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business statistics in practice

Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions

=+19. Insurance claims. An insurance company has maintained data on the number of automobile claims filed at its Washington office over the past 5 years. They would like to predict the number of claims that they will receive next year.They are planning to use two different models: a moving
=+b) Monthly sales that reveal a consistent percentage increase from month to month.c) Quarterly sales for a woman’s clothing company that reveal an annual peak each December.(continued above)M19_SHAR8696_03_SE_C19.indd 708 14/07/14 7:37 AM Exercises 709
=+18. Final concepts. For each of the following time series, suggest an appropriate model:a) Daily stock prices that reveal erratic periods of up and down swings.
=+c) Quarterly sales for a bicycle shop that reveal a seasonal pattern where sales peak in Q2 of each year.
=+b) Annual sales that reveal a consistent percentage annual increase.
=+17. More concepts. For each of the following time series, suggest an appropriate model:a) Weekly stock prices that reveal erratic periods of up and down swings.
=+d) After examining the residuals and using the information provided, you decide to transform the sales data. What transformation are you likely to suggest? Why?
=+c) If you use seasonal dummy variables, specify the dummy variables you would use.
=+5.25 ounces. One could look at this standard as a target weight of 5.125 ounces with a tolerance of + > -0.125 ounces. The following data were taken from a random sample of 50 baseballs from a large production batch. The actual weight and deviation from the target weight are listed.Using the
=+b) If you identified a seasonal component, what is the period?
=+a) Based on the description of these data, what time series components can you identify?
=+16. Concepts, again. We are trying to forecast monthly sales for a local company that bottles water. Assume that their sales peak during the month of July and that the monthly sales have been growing at a rate of 2% each month.Answer the following questions.
=+c) What is the difference in how historical data are used when the smoothing coefficient in a single exponential smoothing (SES) model is raised from 0.10 to 0.80?
=+b) Which will be smoother, a single exponential smoothing(SES) model using a = 0.10 or a model using a = 0.80?
=+a) Which will be smoother, a 50-day or a 200-day moving average?
=+b) Do you think the predictions from this model are likely to be accurate? Explain.Chapter Exercises 15. Concepts.
=+a) What is the value predicted by this model for January 2010 1Time = 20102?
=+14. An additive model for the Gas prices is:Dependent variable is: Gas R squared = 28.6% R squared (adjusted) = 3.3%s = 0.5524 with 47 - 13 = 34 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 66.3101 146.9 0.451 0.6546 Time -0.031816 0.0732 -0.435 0.6664 Jan -0.036401
=+b) Why is there no predictor variable for December?
=+a) What is the name for the kind of variable called Jan in this model?
=+a) Create a run chart for the baseballs’ weights.
=+13. An Additive regression model for the Apple prices is:Dependent variable is: Apples R squared = 51.9% R squared (adjusted) = 34.9%s = 0.1108 with 47 - 13 = 34 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept -114.825 29.46 -3.90 0.0004 Time 0.057746 0.0147 3.94
=+January 2007 (the value just past those given in the table)?Section 19.6
=+12. A second-order autoregressive model for the gas prices is:Dependent variable is: Gas R squared = 82.2% R squared (adjusted) = 77.1%s = 0.1498 with 10 - 3 = 7 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 1.28207 0.4644 2.76 0.0281 Lag18Gas9 1.31432 0.2383 5.51
=+Using the values from the table, what is the predicted value for January 2007 (the value just past those given in the table)?
=+b) Is the process for making baseballs in control?
=+Variable Coefficient SE(Coeff) t-ratio P-value Intercept 0.327717 0.1881 1.74 0.1250 Lag18Apples9 1.32814 0.3114 4.27 0.0037 Lag28Apples9 -0.634127 0.2959 -2.14 0.0693
=+11. A second-order autoregressive model for the apple prices (for all 4 years of data) is Dependent variable is: Apples R squared = 78.1% R squared (adjusted) = 71.9%s = 0.0574 with 10 - 3 = 7 degrees of freedom M19_SHAR8696_03_SE_C19.indd 707 14/07/14 7:37 AM 708 CHAPTER 19 Time Series Analysis
=+10. For the Gas prices of Exercise 6, find the lag2 version of the prices.
=+8. For the Gas prices of Exercise 6, the actual value for January 2007 was 2.321. Find the absolute percentage error of your forecast.Section 19.5
=+b) Use it to predict the value for January 2007.Section 19.4
=+6. For the Gas prices:a) Find a 2-point moving average of the first year.
=+Here are data on the monthly price of Delicious apples and gas, which are both components of the Consumer Price Index.16 The timeplot shows the years 2006–2009 for apples; the data table shows just 2006, for both.Month Apples Gas Jan 0.963 2.359 Feb 0.977 2.354 Mar 0.935 2.444 Apr 0.958 2.801
=+4. For the series of Output per unit of capital:a) Make a time series plot.b) Describe the Trend component.c) Is there evidence of a Seasonal component?d) Is there evidence of a cyclic component?Section 19.3
=+b) Describe the Trend component. (Remember: Direction, Form, and Strength)c) Is there evidence of a Seasonal component?
=+3. For the series of Output per hour of labor:a) Make a time series plot.
=+Here is a table of values from the U.S. Bureau of Labor Statistics (disk file BLS_Output):Year Output/hr Labor(2005 = 100)Output/unit Capital(2005 = 100)1993 73.407 86.944 1994 74.049 90.416 1995 74.086 92.913 1996 76.248 94.391 1997 77.577 97.576 1998 79.879 99.502 1999 82.692 101.488 2000
=+16The Consumer Price Index (CPI) represents changes in prices of all goods and services purchased for consumption by urban households.User fees (such as water and sewer service) and sales and excise taxes paid by the consumer are also included. Income taxes and investment items (such as stocks,
=+d) The number of cases of flu reported by the CDC each week during a flu season.Exercises M19_SHAR8696_03_SE_C19.indd 706 14/07/14 7:37 AM Exercises 707
=+b) The quarterly Gross Domestic Product (GDP) of France from 1980 to the present.c) The dates on which a particular employee was absent from work due to illness over the past two years.
=+2. Are the following data time series? If not, explain why.a) Reports from the Bureau of Labor Statistics on the number of U.S. adults who are employed full-time in each major sector of the economy.
=+d) The number of car accidents reported on a monthly basis by the local police.
=+1. Are the following data time series? If not, explain why.a) Yearly earnings of a local company.b) Number of SMS messages handled by a local telephone exchange company on a daily basis.c) Time spent in training to use new software for professional development.
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+7 Is the average value for Q4 higher or lower than the other three quarters? Why?
=+6 Why is there no term for Q4?
=+d) When should the quality team have investigated the production process?Sample Weight (oz.) Deviation Sample Weight (oz.) Deviation 1 5.060 -0.065 26 5.073 -0.052 2 5.014 -0.111 27 5.133 0.008 3 5.118 -0.007 28 5.075 -0.050 4 5.098 -0.027 29 4.971 -0.154 5 5.069 -0.056 30 5.121 -0.004 6 5.159
=+Locate and interpret the trend coefficient.
=+ Describe the components. Which month was left out? Why?
=+Is the model for Alaska truck border crossings in the previous example (see page 692) an additive or a multiplicative model?
=+Find and interpret a multiple regression model for the Alaska truck border crossing data from the example on page 675. (The data are in the file Trucks.)
=+Find and interpret an autoregressive model for the euro prices.
=+For the euro values in the example on page 679, find the forecasts, the errors, and the measures of forecast error.
=+Find a 3-term moving average for these data and predict the value for the next week?
=+Describe the components of this time series.
=+36. HDI, model comparison. In Exercise 35 you identified several countries that had potentially large influence on the model in Chapter 17, Exercise 36 predicting HDI. Set those countries aside and rerun the model. Write up a few sentences on the impact that leaving these countries out has on the
=+35. HDI diagnostics. In Chapter 17, Exercise 36 we found a model for HDI (the UN’s Human Development Index)from 7 socio-economic variables for 96 countries. Using software that provides regression diagnostics (leverage values, Cook’s distance, studentized residuals), find two countries that
=+b) Why might this be problematic? What might you suggest to the researcher before proceeding?
=+a) What assumption and/or condition does the model violate?A histogram of GDP per capita shows:0# of Countries GDP per Capita 20000 40000 60000 80000 60 50 40 30 20 10
=+34. Gross domestic product diagnostics revisited. In Exercise 33 we saw that there were several potential high influence points. After a researcher set aside those four countries, she refit the model in Exercise 33. A plot of residuals vs. predicted values showed:Predicted 0 10000 20000 30000
=+b) What might you consider doing next?
=+a) Explain why each country was identified as a possible high influence point.
=+33. Gross domestic product diagnostics. In Chapter 17, Exercise 33 we found a model for GDP per Capita from three country characteristics: Cell phones/100 people, Internet Users/100 people, and Primary Completion Rate. A look at leverage values and Cook’s distance identifies three countries
=+b) Find the value of the Variance Inflation Factor for Displacement in the regression on MSRP.
=+a) What term describes the reason Displacement doesn’t contribute to the regression model for MSRP?
=+32. Dirt bikes, part 2. The model in Exercise 30 is missing one predictor that we might have expected to see. Engine Displacement is highly correlated 1r = 0.7832 with MSRP, but that variable has not entered the model (and, indeed, would have a P-value of 0.54 if it were added to the model).
=+c) Try a re-expression of US Gross by logarithms and refit the model. Examine the residual plot and comment briefly.
=+b) What would you recommend doing next to help improve the model?
=+a) What assumptions and/or conditions are violated by this model?
=+31. Movie revenue revisited. In Exercise 8 we found a model for the gross revenue from U.S. movie theatres for 106 recent movies that were rated either R or PG-13. A plot of residuals against predicted revenue shows:Predicted Values 50 100 150 200 250 Residuals 200 100 0–100–200 A histogram
=+b) What aspects of the displays indicate that the model is a good one?
=+a) List aspects of this regression model that lead to the conclusion that it is likely to be a useful model.
=+Here’s a regression model and some associated graphs.Dependent variable is: MSRP R-squared = 91.0% R-squared (adjusted) = 90.5%s = 606.4 with 100 - 6 = 94 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 349911096 5 69982219 190 Residual 34566886 94 367733 Variable
=+goal was to study market differentiation among brands.(The Dirt on Bikes: An Illustration of CART Models for Brand Differentiation, Jiang Lu, Joseph B. Kadane, and Peter Boatwright). In Chapter 17, Exercises 41, 42, and 43 dealt with these data, but several bikes were removed from those data to
=+30. Dirt bikes. Off-road motorcycles (often called “dirt bikes”) are a segment (about 18%) of the growing motorcycle market. Because dirt bikes offer great variation in features, they are a good market segment to study to learn about which features account for the cost (manufacturer’s
=+b) Find the regression model as in Chapter 17, Exercise 46 without these points and discuss briefly the difference in the two models. Should you report the model with or without these points?
=+a) From the data, find the distribution of each variable and explain why each country was identified as a possible high influence point.
=+29. Health expenditures revisited. In Chapter 17, Exercise 46 we found a model for national Health Expenditures from an economic variable, Internet Users/100 people, and Primary Completion Rate. A look at leverage values and Cook’s distances identifies several countries as possible high
=+b) Why doesn’t Hong Kong show up as an influential point in the diagnostics of the 3 predictor model?
=+a) By examining the values of their predictor variables find out why these two cities might be such high leverage points.
=+28. Cost of Living 2013, revisited. For the first model considered in Exercise 27, with all four predictors in the model, a plot of Leverage values shows the two largest values are Hong Kong (0.18) and Luanda, Angola (0.15).0.00 Number of Cities Leverage 0.05 0.10 0.15 0.20 150 100 50
=+d) Do you think the model with three predictors is better?Explain briefly.
=+c) Why did the researcher remove the Rent Index from the model?
=+b) What are the advantages of this model compared to the previous model with four predictors?
=+a) What might you recommend as a next step for developing a regression model? Why?M18_SHAR8696_03_SE_C18.indd 667 14/07/14 7:38 AM 668 CHAPTER 18 Building Multiple Regression Models The researcher looking at this problem has proposed the following model:Dependent variable is: CPI R-squared =
=+of buying goods and services in a city compared to the average wage in that city. Can we reconstruct the overall Cost of Living Index from the four component indices? Here is some multiple regression output:Dependent variable is: CPI R-squared = 97.34% R-squared (adjusted) = 97.30%s = 4.562 with
=+27. Cost of Living 2013. The Brief Case in Chapter 4 introduced the Cost of Living dataset that contains an estimate of the cost of living for 322 cities worldwide in 2013. In addition to the overall Cost of Living Index are: the Rent Index, Groceries Index, Restaurant Index, and the Local
=+d) As you can see from the scatterplot, there’s another cereal with high potassium. Not too surprisingly, it is 100%Bran. But it does not have leverage as high as the other two bran cereals. Do you think it should be treated like them(i.e., removed from the model, fit with its own dummy, or
=+c) Which regression would you select for understanding the interplay of these nutrition components. Explain.(Note: Both are defensible.)
=+b) Explain what the coefficients of the bran cereal dummy variables mean.
=+a) What do the displays say about the influence of these two cereals on this regression? (The histogram is of the Studentized residuals.)Here’s another regression with dummy variables defined for each of the two bran cereals.Dependent variable is: Calories R-squared = 50.7% R-squared (adjusted)
=+26. Cereal nutrition. Breakfast cereal manufacturers publish nutrition information on each box of their product. As we saw in Chapter 16, there is a long history of cereals being associated with nutrition. Here’s a regression to predict the number of Calories in breakfast cereals from their
=+c) Which model would you prefer for understanding or predicting Life Expectancy? Explain.M18_SHAR8696_03_SE_C18.indd 666 14/07/14 7:38 AM Exercises 667
=+b) What does the coefficient for the dummy variable for Alaska mean? Is there evidence that Alaska is an outlier in this model?
=+a) The state with the highest leverage and largest Cook’s Distance is Alaska. It is plotted with an x in the residuals plot. Here are a scatterplot of the residuals, a normal probability plot of the leverage values, and a histogram of Cook’s distance values. What evidence do you have from
=+25. Insurance (life expectancy). Insurance companies base their premiums on many factors, but basically all the factors are variables that predict life expectancy. Life expectancy varies from place to place. Here’s a regression that models Life Expectancy in terms of other demographic
=+c) Does this model improve on the model in Exercise 18?Explain.
=+b) What does the predictor AM*Sml (ArterialMPH by Small) do in this model? Interpret the coefficient.

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