Dear Researchers
I need assistance on solving the following third order polynomial regression analysis: Y= -1E-06x3 + 0.002x2-0.004x+6. To be specific, i need somebody to explain to me how the values of X= 66.7 was obtained from this equation. Make it simple and easy to understand because I'm a layman in area of maths. Your assistance will be highly appreciated.
Dear Nadakalimwe,
I do not understand exactly your question, but if you want to determine the value of x corresponding to a given value of Y you have simply to solve a third-order polynomial equation. You can use for this the classical Cardan method (see wikipedia for example).
Richard
Dear Richard.
see the attached document to understand my question clear. On the graph you find the earlier mentioned formular, the value highlighted in yellow I guess is obtained by using the formular on the graph like what they do with second order polynomial functions. What I need is just simple step on how the authors got that value 66.7.
Looking forward to hear from you soon.
Dear Ndakalimwe,
looking to the figure, the value 66.7 seems to be the value leading to the maximum of Y.
To check this you have just to verify that :
dY/dx = 0 and d2Y/dx2
Thanks Peter, I guess I have to ask them. I understand x=66.7 is the highest point on y axis (maximum point). but getting on the regression formulae is challenge. I was showed how to solve a second order polynomial analysis and it work well. For instance, Y=- 0.5003x2 + 1.8622x + 9.8219, to get the value of X at the highest value of Y, see the following steps. 1.8622/0.5003 = 3.722; 3.722/2 = 1.861, Then x will be equal to 1.861. Perhaps as a mathematician you can deduce something from this, and relate it to the third order polynomial regression analysis. Also see the attached doc for the example given. Thanks.
Hello Ndakalimwe,
First of all, I found little discrepancy between equation in the graph and equation you put in the question. However, I took the equation of the graph as a reference. If 1st derivative taken to zero, (dy/dx =0) the x values I get is [11, 122.33]. At second derivative, pluging those two x values, it is found that at 122.33 the function has maxima value (ymax =3.27) as dy2/dx2 is negative at that value. Unfortunately, this value is out of your graph. If dy2/dx2 is taken equal to zero you will find X=66.67 (this is not for maxima or minima criteria). I don't know is that answere your question but I just put some of my findings.
Thanks,
Shah
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