Quadratic regression models
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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
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Solution Summary
The quadratic regression models are examined. The parabola to open upward or downward are given.
Solution Preview
Recall that the equation of a quadratic regression is
y = b0 + b1x + b2x^2 + e
Substituting in the estimated coefficients gives
y = 8.01 - 1.35x + 0.46x^2 + e
This parabola opens upwards as the coefficient of x^2 is positive (remember that the coefficient of the term with the square term decides whether the parabola opens up or down).
The ...
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