Refer to the three models given in Exercise 11.88. Let

Chapter 11, Problem 88E

(choose chapter or problem)

Television advertising would ideally be aimed at exactly the audience that observes the ads. A study was conducted to determine the amount of time that individuals spend watching TV during evening prime-time hours. Twenty individuals were observed for a 1-week period, and the average time spent watching TV per evening, Y , was recorded for each. Four other bits of information were also recorded for each individual: x1 = age, x2 = education level, x3 = disposable income, and x4 = IQ. Consider the three models given below:

Model I: \(Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\varepsilon\)

Model II: \(Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\imath\)

Model III: \(Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\varepsilon\)

Are the following statements true or false?

a If Model I is fit, the estimate for σ2 is based on 16 df.

b If Model II is fit, we can perform a t test to determine whether x2 contributes to a better fit of the model to the data.

c If Models I and II are both fit, then SSEI ≤ SSEII.

d If Models I and II are fit, then \(\vartheta_{1}^{2} \leq \vartheta_{I I}^{2})

e Model II is a reduction of model I.

f Models I and III can be compared using the complete/reduced model technique presented in Section 11.14.

Equation transcription:

Text transcription:

Y=beta{0}+\beta{1} x{1}+\beta_{2} x{2}+\beta{3} x{3}+\varepsilon

Y=beta{0}+\beta{1} x{1}+\beta_{2} x{2}+\imath

Y=beta{0}+\beta{1} x{1}+\beta_{2} x{2}+\beta{3} x{1} x{2}+\varepsilon

vartheta{1}^{2} leq vartheta{I I}^{2}