Question

the method of least square provides a relationship y=f(x) such that the sum of squares of the residuals is​

Answer 1

Answer:

The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve. Least squares regression is used to predict the behavior of dependent variables

Answer 2

The method of least squares is a statistical technique used to find the best-fit line or curve for a set of data points. It aims to minimize the sum of squares of the residuals (the difference between the predicted values and the actual values) to find the most accurate fit.

Here are the steps involved in the method of least squares:

• Collect data: Gather a set of data that includes both independent and dependent variables.

• Choose a model: Decide on the type of model you want to use to represent the relationship between the variables, such as linear or polynomial.

• Determine the parameters: The model will have parameters that need to be determined, such as the slope and intercept for a linear model.

• Calculate the predicted values: Use the chosen model and parameters to calculate the predicted values for the dependent variable.

• Calculate the residuals: Subtract the predicted values from the actual values to calculate the residuals.

• Square the residuals: Square each of the residuals to get rid of the negative values and make them easier to work with.

• Sum the squared residuals: Add up all the squared residuals to get the sum of squares of the residuals.

• Minimize the sum of squares of the residuals: Use optimization techniques to find the values of the model parameters that minimize the sum of squares of the residuals.

• Validate the model: Check the goodness of fit of the model by examining the residual plots and statistical metrics such as R-squared, adjusted R-squared, and root mean square error.

Overall, the method of least squares provides a way to find the best-fit line or curve for a set of data points by minimizing the sum of squares of the residuals.

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