \) million dollars. - The standard error of estimate of the issues for a specific number of proceeds is about \( s_e \) million dollars. **Instructions**: Round to three decimal places as needed.

(a). Given, n=10 The table below shows the required calculation: x y xy x2 y2 415 18867 7829805 172225 355963689 454 28926 13132404 206116 836713476 684 43827 29977668 467856 1920805929 485 30645 14862825 235225 939116025 475 66371 31526225 225625 4405109641 375 66061 24772875 140625 4364055721 56 20396 1142176 3136 415996816 73 11981 874613 5329 143544361 198 30443 6027714 39204 926776249 165 27958 4613070 27225 781649764 Total 3380 345475 134759375 1522566 15089731671 The correlation coefficient is obtained as- r=n∑ijxy-∑ix∑jyn∑ix2-∑ix2n∑jy2-∑jy2=10×134759375-3380×34547510×1522566-3380210×15089731671-3454752=0.5195 Therefore the required coefficient of determination is obtained as- Coefficient of determination (r2)=0.51952=0.269 The coefficient of determination is the fraction of the variation in proceeds that can be explained by the variation in issues. The remaining fraction of the variation is unexplained and is due to other factors or to sampling error. (b). The equation of regression line is given as- y^=47.323x+18552.22 The table below shows the required calculation- x y y' (y-y')^2 415 18867 38191.265 373427217.8 454 28926 40036.862 123451254.4 684 43827 50921.152 50326992.6 485 30645 41503.875 117915166.3 475 66371 41030.645 642133591.5 375 66061 36298.345 885815632.6 56 20396 21202.308 650132.5909 73 11981 22006.799 100516645.6 198 30443 27922.174 6354563.722 165 27958 26360.515 2551958.325 Total 2303143155 The required standard error of the estimate is obtained as- S.Eest=∑jy-y'2n-2=230314315510-2=16967.407 The standard error of estimate of the proceeds for a specific number of issues is about se million dollars.

Math

Statistics

The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y = 47.323x + 18,552.22. Complete parts a and b. 415 454 684 485 475 375 56 73 198 Issues, x Proceeds, 18.867 28.926 43.827 30.645 66.371 66.061 20,396 11,981 30.443 27.958 165 (a) Find the coefficient of determination and interpret the result. (Round to three decimal places as needed.)

The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y = 47.323x + 18,552.22. Complete parts a and b. 415 454 684 485 475 375 56 73 198 Issues, x Proceeds, 18.867 28.926 43.827 30.645 66.371 66.061 20,396 11,981 30.443 27.958 165 (a) Find the coefficient of determination and interpret the result. (Round to three decimal places as needed.)

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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