Which of the following statements are true when creating an approximate linear model for a given data set? Select all that apply.
-The line must pass through all of the points in the data set.
-It provides a way to make predictions on data points outside the given data set
-It can only be done if the data is perfectly linear.
-It is called Linear Regression
-It is called Finding the Line of Best Fit
Well, well, well, let me put on my mathematical clown suit and answer this one!
The true statements when creating an approximate linear model for a given data set are:
- It provides a way to make predictions on data points outside the given data set.
- It is called Linear Regression.
- It is called Finding the Line of Best Fit.
So, the line doesn't necessarily need to pass through all the points, and it can be done even if the data isn't perfectly linear. And remember, not everything has to be straight and perfect in life, right? Embrace the curveballs!
The statements that are true when creating an approximate linear model for a given data set are:
- It provides a way to make predictions on data points outside the given data set.
- It is called Linear Regression.
- It is called Finding the Line of Best Fit.
To determine which statements are true when creating an approximate linear model for a given data set, let's examine each statement one by one:
1. The line must pass through all of the points in the data set:
This statement is false. In linear regression or finding the line of best fit, the line does not necessarily need to pass through every data point. Instead, it aims to minimize the overall distance between the line and the data points.
2. It provides a way to make predictions on data points outside the given data set:
This statement is true. One of the main purposes of creating a linear model is to make predictions on data points that were not part of the original data set. By using the equation of the line, we can estimate the value of the dependent variable corresponding to new values of the independent variable.
3. It can only be done if the data is perfectly linear:
This statement is false. While linear regression assumes a linear relationship between the independent and dependent variables, it can still be used even if the relationship is not perfectly linear. The model will still provide an approximation of the relationship, allowing for predictions to be made.
4. It is called Linear Regression:
This statement is true. The process of creating an approximate linear model is indeed called linear regression. It involves fitting a line to the data points using mathematical techniques to find the best-fit line.
5. It is called Finding the Line of Best Fit:
This statement is also true. Another commonly used term for creating an approximate linear model is finding the line of best fit. This line represents the best overall approximation of the relationship between the variables, minimizing the overall distance between the line and the data points.
So, the true statements are:
- It provides a way to make predictions on data points outside the given data set
- It is called Linear Regression
- It is called Finding the Line of Best Fit
I like B,D,E
though E need not be the linear model used