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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

#### 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 ...

#### Solution Summary

The quadratic regression models are examined. The parabola to open upward or downward are given.

\$2.19

## Building a Quadratic Regression Model

See attachment for data on y = green liquor (g/L) and x = paper machine speed (ft/min) from a Kraft paper machine.

(a) Fit the model Y = Bo + B1x + B2x^2 + e using least squares.
(b) Test for significance of regression using alpha = 0.05. What are your conclusions?
(c) Plot the residuals from the model in part (a) versus y. Does the plot reveal any inadequacies?
(d) Construct a normal probability plot of the residuals. Comment on the normality assumption.

See attachment for given chart.

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