Question
In: Statistics and Probability
Vol% R.I 0 1.3323 10 1.3388 20 1.3446 30 1.3497 40 1.3541 50 1.3580 60 1.3610...
| Vol% | R.I |
| 0 | 1.3323 |
| 10 | 1.3388 |
| 20 | 1.3446 |
| 30 | 1.3497 |
| 40 | 1.3541 |
| 50 | 1.3580 |
| 60 | 1.3610 |
| 70 | 1.3630 |
| 80 | 1.3638 |
| 90 | 1.3630 |
| 100 | 1.3600 |
I tried to graph the following data in excel to obtain the equation of the line which happens to be polynomial 4th order
I am given a R.I of 1.3616 and expected to obtain Vol% by solving the polynomial. i did that with excel and got 9.2 and the correct answer is around (you can guess by liner interpolation) is 63.
here's the polynomial : R.I= 1.3323+6.9476e(-4)X-4.711e(-6)X^2+3.7995e(-5)X^3-3.2634e(-10)X^4
can anyone do hand calculation and excel to confirm this
Solutions
Expert Solution
data
| R I | x | x^2 | x^3 | x^4 |
| 1.3323 | 0 | 0 | 0 | 0 |
| 1.3388 | 10 | 100 | 1000 | 10000 |
| 1.3446 | 20 | 400 | 8000 | 160000 |
| 1.3497 | 30 | 900 | 27000 | 810000 |
| 1.3541 | 40 | 1600 | 64000 | 2560000 |
| 1.358 | 50 | 2500 | 125000 | 6250000 |
| 1.361 | 60 | 3600 | 216000 | 12960000 |
| 1.363 | 70 | 4900 | 343000 | 24010000 |
| 1.3638 | 80 | 6400 | 512000 | 40960000 |
| 1.363 | 90 | 8100 | 729000 | 65610000 |
| 1.36 | 100 | 10000 | 1000000 | 1E+08 |
here x = vol
using excel
| SUMMARY OUTPUT | |||||
| Regression Statistics | |||||
| Multiple R | 0.999995918 | ||||
| R Square | 0.999991836 | ||||
| Adjusted R Square | 0.999986393 | ||||
| Standard Error | 3.98131E-05 | ||||
| Observations | 11 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 4 | 0.001164867 | 0.000291217 | 183723.4853 | 2.17684E-15 |
| Residual | 6 | 9.51049E-09 | 1.58508E-09 | ||
| Total | 10 | 0.001164876 | |||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
| Intercept | 1.332288811 | 3.8106E-05 | 34962.69819 | 3.69551E-26 | 1.332195569 |
| x | 0.00069966 | 5.86868E-06 | 119.2192461 | 2.34825E-11 | 0.0006853 |
| x^2 | -4.93094E-06 | 2.5709E-07 | -19.17986044 | 1.29952E-06 | -5.56002E-06 |
| x^3 | 4.11616E-08 | 3.95622E-09 | 10.40426925 | 4.61841E-05 | 3.14811E-08 |
| x^4 | -3.40909E-10 | 1.96183E-11 | -17.37708938 | 2.32812E-06 | -3.88913E-10 |
RI ^= 1.332288811 + 0.00069966 x -4.93094 * 10^(-6) x^2 + 4.11616* 10^(-8)*x^3 -3.40909 * 10^(-10) x^4
solving
x = 62.4852
orchestra answered 1 year agoRelated Solutions
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