Final answer:
The value of y is determined by solving the algebraic equation presented, which after simplifying and isolating y, gives us a value of y equal to 3200.
Step-by-step explanation:
To find the value of y, we can use the given equations and perform the necessary algebraic manipulations. The question appears to contain a regression analysis problem where ŷ, read as 'y hat', represents the estimated value of y. This value is obtained from the regression line, which helps in making predictions about y based on corresponding values of x.
Here are the steps to solve the provided equations:
- Begin by simplifying the equation with constants and coefficients next to y:
Y = 400 + 0.85(Y - 0.25Y) + 300 + 200 + 500 - 0.1(Y - 0.25Y)
Y = 1400 + 0.6375Y - 0.075Y
Now, combine like terms:
0.4375Y = 1400. - To isolate y, divide both sides by 0.4375:
Y = 3200. - Therefore, the value of y is 3200.