91影视

Question: Determine which pairs of the following models are 鈥渘ested鈥� models. For each pair of nested models, identify the complete and reduced model.

$$\begin{gathered} \mathit{a}\mathbf{.}\mathbf{}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}} \\ \mathit{b}\mathbf{.}\mathbf{}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}} \\ \mathit{c}\mathbf{.}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{{\mathit{x}}_{\mathbf{1}}}^{\mathbf{2}} \\ \mathit{d}\mathbf{.}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{3}}{\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{2}} \\ \mathit{e}\mathbf{.}\mathbf{}\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{3}}{\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{4}}{{\mathbf{x}}^{\mathbf{2}}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{5}}{{\mathbf{x}}_{\mathbf{2}}}^{\mathbf{2}} \end{gathered}$$

Question: Suppose you fit the regression model$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{4}}{{\mathbf{x}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{5}}{{\mathbf{x}}_{\mathbf{2}}}^{\mathbf{2}}$to n = 30 data points and wish to test H₀: 尾₃ = 尾₄ = 尾₅ = 0

Question: The complete model$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{尾}}_{\mathbf{3}}{\mathbf{x}}_3\mathbf{+}{\mathit{尾}}_{\mathbf{4}}{\mathbf{x}}_4\mathbf{+}\mathit{蔚}$was fit to n = 20 data points, with SSE = 152.66. The reduced model,$\mathit{E}\mathbf{\left(}\mathit{y}\mathbf{\right)}\mathbf{=}{\mathit{尾}}_{\mathbf{0}}\mathbf{+}{\mathit{尾}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{尾}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}\mathit{蔚}$, was also fit, with

SSE = 160.44.

Question: Ambiance of 5-star hotels. Although invisible and intangible, ambient conditions such as air quality , temperature , odor/aroma , music , noise level , and overall image may affect guests鈥� satisfaction with their stay at a hotel. A study in the Journal of Hospitality Marketing & Management (Vol. 24, 2015) was designed to assess the effect of each of these ambient factors on customer satisfaction with the hotel . Using a survey, researchers collected data for a sample of 422 guests at 5-star hotels. All variables were measured as an average of several 5-point questionnaire responses. The results of the multiple regression are summarized in the table on the next page.

1. Write the equation of a first-order model for hotel image as a function of the six ambient conditions.
2. Give a practical interpretation of each of the b-estimates shown.
3. A 99% confidence interval for is (.350, .576). Give a practical interpretation of this result.
4. Interpret the value of adjusted .
5. Is there sufficient evidence that the overall model is statistically useful for predicting hotel image ? Test using a = .01.