Answer:
The values for ( a ) and ( b ) in the equation ( \hat{y} = a + bx ) are -4.194118787 and 0.301433595, respectively.
Explanation:
The equation you've provided is a linear regression model in the form of ( \hat{y} = a + bx ), where ( \hat{y} ) is the predicted value, ( x ) is the independent variable, and ( a ) and ( b ) are the intercept and slope of the regression line, respectively.
From the coefficients provided in the regression output:
The intercept ( a ) is given as -4.194118787
The coefficient for the independent variable (slope) ( b ) is given as 0.301433595
Therefore, the values for ( a ) and ( b ) in the equation ( \hat{y} = a + bx ) are:
( a = -4.194118787 )
( b = 0.301433595 )
Thus, the equation becomes [ \hat{y} = -4.194118787 + 0.301433595x ]