Math Problem Statement

Question content area top Part 1 For the data given​ below, answer parts ​(a) through ​(f). x 1 2 3 4 5 6 7 y 4 6 7 10 12 14 16 Graph the line found in y= 2x + 2 on the scatter plot. Use a graphing utility to find the line of best fit.

Solution

The graph above shows the scatter plot of the given data points, the line y=2x+2y = 2x + 2 (in green), and the line of best fit (in red dashed).

Line of Best Fit:

The equation for the line of best fit is: y=2.04x+1.71y = 2.04x + 1.71 This line was calculated using the least squares method to best fit the given data points.

Do you have any questions, or would you like further details on the steps involved?

Here are 5 related questions to explore further:

  1. How is the slope of a line calculated in linear regression?
  2. What is the significance of the rr-value in linear regression?
  3. How do we interpret the y-intercept in a linear equation?
  4. Can the line y=2x+2y = 2x + 2 be considered a good fit for the data?
  5. What is the standard error in the context of the regression line?

Tip: The line of best fit helps predict values of yy for given xx-values by minimizing the squared distances between observed points and the line.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Scatter Plot
Line of Best Fit
Graphing

Formulas

y = mx + b (Equation of a line)
Least squares method for line of best fit

Theorems

Linear regression theorem

Suitable Grade Level

Grades 9-12