Finding equation for regression curve

In summary, The conversation discusses the issue of finding an accurate equation for an interpolated function of any degree, specifically using Mathematica and Excel. It is noted that the plots on Excel can be deceiving and a more accurate method, such as using software like Mathlab or Mathcad, is suggested for finding a polynomial approximation for a given set of data points. The question of whether other equations can be fitted besides polynomials is also raised.

Homework Statement

I want to know how to find equation for the interpolated function of any degree. On Mathematica, for example.

The Attempt at a Solution

Unfortunately, on Excel, the plots are deceiving because the points on the plot are actually out of range.

For example, this equation: - 0.037*Math.pow(i,5) + 0.857*Math.pow(i,4) - 8.406*Math.pow(i,3) + 32.33*Math.pow(i,2) - 46.68*i + 260.2

is displayed to be in the range of 0 and 255 between values 1 and 21 for i.

however, when plugging in numbers, values are clearly not in the range. you get a negative number for i =18.

So therefore, is there a more accurate way of finding regression curves for data AND the equation for the curve?

Are you trying to fit a polynomial to your data, or can you fit other equations?

How many data points do you have?

use some software as Mathlab or Mathcad, find the algorythm for 'Polynomial Approxiamtion' and you will obtain approximating polynomial for given data (x and y values)

What is a regression curve?

A regression curve is a line or curve that best represents the relationship between two variables in a dataset. It is used to predict the value of one variable based on the value of another variable.

Why is it important to find the equation for a regression curve?

Finding the equation for a regression curve allows us to quantify the relationship between two variables and make predictions based on that relationship. It also helps us understand the strength and direction of the relationship between the variables.

How do you find the equation for a regression curve?

The equation for a regression curve can be found by using statistical methods such as least squares regression or maximum likelihood estimation. These methods involve minimizing the distance between the data points and the regression line to find the best fit.

What is the difference between linear and non-linear regression?

Linear regression involves finding a straight line that best represents the relationship between two variables, while non-linear regression involves finding a curve that best represents the relationship. Non-linear regression can be used when the relationship between the variables is not linear.

How do you determine the accuracy of a regression curve?

The accuracy of a regression curve can be determined by calculating the coefficient of determination (R-squared value). This value ranges from 0 to 1 and represents the proportion of the variation in the dependent variable that is explained by the independent variable. A higher R-squared value indicates a more accurate regression curve.

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