Finding the equation of the least square line.Ex=110, Ex^2 =1540, Ey=468, Ey^2=22,434, Exy=5524.
The answer is Y=1.139x+34.27. I can figure out the 1.139 but not the 34.27. Pls Help
To find the equation of the least squares line, you can follow the steps of the least squares regression method. Here's how you can calculate the coefficients for the equation:
Step 1: Calculate the slope (m)
The slope of the least squares line can be calculated using the formula:
m = (n * Σ(xy) - Σx * Σy) / (n * Σ(x^2) - (Σx)^2)
Given:
Ex = 110
Ey = 468
Ex^2 = 1540
Ey^2 = 22,434
Exy = 5524
n = the number of data points
Substituting the given values:
m = (n * Exy - Ex * Ey) / (n * Ex^2 - (Ex)^2)
Step 2: Calculate the y-intercept (b)
The y-intercept can be calculated using the formula:
b = (Σy - m * Σx) / n
Substituting the given values:
b = (Ey - m * Ex) / n
Step 3: Substitute the values into the equation
Once you have the values of m and b, you can write the equation of the least squares line:
Y = m * x + b
Substituting the calculated values of m and b will give you the final equation.
In your case, I'll calculate the values for you, assuming there are n data points. Please provide the value of "n" before proceeding.