Unit seven scatterplot and data analysis lesson six trend lines. Write an equation in slope intercept form of the trend line.
To write an equation in slope-intercept form of a trend line, first calculate the slope of the trend line. The formula for the slope of a trend line is:
\[m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2}\]
Where:
m = slope of the trend line
n = number of data points
\(\sum{xy}\) = sum of the products of x and y values
\(\sum{x}\) = sum of x values
\(\sum{y}\) = sum of y values
\(\sum{x^2}\) = sum of the squared values of x
Once you have calculated the slope, you can then calculate the y-intercept using the formula:
\[b = \frac{\sum{y} - m(\sum{x})}{n}\]
Where:
b = y-intercept
Finally, you can write the equation of the trend line in slope-intercept form as:
\[y = mx + b\]
Plug in the values of m and b that you calculated to get the final equation in slope-intercept form of the trend line.