# Finding least squares solution of Ax=b?

• Math100
In summary, the least squares solution of Ax=b is a method used to find the best fit line or curve for a set of data points that do not perfectly align with a linear equation. It is calculated by finding the values of the coefficients in the linear equation that minimize the sum of the squared errors. The method is best used when there is no exact solution to the linear equation or when the data points do not align perfectly with a linear equation. The least squares solution is different from the exact solution as it finds the best possible fit for the data points rather than satisfying the equation exactly. This method has various applications in fields such as engineering, economics, and statistics, including regression analysis, data smoothing, image processing, and time series analysis.
Math100
TL;DR Summary
Does anyone know the command or how to find the least squares solution of Ax=b on Ti-89 graphing calculator?
Does anyone know the command or how to find the least squares solution of Ax=b on Ti-89 graphing calculator? I'm trying to check my answers on Ti-89 for those linear algebra problems.

I have a ti-84 and i am not with it right now so don't quote me on this lol but did you enter your x values into L1 and your y values into L2? on my Ti84 after that, you go to stat --> calc --> 8 (which is LinReg(a+bx)) and press enter.

## 1. What is the purpose of finding the least squares solution of Ax=b?

The least squares solution of Ax=b is used to find the best fitting line or curve for a set of data points. It minimizes the sum of the squared distances between the data points and the line or curve, making it a useful tool in statistical analysis and data modeling.

## 2. How is the least squares solution of Ax=b calculated?

The least squares solution of Ax=b is calculated using linear algebra techniques, such as matrix multiplication and inversion. It involves finding the transpose of matrix A, multiplying it by A, and then solving for the values of x that satisfy the equation Ax=b.

## 3. What makes the least squares solution of Ax=b different from other methods of solving equations?

The least squares solution of Ax=b takes into account the errors or discrepancies in the data points, rather than just finding a solution that satisfies the equation exactly. This makes it a more robust method for finding a line of best fit that can account for outliers and noise in the data.

## 4. Can the least squares solution of Ax=b be used for non-linear data?

Yes, the least squares solution of Ax=b can be used for non-linear data by transforming the data points into a linear form. This can be done by taking the logarithm, inverse, or other mathematical functions of the data points before applying the least squares method.

## 5. What are some practical applications of the least squares solution of Ax=b?

The least squares solution of Ax=b has many applications, including linear regression analysis in statistics, curve fitting in data modeling, and image processing in computer vision. It is also commonly used in fields such as economics, engineering, and physics to analyze and interpret data.

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