Below is a partial multiple regression computer output based on a quadratic regression model to predict student enrollment at a local university. The dependent variable is the annual enrollment given in thousands of students, the independent variable X is the increase in tuition stated in thousands of dollars per year, and X2is the square of tuition increase given in squared thousands of dollars per year.
Interpret β0 (the y intercept) and β1(the β coefficient for the X variable). Does the parabola open upward or downward? Why?
Source SS df
Model 29.44 2
Error 59.66 15
Standard Error
Variable Coefficient (Sb)
Intercept 8.01 1.45
x -1.35 0.55
x2 0.46 0.43