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  3. vol% r.i 0 1.3323 10 1.3388 20 1.3446 30 1

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...

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Statistics

Vol%R.I
01.3323
101.3388
201.3446
301.3497
401.3541
501.3580
601.3610
701.3630
801.3638
901.3630
1001.3600

I tried to graph the following data in excel to obtain theequation of the line which happens to be polynomial 4th order

I am given a R.I of 1.3616 and expected to obtain Vol% bysolving the polynomial. i did that with excel and got 9.2 and thecorrect answer is around (you can guess by liner interpolation) is63.

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

Answer & Explanation Solved by verified expert
4.3 Ratings (1083 Votes)

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
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