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juice34
Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.
Oops. I thought you were looking for a derivation of the quadratic formula itself (which happens to be done via "completing the square"). But you are looking to derive the parameters of a least squares fit to a quadratic function. My bad!juice34 said:Really, my professor said that its the least squares method. Is it the same thing i assume then. I appreciate it very much doc.
juice34 said:Here is what i have Y=ax^2+bx+c. Then the residual is d(i)=y(xi) so di=yi-(ax^2i+bxi+c). Then i take the sum of the square of the residuals. &(a,b,c)=E di^2=E((ax^2i+bxi+c))^2 and then I am lost after that!
The purpose of deriving the quadratic equation using least squares is to find the best fitting quadratic curve for a set of data points. This technique is commonly used in statistics and data analysis to determine the relationship between two variables.
The least squares method works by minimizing the sum of the squared differences between the actual data points and the predicted values on the quadratic curve. This is achieved by finding the values for the coefficients of the quadratic equation that result in the smallest sum of squared errors.
One advantage of using least squares is that it is a relatively simple and straightforward method for finding the best fitting quadratic curve. It also allows for a quantitative measure of how well the curve fits the data, as the sum of squared errors can be calculated. Additionally, least squares can be used with any number of data points, making it applicable to a wide range of data sets.
One limitation of using least squares is that it assumes that the relationship between the variables is linear. This means that it may not be suitable for data sets with non-linear relationships. Additionally, the least squares method can be sensitive to outliers in the data, which can skew the results of the analysis.
The results of deriving the quadratic equation using least squares can be interpreted as the best fitting curve for the given data set. The coefficients of the quadratic equation can also provide information about the direction and strength of the relationship between the variables. Additionally, the sum of squared errors can be used as a measure of the accuracy of the curve in representing the data.