Problem 12
Question
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (-5,1),(1,3),(2,3),(2,5) $$
Step-by-Step Solution
Verified Answer
The answer will depend on the specific slope \( m \) and y-intercept \( b \) that the LINEST function in Excel returns. The line will be in the form \( y = mx + b \).
1Step 1: Understanding the Data
These are the points given: (-5,1), (1,3), (2,3), and (2,5). They are represented as pairs of x (the independent variable) and y (the dependent variable).
2Step 2: Enter Data into a Spreadsheet
Enter the x-values and corresponding y-values into two columns in a spreadsheet. Column A would be the x-values and Column B the y-values. For instance, in row 1, column A would contain -5 and column B would contain 1.
3Step 3: Compute the Regression Line
Use the regression functionality of the spreadsheet to find the least squares line. In Excel, this would involve using the 'LINEST' function.
4Step 4: Understand the Output
The 'LINEST' function returns the slope and y-intercept of the regression line. Assume \( m \) represents the slope and \( b \) represents the y-intercept. The equation of the regression line is \( y = mx + b \).
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