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Chapter 12: Q57E. (page 747)

Commercial refrigeration systems. The role of maintenance in energy saving in commercial refrigeration was the topic of an article in the Journal of Quality in Maintenance Engineering (Vol. 18, 2012). The authors provided the following illustration of data relating the efficiency (relative performance) of a refrigeration system to the fraction of total charges for cooling the system required for optimal performance. Based on the data shown in the graph (next page), hypothesize an appropriate model for relative performance (y) as a function of fraction of charge (x). What is the hypothesized sign (positive or negative) of the 尾2parameter in the model?

Short Answer

Expert verified

The appropriate model for the scatterplot above is a quadratic model of y on x.

The sign of 尾2will be positive as it can be seen in the graph that the parabola is an upward-sloping curve.

Step by step solution

01

model for the fitted data

The second-order model equation for the fitted data isy=尾0+尾1x+尾2x2

02

Sign of β2

The sign of 尾2will be positive as it can be seen in the graph that the parabola is an upward-sloping curve.

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Most popular questions from this chapter

Question: The complete modelE(y)=尾0+尾1x1+尾2x2+尾3x3+尾4x4+蔚was fit to n = 20 data points, with SSE = 152.66. The reduced model,E(y)=尾0+尾1x1+尾2x2+蔚, was also fit, with

SSE = 160.44.

a. How many 尾 parameters are in the complete model? The reduced model?

b. Specify the null and alternative hypotheses you would use to investigate whether the complete model contributes more information for the prediction of y than the reduced model.

c. Conduct the hypothesis test of part b. Use 伪 = .05.

The first-order model E(y)=尾0+尾1x1was fit to n = 19 data points. A residual plot for the model is provided below. Is the need for a quadratic term in the model evident from the residual plot? Explain.

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.

Buy-side vs. sell-side analysts鈥� earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The Harvard Business School professors used regression to model the relative optimism (y) of the analysts鈥� 3-month horizon forecasts. One of the independent variables used to model forecast optimism was the dummy variable x = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm}.

a) Write the equation of the model for E(y) as a function of type of firm.

b) Interpret the value of尾0in the model, part a.

c) The professors write that the value of尾1in the model, part a, 鈥渞epresents the mean difference in relative forecast optimism between buy-side and sell-side analysts.鈥� Do you agree?

d) The professors also argue that 鈥渋f buy-side analysts make less optimistic forecasts than their sell-side counterparts, the [estimated value of尾1] will be negative.鈥� Do you agree?

Question: Bus Rapid Transit study. Bus Rapid Transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (Transportation Research Board Annual Meeting, January 2003). Data on the following variables (all measured on a 5-point scale, where 1 = very unsatisfied and 5 = very satisfied) were collected for a sample of over 500 bus riders: overall satisfaction with BRT (y), safety on bus (x1), seat availability (x2), dependability (x3), travel time (x4), cost (x5), information/maps (x6), convenience of routes (x7), traffic signals (x8), safety at bus stops (x9), hours of service (x10), and frequency of service (x11). CUTR analysts used stepwise regression to model overall satisfaction (y).

a. How many models are fit at step 1 of the stepwise regression?

b. How many models are fit at step 2 of the stepwise regression?

c. How many models are fit at step 11 of the stepwise regression?

d. The stepwise regression selected the following eight variables to include in the model (in order of selection): x11, x4, x2, x7, x10, x1, x9, and x3. Write the equation for E(y) that results from stepwise regression.

e. The model, part d, resulted in R2 = 0.677. Interpret this value.

f. Explain why the CUTR analysts should be cautious in concluding that the best model for E(y) has been found.
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