For the multiple regression equation ŷ = 100 + 20x©û - 3x©ü + 120x©ý

a. Identify the y-intercept and partial regression coefficient.
b. If x©û = 12, x©ü = 5, and x©ý
c. If x©ý were to increase by 4, what change would be necessary in x©ü in order for the estimated value of y to remain unchanged?

The question in western encoding is as follows:

"For the multiple regression equation ŷ = 100 + 20x₁ - 3x₂ + 120x₃
a. Identify the y-intercept and partial regression coefficient.
b. If x₁ = 12, x₂ = 5, and x₃
c. If x₃ were to increase by 4, what change would be necessary in x₂ in order for the estimated value of y to remain unchanged? "

a.
The y intercept is 100. The partial regression coefficients are +10, -3 and +120.
The question is incomplete for parts (b) and cnosequently (c).
Please supply information.

a. In the multiple regression equation ŷ = 100 + 20x©û - 3x©ü + 120x©ý:

- The y-intercept is the constant term, which is 100. It represents the predicted value of y when all other variables are set to zero.
- The partial regression coefficients represent the effect each independent variable has on the dependent variable, holding all other variables constant. In this equation:
- The partial regression coefficient for x©û is 20.
- The partial regression coefficient for x©ü is -3.
- The partial regression coefficient for x©ý is 120.

b. To find the estimated value of y when x©û = 12, x©ü = 5, and x©ý:
- Substitute the given values into the equation:
ŷ = 100 + 20(12) - 3(5) + 120(x©ý)
- Since x©û = 12, x©ü = 5, the equation becomes:
ŷ = 100 + 240 - 15 + 120(x©ý)
- Simplify the equation further:
ŷ = 325 + 120(x©ý)

c. To determine the change necessary in x©ü when x©ý increases by 4 for the estimated value of y to remain unchanged:
- Start by considering the equation when x©ý increases by 4:
ŷ' = 325 + 120(x©ý + 4)
- Since we want the estimated value of y to remain unchanged, set ŷ' equal to ŷ:
325 + 120(x©ý + 4) = 325 + 120(x©ý)
- Simplify the equation:
120(x©ý + 4) = 120(x©ý)
- Divide both sides of the equation by 120:
x©ý + 4 = x©ý
- Subtract x©ý from both sides of the equation:
4 = 0

The equation 4 = 0 is not true, which means that it is not possible for the estimated value of y to remain unchanged when x©ý increases by 4. Therefore, there is no change in x©ü that would fulfill this condition.