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Business Statistics
We have seen that we can use a bubble plot to show a third quantitative variable on a scatterplot. Another way to show three quantitative variables together is to use a 3-dimensional scatterplot,
Look at the visualization titled "Changing Face of America" (the second visualization on the page). This is a new kind of visualization in which the total for each year is scaled to $100 %$, and the
The Wind Map The website hint.fm/wind/ shows the current wind patterns across the US. In order to generate this map, what two variables are being recorded at weather stations across the US?
Are Carbon or Steel Bikes Faster? Dr. Jeremy Groves was interested in whether his carbon bike or his steel bike led to a shorter commute time. To answer this, he flipped a coin each day to randomly
Pew Research Center collected data on the same 10 political value questions from 1994 to 2014 and combines these responses to place each person on a scale ranging from consistently liberal to
Regional Support for Same Sex Marriage The website http://www.pewresearch.org/ fact-tank/2014/10/15/gay - marriage - arrives - in -the - south-where-the-public-is-less-enthused shows the changing
A study collected data comparing treatments for kidney stones. Two of the treatments studied were open surgery and percutaneous nephrolithotomy. Treatment was deemed "successful" if, after three
Draw a Graph for Income vs College! The New York Times created an interesting interactive graph on income versus percent of children who attend college. They ask you to first draw what you think the
Scientists at NASA collected data to study which forces, including both natural and human factors, are responsible for the increase in observed temperature in the last two centuries. Go to http://www
The Racial Divide The website http://vallandingham.me/racial_divide/\#pt uses data from the US Census to visualize where whites and blacks live in different cities. Figure 2.98 gives a heat map of
Cloud Cover in San Francisco Often, the same dataset can be visualized in many different ways. Figure 2.99 shows two different visualizations of San Francisco's typical cloud cover (as a percent of
Cloud Cover in San Francisco-Online The plots in Exercise 2.254 on cloud cover in San Francisco can be found online at weatherlines.zanarmstrong.com if you prefer Figure 2.99(a)
The Corporate Winner and People's Choice Winner was Daniel Gallagher from NASA's Scientific Visualization Studio, for his video "Martian Atmosphere Loss Explained by NASA." Watch this video and
The Student Winner was Ulf Aslak Jensen, for the video "How People Gather: An Interactive Visualization Approach." Watch this video, and answer the following questions:(a) What data are this video
The finalists can be viewed at http://www .sciencemag.org/projects/data-stories/finalists. Pick a video that interests you, watch it, and answer the following questions:(a) Give a link to the chosen
Find an example of an augmented scatterplot and click on the image. You can answer the following questions using either the default variables and cases, or else use the menu on the left to select
Find an example of plot displaying geographic data and click on the image. You can answer the following questions using either the default variables and cases, or else use the menu on the left to
Find an example of a spaghetti plot and click on the image. You can answer the following questions using either the default variables and cases, or else use the menu on the left to select variables
Monthly City Temperatures The data file CityTemps contains the average monthly temperature (in ${ }^{\circ} \mathrm{C}$ ) for the cities of Moscow (Russia), Melbourne (Australia), and San Francisco
Using any of the datasets that come with this text that include at least two quantitative variables and at least one categorical variable (or any other dataset that you find interesting and that
Create Your Own: Bubble Plot Using any of the datasets that come with this text that include at least three quantitative variables (or any other dataset that you find interesting and that meets this
Help for Insomniacs A recent study shows that just one session of cognitive behavioral therapy can help people with insomnia. In the study, forty people who had been diagnosed with insomnia were
To estimate the average number of tweets from all twitter accounts in 2015, one of the authors randomly selected 10 of his followers and counted their tweets.A biased sampling situation is described.
Wearing a Uniform to Work The website fox6now.com held an online poll in June 2015 asking "What do you think about the concept of having an everyday uniform for work, like Steve Jobs did?" Of the
In July 2015, a poll asked a random sample of 1,236 registered voters in Iowa whether they agree or disagree that the world needs to do more to combat climate change. The results show that 65%65%
Diet Cola and Weight Gain in Rats A study fed one group of rats a diet that included yogurt sweetened with sugar, and another group of rats a diet that included yogurt sweetened with a zero calorie
Armoring Military Planes During the Second World War, the U.S. military collected data on bullet holes found in B-24 bombers that returned from flight missions. The data showed that most bullet holes
There were 970 movies made in Hollywood between 2007 and 2013. Suppose that, for a documentary about Hollywood film crews, a random sample of 5 of these movies will be selected for in-depth
"Is there a sprinting gene?" Introduced in Example 1.5. Indicate whether the data come from an experiment or an observational study.Data From Example 1.5:Is There a “Sprinting Gene”?Agene called
Nuts and Cholesterol Several studies have been performed to examine the relationship between nut consumption and cholesterol levels. Here we consider two such studies. In Study 1, participants were
Antibiotics in Infancy and Obesity in Adults "Antibiotics in infancy may cause obesity in adults," claims a recent headline. A study in mice randomly assigned infant mice to either be given
Green Spaces Make Kids Smarter A recent article claims that "Green Spaces Make Kids Smarter." The study described in the article involved 2,623 schoolchildren in Barcelona. The researchers measured
Infections Can Lower IQ A headline in June 2015 proclaims "Infections can lower IQ." The headline is based on a study in which scientists gave an IQ test to Danish men at age 19. They also analyzed
Late Night Eating It is well-known that lack of sleep impairs concentration and alertness, and this might be due partly to late night food consumption. A 2015 study took 44 people aged 21 to 50 and
Does Early Language Reduce Tantrums? A recent headline reads "Early Language Skills Reduce Preschool Tantrums, Study Finds," and the article offers a potential explanation for this: "Verbalizing
Sleep and Recognition of Facial Expressions. The ability to recognize and interpret facial expressions is key to successful human interaction. Could this ability be compromised by sleep deprivation?
Diet Cola and Weight Gain in Humans A study found that American senior citizens who report drinking diet soda regularly experience a greater increase in weight and waist circumference than those who
Split the Bill? When the time comes for a group of people eating together at a restaurant to pay their bill, sometimes they might agree to split the costs equally and other times will pay
Table 6.4 reports that the P‐value for the comparison of mean corn size at 12 months between the corn plaster and scalpel groups is P = 0.010.Which, if any of the following statements is
Calculate the 95% CI for the difference in mean EORTC QLQ‐C30 physical function domain scores before and after exercise for the data reported in Table 7.15.A. −5.6 to 18.1 B. −9.0 to 9.0 C.
Endophyte is a fungus Neotyphodium lolli, which lives inside ryegrass plants. It does not spread between plants, but plants grown from endophyteinfected seed will be infected. One of its eects is
For ryegrass that was not infected with endophyte the following data were observed: Infestation Rate Number of Ryegrass Plants (n) log (n+1) X Y 0 16 2.83321 0 23 3.17805 0 2 1.09861 0 16 2.83321 0 6
The strength of an item is known to be normally distributed with mean 200 and unknown variance σ2. A random sample of ten items is taken and their strength measured. The strengths are: 215 186 216
Let a random sample of 5 observations from a normal (μ, σ2) distribution (where it is known that the mean μ = 25) be(a) What is the equation for the shape of the likelihood function of the
The weight of milk powder in a "1 kg" package is normal(μ, σ2) distribution (where it is known that the mean μ = 1015 g). Let a random sample of 10 packages be taken and weighed. The weights
Suppose our prior belief is σ is just as likely to be below 8 as it is to be above 8. (Our prior distribution g(σ) has median 8.) Determine an S x an inverse chi-squared(k) that matches our prior
We will use the Minitab macro NormGCP to nd the posterior distribution of the normal mean when we have a random samples of size n of normal(μ, σ2) observations with known σ2 = 22, and we have a
A medical researcher collected the systolic blood pressure reading for a random sample of n = 30 female students under the age of 21 who visited the Student's Health Service. The blood pressures are:
We will use the Minitab macro BinoBP or R function binobp to nd the posterior distribution of the binomial probability π when the observation distribution of YΙπ is binomial(n,π) and we have a
We will use the Minitab macro BinoGCP or the R function binogcp to nd the posterior distribution of the binomial probability π when the observation distribution of Y Ι π is binomial (n , π) and
Use the Minitab macro NormDP to nd the posterior distribution of the mean μ when we have a random sample of observations from a normal(μ, σ2), where σ2 is known, and we have a discrete prior for
We will use the Minitab macro NormNP, or the R function normnp, to nd the posterior distribution of the normal mean μ when we have a random sample of size n from a normal(μ ,σ2) distribution with
A textile manufacturer is concerned about the strength of cotton yarn. In order to nd out whether fiber length is an important factor in determining the strength of yarn, the quality control manager
In the previous two problems we found the posterior distribution of the slope of y on x, the rate of weevil infestation for endophyte infected and noninfected ryegrass. Let β1 be the slope for
The following 10 observations come from a simple linear regression model where the variance σ2 = 32 is known. I 22 31 21 23 19 26 27 16 28 21 24.2 25.4 23.9 22.8 22.6 29.7 24.8 22.3 28.2 30.7 (a)
The moisture level of a dairy product is normally distributed with mean 15% and unknown variance σ2. A random sample of size 10 is taken and the moisture level measured. They are: 15.01 14.95 14.99
Suppose we take five additional observations from the normal(μ, σ2) distribution where μ = 200 is known. They are(a) Use the posterior from Exercise 15.3 as the prior for the new observations and
You are going to conduct a survey of the students in your university to nd out whether they read the student newspaper regularly. Based on your friends opinions, you think that a strong majority of
You are going to take a sample of measurements of specific gravity of a chemical product being produced. You know the specific gravity measurements are approximately normal(μ , σ2) where σ2 =
Suppose that a second ball is drawn from the urn, without replacing the first. Let Y2 = 1 if the second ball is red, and let it be 0 otherwise. Use the posterior distribution of X from the previous
For the following regression equation: Production = 1.5 + 0.7 Experience + 0.5 Aptitude Testa. Specify the dependent and independent variables.b. Rewrite the regression equation using Yi and Xi
For the following regression equation: Demand = 1.5 + 0.7 Income + 0.5 Needa. Specify the dependent and independent variables.b. What will be the demand when income is 0 and need is 1?
The popularity of a websites dedicated to food and cooking depends on the number of people who visit them and consume the content they host. The file Chicken contains data on 40 chicken-based main
An Italian food company that operates several restaurants across seven European countries plans to open a second outlet in Paris. As part of the planning phase, the management would like to see how
An analyst engaged in the tourism industry obtained detailed information on 76 travel packages offered by a Viennese travel agency. The file Travel contains the following variables:a. Develop a
How do multiple regression equations help in forecasting?
Explain r2 and adjusted r2 ? Why is it important to report adjusted r2 as a part of multiple regression model?
Discuss how to test the significance of each of the independent variables and the entire multiple regression model.
How can you decide on the number of independent variables and that adding one more would improve the predictability of the dependent variable?
Explain the purpose of calculating F test statistic and t test statistic. Are they interrelated?
What is variance inflationary factor (VIF)? Assuming VIFj = 7, what conclusion can you draw regarding the applicability of the regression model?
Define collinearity. How does it make the interpretation of multiple regression model difficult?
What are the steps involved in formulating an overall regression model building?
How does the correlation between independent variables impact multiple regression model building?
What is exponential smoothing? Explain how the weights are assigned to a time series data. Comment on the relative importance of the time series data if,a. W = 0b. W = 1c. W = 0.5
Which graph would you require to get a visual expression of time series data? Explain which trend model should be used in case the time series data rejects the following types of graphs:a. straight
The thickness of items produced by a machine is normally distributed with mean μ= .001 cm and unknown variance σ2. A random sample of ten items are taken and measured. They are: .00110 .00146
The level of saturated fats in a brand of cooking oil is normally distributed with mean μ = 15% and unknown variance σ2. The percentages of saturated fat in a random sample of ten bottles of the
We will use the Minitab macro NVarICP, or the function nvaricp in R, to nd the posterior distribution of the standard deviation σ when we have a random sample of size n from a normal(μ, σ2)
Suppose we start with a Jeffreys' prior for the standard deviation . What value of S x an inverse chi-squared(k) will we use?(a) Find the posterior using the macro NVarICP in Minitab or the function
You are going to conduct a survey of the voters in the city you live in. They are being asked whether or not the city should build a new convention facility. You believe that most of the voters will
We are taking a random sample from the normal(μ, σ2) distribution where we know the standard deviation σ = 4. Suppose that our prior experience in similar situations leads us to believe that the
We will use the Minitab macro BinoMixP, or function binomixp in R, to nd the posterior distribution of π given an observation y from the binomial(n,π) distribution when we use a mixture prior for
We are going to observe the number of "successes" in n = 100 independent trials. We have prior experience and believe that a beta(6,14) summarizes our prior experience. However, we consider that our
You are going to take a sample of 500 g blocks of cheese. You know they are approximately normal(μ, σ2), where σ2 = 22. You have a precise normal(502, 12) prior for μ because this is what the the
We are taking a random sample from the normal(μ, σ2) distribution where we know the standard deviation σ = 4. Suppose that our prior experience in similar situations leads us to believe that the
The strength of an item is known to be normally distributed with an unknown mean and unknown variance \({ }^{2}\). A random sample of ten items is taken and their strength measured. The strengths
Wild and Seber (1999) describe a data set collected by the New Zealand Air Force. After purchasing a batch of ight helmets that did not \(t\) the heads of many pilots, the NZ Air Force decided to
Bennett et al. (2003) measured the refractive index (RI) of a pane of glass at 49 di erent locations. She took a sample of 10 fragments at each location and determined the RI for each. The data from
Curran (2010) gives the elemental concentrations of five elements (manganese, barium, strontium, zirconium, and titanium) measured in six different beer bottles. Each bottle has measurements taken
A matrix of scatterplots is a good way to examine data like this.Select Matrix Plot. . . from the Graph menu. Click on Matrix of Plots, With Groups which is the second option on the top row of the
In this exercise we will test the hypothesis that the mean vector for bottle number 5 is not contained in a credible interval centered around the mean of the remaining observations. We can think of
The data in this exercise and those that follow can be downloaded from http://www.stat.berkeley.edu/ statlabs/data/babies.data. The variables in the data set are:[Minitab:] The data on the webpage
It is important to make sure that we are working with only the complete data; otherwise we have to have a model for the missing values.[Minitab:] Select Copy > Columns to Columns. . . from the
It is always useful to plot the data before we contemplate models. This sometimes can reveal features which we may not have noticed in the data, and can warn us of potential issues. A scatterplot
Use the Minitab macro BayesMultReg or the R function bayes.lm with a multivariate normal prior to t a multiple linear regression model to this data set. An initial choice of prior might be b0 = 0 and
Use the posterior mean and covariance of the regression coeffcients to test the hypothesis Ho: Bage Bweight
The following 8 observations come from a simple linear regression model where the variance \({σ}^{2}=2^{2}\) is known.(a) Use BayesLinReg in Minitab, or bayes.lin.reg in R, to nd the posterior
What does r2 determine about the statistical significance of a relationship between a dependent and an independent variable?
Every December 15, a certain company offers its employees a choice of one of the following three health care plans for the new year beginning on January 1: An employee may keep her current plan or
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