Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line. Please round the coefficients in your equation to two decimal places.

Question

Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line.  Please round the coefficients in your equation to two decimal places.

Quizplus · Accepted Answer

The least-squares line is a line that best fits the given data points minimizing the sum of the squares of the residuals. The equation of the least-squares line is given by: 
y = a + bx 
where a is the y-intercept and b is the slope of the line.

Using a calculator or statistical software, we can find that the equation of the least-squares line for the given data is: 
y = 9.48 + 0.80x

To confirm, we can plot the data on a scatter diagram and graph the least-squares line as shown below: 
scatter diagram

The red line is the least-squares line which fits the data points best. Therefore, the correct choice is B.

Find the Equation of the Least-Squares Line for the Given