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Select the correct definition of a least squares regression line.

1) A line that minimizes the sum of the squared differences between the observed and predicted values.
2) A line that passes through the point (0,0) and has a slope of 1.
3) A line that is drawn to fit the data points as closely as possible.
4) A line that is used to predict future values based on past data.

User RTBarnard
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1 Answer

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Final answer:

The least squares regression line is a line that minimizes the sum of the squared differences between observed and predicted values, used in linear regression to find the best-fit line for a data set.

Step-by-step explanation:

The correct definition of a least squares regression line is a line that minimizes the sum of the squared differences between the observed values and predicted values, which is option 1. This line is the result of a process called linear regression, where the sum of squared errors (SSE) is minimized to find the best-fit line for the data. While there may be several ways to find a regression line, the least-squares method is widely used due to its uniform and objective approach to fitting a line within a scatter plot of data points. Once the least-squares regression line is established, it can be used for making predictions within the data set, but should be applied cautiously for values outside of it. However, the line does not necessarily have to pass through the point (0,0) with a slope of 1, which makes option 2 incorrect. Option 3 refers to a line that closely fits the data but doesn't specify the minimization of SSE, and option 4 refers to a general use without specifying the least-squares method.

User Loveleen
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