212k views
4 votes
Use the data and a linear regression to find the equation for the line of best fit.

Use the data and a linear regression to find the equation for the line of best fit-example-1
User Kanuos
by
7.5k points

1 Answer

3 votes

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.

User Muhammad Amjad
by
7.6k points