Question
Unit seven scatterplot and data analysis lesson six trend lines. Write an equation in slope intercept form of the trend line.
Answers
GPT 3.5
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.
\[m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2}\]
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.