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statistics

Questions and Answers of Statistics

In Chapter 16, Exercise 54 predicted the price ($/lb) of lobster harvested in the Maine lobster fishing industry. Here€™s a multiple regression to predict the Price from the number of Traps
In 1990, the United Nations created a single statistic, the Human Development Index or HDI, to summarize the health, education, and economic status of countries.Using data from 96 countries, here is
Wal-Mart is the second largest retailer in the world. The data file on the disk holds monthly data on Wal-Mart’s revenue, along with several possibly related economic variables.a) Using computer
Consider the model you fit in Exercise 37 to predict Wal-Mart’s revenue from the Retail Index, CPI, and Personal Consumption index. a) Plot the residuals against the predicted values and comment on
An important challenge in clinical trials is patients who drop out before the trial is completed. This can cost pharmaceutical companies millions of dollars because patients who have received a
Are there fundamental differences between liberal arts colleges and universities? In this case, we have information on the top 25 liberal arts colleges and the top 25 universities in the United
What can predict how much a motion picture will make? We have data on a number of recent releases that includes the USGross (in $M), the Budget ($M), the Run Time (minutes), and the average number of
More than one million motorcycles are sold annually (www.webbikeworld.com). Off-road motorcycles (often called €œdirt bikes€) are a market segment (about 18%) that is highly
In Exercise 41, we saw data on off-road motorcycles and examined scatterplots. Review those scatterplots. Here€™s a regression of MSRP on both Displacement and Bore. Both of the predictors
Here€™s another model for the MSRP of off-road motorcycles.a) Would this be a good model to use to predict the price of an off-road motorcycle if you knew its bore, clearance, and engine
The dataset corresponding to the exercise on the DVD holds various measures of the 50 United States. The Murder rate is per 100,000, HS Graduation rate is in %, Income is per capita income in
Like many fast-food restaurant chains, Burger King (BK) provides data on the nutrition content of its menu items on its website. Here€™s a multiple regression predicting calories for Burger
Can the amount of money that a country spends on health (as % of GDP) be predicted by other economic indicators? Here€™s a regression predicting Expenditures on Public Health (as % of GDP)
A middle manager at an entertainment company, upon seeing the analysis of Exercise 3, concludes that the longer you make a movie, the less money it will make. He argues that his company’s films
For the movies examined in Exercise 4, here is a scatterplot of USGross vs. Budget:What (if anything) does this scatterplot tell us about the following Assumptions and Conditions for the
For the movies regression, here is a histogram of the residuals. What does it tell us about these Assumptions and Conditions?a) Linearity condition b) Nearly Normal condition c) Equal Spread condition
In the regression output for the movies of Exercise 3, a) What is the null hypothesis tested for the coefficient of Stars in this table? b) What is the t-statistic corresponding to this test? c)
a) What is the null hypothesis tested for the coefficient of Run Time in the regression of Exercise 3? b) What is the t-statistic corresponding to this test? c) Why is this t-statistic negative? d)
For each of the following, show how you would code dummy (or indicator) variables to include in a regression model. a) Company unionization status (Unionized, No Union) b) Gender (Female, Male) c)
For the same regression as in Exercise 9, the Cook€™s Distances look like this:The outlier, once again, is John Carter, whose budget was more than $200M more than its gross revenue in the
An analyst wants to build a regression model to predict spending from the following four predictor variables: Past Spending, Income, Net Worth and Age. A correlation matrix of the four predictors
The analyst in Exercise fits the model with the four predictor variables. The regression output shows:Response Variable: SpendingR2 = 84.92% Adjusted R2 = 84.85%s = 48.45 with 908 - 5 = 903 degrees
The analyst from Exercise, worried about collinearity, regresses Age against Past Spending, Income, and Networth. The output shows:Response Variable: AgeR2 = 98.75% Adjusted R2 = 98.74%s = 2.112 with
If the VIF for Networth in the regression of Exercise 11 was 20.83, what would the R2 be from the regression of Networth on Age, Income, and Past Spending?In exercise
A collection of houses in a neighborhood of Boston shows the following relationship between Price and Age of the house:a) Describe the relationship between Price and Age. Explain what this says in
A regression model from the collection of houses in Exercise 15 shows the following:a) The slope of Age is negative. Does this indicate that older houses cost less, on average? Explain. b) Why did
Manufacturers of frozen foods of-ten reformulate their products to maintain and increase customer satisfaction and sales. So they pay particular attention to evaluations of their products in
The Texas Transportation Institute (tti.tamu.edu) studies traffic delays. They estimate that in the year 2011, 498 urban areas experienced 5.5 billion vehicle hours of delay, resulting in 2.9 billion
Here€™s a scatterplot of the residuals against predicted values for the regression model found in Exercise.a) The two extraordinary points in the lower right are Reggio€™s and
A marketing manager has developed a regression model to predict quarterly sales of his company’s down jackets based on price and amount spent on advertising. An intern suggests that he include an
Here€™s a scatterplot of the residuals from the regression in Exercise 18 plotted against mean Highway mph.a) The point plotted with an x is Los Angeles. Read the graph and explain what it
Each week about 100 million customers€”nearly one-third of the U.S. population€”visit one of Walmart€™s U.S. stores. How does Walmart€™s revenue relate to the
Pedro Martinez, who retired from Major League Baseball in 2012, had a stellar career, helping the Boston Red Sox to their first World Series title in 86 years in 2004. The next year he became a free
In Exercise 19, we raised questions about two gourmet pizzas. After removing them, the resulting regression looks like this.A plot of the residuals against the predicted values for this regression
Here€™s a plot of the Studentized residuals from the regression model of Exercise 18 plotted against ArterialMPH. The plot is colored according to City Size (Small, Medium, Large, and Very
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
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.
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
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
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
Do movies of different types have different rates of return on their budgets? Here€™s a scatterplot of Gross Revenue in US ($M) vs. Budget ($M) for recent movies whose MPAA Rating is either
Off-road motorcycles (often called €œdirt bikes€) are a segment (about 18%) of the growing motorcycle market. Because dirt bikes offer great variation in features, they are a
In Exercise we found a model for the gross revenue from U.S. movie theatres for 106 recent movies that were rated either R or PG-13. A plot of residuals against predicted revenue shows:A histogram of
The model in Exercise 30 is missing one predictor that we might have expected to see. Engine Displacement is highly correlated 1r = 0.7832 with MSRP, but that variable has not entered the model (and,
In Chapter 17, Exercise 33 we found a model for GDP per Capita from three country characteristics: Cell phones/100 people, Internet Users/100 people, and Primary Completion Rate. A look at leverage
In Exercise we saw that there were several potential high influence points. After a researcher set aside those four countries, she refit the model in Exercise 33. A plot of residuals vs. predicted
In Chapter 17, Exercise 36 we found a model for HDI (the UN’s Human Development Index) from 7 socio-economic variables for 96 countries. Using software that provides regression diagnostics
In Exercise 35 you identified several countries that had potentially large influence on the model in Chapter 17, Exercise 36 predicting HDI. Set those countries aside and rerun the model. Write up a
Here is the regression for Exercise 3 with an indicator variable:Dependent variable is: US Gross($M)R-squared = 0.193, Adjusted R-squared: 0.166s = 37.01 with 62 - 3 = 59 degrees of freedoma) Write
For each of the following, show how you would code dummy (indicator) variables to include in a regression model. a) Type of residence (Apartment, Condominium, Townhouse, Single family home) b)
A marketing manager has developed a regression model to predict quarterly sales of his company’s mid-weight microfiber jackets based on price and amount spent on advertising. An intern suggests
Are R rated movies as profitable as those rated PG-13? Here€™s scatterplot of US Gross ($M) vs. Budget ($M) for PG-13 (green) and R (purple) rated moviesa) How would you code the indicator
Here is the scatterplot of the variables in Exercise 7 with regression lines added for each kind of movie:The regression model is:Dependent variable is: US Gross ($M)R-squared = 0.3674, Adjusted
Are the following data time series? If not, explain why. a) Quarterly earnings of Microsoft Corp. b) Unemployment in August 2010 by Education level. c) Time spent in training by workers in NewCo.
For the Gas prices of Exercise 6, find the lag2 version of the prices.
A second- order autoregressive model for the apple prices (for all 4 years of data) isDependent variable is: ApplesR squared = 78.1% R squared (adjusted) = 71.9%s = 0.0574 with 10 - 3 = 7 degrees of
A second-order autoregressive model for the gas prices is:Using values from the table, what is the predicted value for January 2007 (the value just past those given in the table)?
An Additive regression model for the Apple prices is:a) What is the name for the kind of variable called Jan in this model? b) Why is there no predictor variable for December?
An additive model for the Gas prices is:a) What is the value predicted by this model for January 2010 (Time = 2010)? b) Do you think the predictions from this model are likely to be accurate?
a) Which will be smoother, a 50-day or a 200-day moving average? b) Which will be smoother, a single exponential smoothing (SES) model using α = 0.10 or a model using α = 0.80? c) What is the
We are trying to forecast monthly sales for a company that sells ski equipment and clothing. Assume that the company’s sales peak each December and that the monthly sales have been growing at the
For each of the following time series, suggest an appropriate model: a) Weekly stock prices that reveal erratic periods of up and down swings. b) Annual sales that reveal a consistent percentage
For each of the following time series, suggest an appropriate model: a) Daily stock prices that reveal erratic periods of up and down swings. b) Monthly sales that reveal a consistent percentage
The Bank of New York Company was founded by Alexander Hamilton in 1784 and was a major commercial bank until its merger with the Mellon Financial Corporation in 2007. Their year- end financial
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.
Sara Lee Corp., maker of food, beverage, and household products, is known especially for its baked products, marketed under its corporate name. For the five years ending July 1 of each year from 2002
The price of bananas fluctuates on the world market. Here are the prices ($/tonne) for the years 2000€“2004.a) Find a 3- year moving average prediction for the price in 2005.b) Find a prediction
Target Corp. operates €œbig box€ stores that sell everyday essentials and fashionable differentiated merchandise. It also operates an online business at target.com. Target€™s reported
Suppose an autoregressive model is used for data in which quarterly sales in 2013 were: 1.9, 1.7, 2.2, and 2.3 ($ Billion). a) If a first-order autoregressive model is developed with estimated
Suppose an autoregressive model is used to model sales for a company that peaks twice per year (in June and December). a) What lagged variables would you try in a regression to forecast sales?
Coffee is the world€™s second largest legal export commodity (after oil) and is the second largest source of foreign exchange for developing nations. The United States consumes about
The Gallup organization periodically asks the following question: If your party nominated a generally well-qualified person for president who happened to be a woman, would you vote for that person?
The most common use of the CPI is as an economic indicator to forecast inflation and evaluate the effectiveness of government policies. Following is the time series plot for the monthly CPI (not
In Exercise 30 we looked at the weekly average retail price (cents per gallon) of regular gas nationwide from 2011 through June 2013. Here€™s the time series plot again:a) What components
Average annual interest rates (banks prime lending) in the United States from 1966 through 2009 are shown in the following time series graph.a) What components do you see in this series?
For the series of Output per hour of labor: a) Make a time series plot. b) Describe the Trend component. (Remember: Direction, Form, and Strength) c) Is there evidence of a Seasonal component?
Use the following model to forecast quarterly sales ($ Million) for a company (where time is rescaled to begin at zero and Q2, Q3, and Q4 are dummy variables for the indicated quarters), and answer
Use the following model to forecast quarterly sales ($ 000) for a start-up (where time is rescaled to begin at zero and Q2, Q3, and Q4 are dummy variables for the indicated quarters), and answer the
Walmart grew rapidly in the years leading up to the financial crisis. Here is the monthly revenue ($ Billion) for Walmart from November 2003 to January 2007.a) What components of a time series do you
The movie Harry Potter and the Sorcerer€™s Stone opened as a great success. But every movie sees declining revenue over time. Here are the daily revenues for the movie during its first 17
Much of the public and private industry in Hawaii depends on tourism. The following time series plot shows the number of domestic visitors to Hawaii by air from the rest of the United States per
In Exercise 39 we examined domestic tourists who visit Hawaii. Now, let€™s consider international tourism. Here€™s a time series plot of international visitors for the same time
The Port of Oakland airport reports the number of passengers passing through each month. At first glance, this is just simple growth, but by recognizing the series as a time series, we may learn
We have seen that gas prices can fluctuate. But during some periods they have moved consistently. Here are the data extracted for one week of each month from January 2002 to May 2007.The bend in the
The plot of residuals in Exercise 41 shows an outlier that wasn€™t as evident in the data. The outlier is September 2001. Clearly, this wasn€™t a typical month for air travel.
Quarterly e-commerce retail sales (in millions of dollars) in the United States are provided. Use this time series to answer the following questions. a) Fit a linear trend model to this series but
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?
a) Fit a linear trend model with dummy variables for the seasonal effect to the e-commerce data in Exercise 44.b) Fit an exponential trend (multiplicative) model with dummy variables to these data.c)
Using the data from Exercise 42, develop and compare the following models.In exercisea) Fit an appropriate autoregressive model by testing for the significance of each autoregressive term.b) Obtain a
A time series plot of monthly crude oil price ($/ barrel) from January 2001 to March 2007 is shown here.Using these data,a) Fit a first-order autoregressive model.b) Obtain a forecast for March 2007.
Return to the oil price data of Exercise 47. a) Find a linear model for this series. b) Find an exponential (multiplicative) model for this series. c) For the model of Exercise 47 and the models of
Following is the time series plot for the monthly U.S. Unemployment rate (%) from January 2003 to June 2013. These data have been seasonally adjusted (meaning that the seasonal component has already
Using the data from Exercise 49 develop and compare the following models:In exercisea) Fit a regression model with just Year as the predictor.b) Add a lag1 component to the model of (a). How does it
In Exercise 39, we fit a linear regression for the number of monthly domestic visitors to Hawaii (for the years 2002 through 2006) using Time and dummy variables for the months as predictors. The R2
In Exercise 40, we fit a linear regression for the number of monthly international visitors to Hawaii (for the years 2002 through 2006) using Time and dummy variables for the months as predictors.
For the Apple prices:a) Find a 2-point moving average of the first year (2006).b) Use it to predict the value for January 2007.
For the Gas prices:a) Find a 2-point moving average of the first year.b) Use it to predict the value for January 2007.
For the Apple prices smoothed in Exercise 5, the actual value for January 2007 was 1.034. Find the absolute percentage error of your forecast.
For the Gas prices of Exercise 6, the actual value for January 2007 was 2.321. Find the absolute percentage error of your forecast.
For the Apple prices of Exercise 5, find the lag1 version of the prices.

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