The equation for the line of best fit is y = 220x + 500.
To find the equation for the line of best fit using linear regression, we can use the following formula:
y = mx + b
where:
y is the dependent variable (SAT score)
m is the slope of the line
x is the independent variable (GPA)
b is the y-intercept of the line
To find the slope of the line, we can use the following formula:
m = (y1 - y2) / (x1 - x2)
where:
y1 and y2 are two points on the line
x1 and x2 are the corresponding x-values of those two points
To find the y-intercept of the line, we can use the following formula:
b = y - mx
where:
y and x are any point on the line
m is the slope of the line
Using the data in the image, we can find the following:
Slope:
m = (1380 - 940) / (4 - 2) = 220
Y-intercept:
b = 940 - 220 * 2 = 500
Therefore, the equation for the line of best fit is:
y = 220x + 500
This means that for every 1 point increase in GPA, the SAT score is predicted to increase by 220 points.
Therefore ,the equation for the line of best fit is y = 220x + 500.