Final answer:
The estimated value of y when x = 4 can be determined using the given coefficients. The value of y can be calculated using the linear regression equation: y = β0 + β1x, where β0 is the intercept and β1 is the coefficient of the independent variable x. Substituting the values, the estimated value of y when x = 4 is approximately 4.3588.
Step-by-step explanation:
Given the coefficients from the linear regression analysis, the equation for the regression line is: y = -12.8094 + 2.1794x. To find the estimated value of y when x = 4, substitute x = 4 into the regression equation: y = -12.8094 + 2.1794 * 4. Solving this equation, we get y ≈ 4.3588. Therefore, when x = 4, the estimated value of y is approximately 4.3588.
The regression equation represents the relationship between the independent variable x and the dependent variable y. The coefficient of x (2.1794) indicates the change in y for a unit change in x. In this case, for every one-unit increase in x, y is expected to increase by 2.1794 units. The intercept (-12.8094) represents the value of y when x = 0. By plugging in the given x-value (4) into the regression equation, the estimated value of y is computed.
Therefore, based on the given coefficients, the estimated value of y when x = 4 is approximately 4.3588. This value signifies the expected value of the dependent variable corresponding to the specified value of the independent variable in the linear regression model.