The correct answer is: C. Least squares is not an estimation tool.
Least squares is a method of estimating the parameters of a linear model. It is the most common method of linear regression, and it is used in a variety of fields, including statistics, economics, and machine learning.
The least squares estimator is the line that minimizes the sum of the squared distances between the data points and the line. This line is called the regression line.
The least squares estimator is unbiased, which means that it is the line that minimizes the expected squared error. It is also consistent, which means that it converges to the true line as the number of data points increases.
Least squares is a powerful tool for estimating the parameters of a linear model. However, it is important to note that it is not the only method of estimation. Other methods, such as maximum likelihood estimation, may be more appropriate in some cases.
Here is a brief explanation of each option:
- A. Regression through the origin yields an equivalent slope if you center the data first. This is true. If you center the data first, the slope of the regression line will be the same as the slope of the regression line through the origin.
- B. Normalizing variables results in the slope being the correlation. This is also true. If you normalize the variables, the slope of the regression line will be the correlation between the two variables.
- D. None of the mentioned. This is not true. Option C is false.
I hope this helps!