Please include all anwsers! Which of the following are correct interpretations of the value of y-hat (ŷ = a + bx)?[Select all correct answers.]It is the observed value of the dependent variable.00 00It is the point estimate for the mean value of all units or subjects at a givenvalue of the independent variable(s).It is the predicted value of the independent variable.It is the predicted value for a single specific unit or subject at a given value ofthe independent variable(s).

For a provided linear regression equation, the model with the least square error is: y^=a+bx. Here, b is the slope of the regression line. And a is the value of the y-intercept. Considering y^ is obtained as the best-estimated value for a specified value of x, for a linear regression model, the value of y^ is inferred to fall on the regression line of a+bx. With this assumption, the value of y^ may not always be indifferent to the value of y (i.e., the observed value). So the 1st option is rejected. The regression line y^=a+bx passes through the value x¯, y¯ provided that the estimated model is fitted with the least sum of squares. However, considering the line that passes through x¯, y¯, y^ is considered as the expected value for a specified value of the independent variable x, provided that x=x¯. So the 2nd option is incorrect. By assumption, the value of y^ is the predicted value for the considered independent variable x. So 3rd option is applied. For a specified value of x, y^ is obtained a numerical value, and it is interpreted as the predicted value for the specified unit or subject for a given value of x (i.e., the independent variable). So the 4th option is applied.