In the least squares equation, Ŷ = 10 + 20X the value of 20 indicates ____________.
The Y-intercept increases by 20 units for each unit increase in X
That Y increases by 20 units for each unit increase in X
That X increases by 20 units for each unit increase in Y
The error in prediction
In the least squares equation Ŷ = 10 + 20X, the value of 20 indicates that Y increases by 20 units for each unit increase in X.
To understand this, let's break down the equation:
- Ŷ represents the predicted value of Y.
- 10 is the Y-intercept, which is the value of Y when X is equal to 0.
- 20X represents the linear relationship between X and Y. The coefficient 20 indicates the rate at which Y changes with respect to X.
Therefore, for each unit increase in X, Y (Ŷ) will increase by 20 units.
20 represents the slope.
Slope is defined as the increase in y-value divided by the increase in x-value, that is:
slope = Δy / Δx