Regression Equation and BXY in CA Foundation

Regression Equation

The regression equation is used to determine the relationship between two variables, x and y. It is represented as y = a + bx, where y is the dependent variable, x is the independent variable, a is the intercept, and b is the slope of the line.

In this given regression equation, x on y is: X= 35 /8 -2Y / 5, which means that x is the dependent variable and y is the independent variable. The equation can be rearranged to represent y in terms of x as follows:

Y= 5/2 - 5/2 x (35/8 - x/5)

BXY

BXY is the slope of the regression line and represents the change in y for a unit change in x. It is calculated using the formula:

BXY = Σ (xi - x̄)(yi - ȳ) / Σ (xi - x̄)2

where xi and yi are the values of x and y for each observation, x̄ and ȳ are the mean values of x and y, and Σ represents the sum of all observations.

Using the given regression equation, we can find the values of xi and yi for each observation. Substituting X= 35 /8 -2Y / 5 in the equation Y= a + bx, we get:

Y= a + b (35 /8 -2Y / 5)

Simplifying the equation, we get:

Y = (35/8)b/5 + (a - 2/5)bY/5

Comparing the equation with y = a + bx, we can see that:

a = (35/8)b/5
b = -(2/5)b/5

Substituting these values in the formula for BXY, we get:

BXY = Σ [(35/8 - 2yi/5) - (35/8)(-2/5)b/5 - yi(2/5)b/5 - (35/8)b/5] / Σ [(35/8 - 2yi/5) - (35/8)(-2/5)b/5]2

Simplifying the equation, we get:

BXY = 35/8 - (2/5)(2/5)(5/2)

Therefore, BXY is equal to 35/8 - 2/25 = 267/200.

In the regression equation x on y, X = 35/8 – 2Y /5, bxy is equal to