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business statistics using excel
Basic Business Statistics Concepts And Applications 5th Edition L. Berenson Mark, David Levine, Kathryn Szabat, Judith Watson, Nicola Jayne, Martin O'brien - Solutions
Provide examples of business scenarios where forecasting is important.
The following data represent the prices (in cents) of a basket of staple food items in September 2007 and September 2017 in Sydney and Melbourne.
The data below represent the CPI for tradables in New Zealand from the second quarter of 1999 to the third quarter of 2011(second quarter 2006 is the base)a. Calculate the simple price index for this period using the third quarter of 2000 as the base period.b. Interpret the simple price index for
The following data represent the annual domestic supply price index for Singapore from 1999 to 2013.
Refer to the CPI data used in problem 14.14.a. Form the price index for the CPI using September 2006 as the base period.b. Discuss the changes in consumer prices during this fiveyear period.
The data in the following table represent the closing value of the Dow Jones Industrial Average (DJIA) from 1979 to 2003.
The data in the file reflect the annual values of the United States Consumer Price Index (US CPI), constructed over the 50-year period from 1965 to 2014, using the year 1982 as the base period.a. Form the price index for the US CPI with 1965 as the base year.b. Shift the base of the US CPI to 1990
The following are prices and consumption quantities for three commodities in 2007 and 2017:
The following are prices for a commodity from 2015 to 2017:2015 $5 2016 $8 2017 $7a. Calculate the simple price indices for 2015–2017, using 2015 as the base year.b. Calculate the simple price indices for 2015–2017, using 2016 as the base year.
The simple price index for a commodity in 2014, using 1998 as the base year, is 125. Interpret this index number.
Use the female average weekly earnings data in question 14.13.a. Do you think that the female earnings are subject to seasonal variation? Explain.b. Plot the data. Does this chart support your answer to (a)?c. Develop an exponential trend forecasting equation with quarterly components.d. Interpret
The following data represent the number of married females aged 25–34 in the labour force in Australia from November 2005 to September 2008.
Use the Australian CPI data from question 14.14 on page 565.a. Construct the time-series plot.b. Describe the quarterly pattern that is evident in the data.c. Develop an exponential trend forecasting equation with quarterly components.d. Interpret the quarterly compound growth rate.e. Interpret the
The data below show the quarterly underemployment rate(those who are employed but would prefer more hours) for male youth aged 15–24 in Australia from the August quarter 2008 to the May quarter 2014.
The data given in the following table represent Standard & Poor’s Composite Stock Price Index recorded at the end of each quarter from 1994 to the second quarter of 2004. a. Plot the data.b. Develop an exponential trend forecasting equation with quarterly components.c. What is the fitted value in
Refer to the exponential model given in problem 14.42.a. What is the fitted value of the series in the third quarter of 2017?b. What is the fitted value of the series in the fourth quarter of 2017?c. What is the forecast in the first quarter of 2018?d. What is the forecast in the second quarter of
In forecasting a quarterly time series over the five-year period from the first quarter 2013 to the fourth quarter 2017, the exponential trend forecasting equation is given by:log Yˆi 5 4.5 + 0.03Xi − 0.32Q1 + 0.40Q2 + 0.17Q3 where the origin is first quarter 2013 and units of X 5 1 quarter.Take
If forecasting weekly time-series data, how many dummy variables are needed to account for the seasonal categorical variable week?
In forecasting a monthly time series over a five-year period from January 2010 to December 2017, the exponential trend forecasting equation for January is:log Yˆi 5 2.6 + 0.03Xi+ 0.18 January Take the antilog of the appropriate coefficient from the above equation and interpret:a. the Y interceptb.
Refer to the results in problem 14.17 on page 566 and problems 14.25 and 14.33 concerning overseas arrivals in Australia.a. Perform a residual analysis for each model.b. Calculate the standard error of the estimate (SYX) for each model.c. Calculate the MAD for each model.d. On the basis of (a),
Refer to the results in problem 14.13 on page 565, and problems 14.24 (page 570) and 14.31 (page 579) concerning female earnings in Australia.a. Perform a residual analysis for each model.b. Calculate the standard error of the estimate (SYX) for each model.c. Calculate the MAD for each model.d. On
Refer to the results in problem 14.12 on page 564 and problem 14.30 on page 578 concerning welfare as a percentage of GDP in New Zealand.a. Perform a residual analysis for each model.b. Calculate the standard error of the estimate (SYX) for each model.c. Calculate the MAD for each model.d. On the
Refer to the results in problem 14.15 on page 566.a. Perform a residual analysis.b. Calculate the standard error of the estimate (SYX).c. Calculate the MAD.d. On the basis of (a), (b) and (c), are you satisfied with your linear trend forecast in problem 14.15? Discuss.
Refer to problem 14.34. Suppose the first residual is 4.0(instead of 3.0) and the last value is −0.7 (instead of 0.3).
The following residuals are from a linear trend model used to forecast sales:3.0 −0.5 0.0 −0.2 0.7 −2.7 −0.5 −0.1 0.3a. Calculate SYX and interpret your findings.b. Calculate the MAD and interpret your findings.
Refer to the data given in problem 14.17 on page 566 that represent the number of overseas arrivals into Australia.a. Fit a first-order autoregressive model to the data and test for the significance of the first-order autoregressive parameter. (Use α 5 0.05.)b. If appropriate, forecast arrivals
Refer to the data given in problem 14.14 on page 565 that represent the CPI for Australia from September 2006 to September 2011.a. Fit a third-order autoregressive model to the data and test for the significance of the third-order autoregressive parameter. (Use α 5 0.05.)b. Fit a second-order
Refer to the data introduced in problem 14.13 on page 565 concerning average weekly earnings of female employees in Australia.a. Fit a third-order autoregressive model to the earnings data and test for the significance of the third-order autoregressive parameter. (Use α 5 0.05.)b. If necessary,
Refer to the data given in problem 14.11 on page 564 that represent New Zealand GDP.a. Fit a third-order autoregressive model to the GDP data and test for the significance of the third-order autoregressive parameter. (Use α 5 0.05.)b. Fit a second-order autoregressive model to the GDP data and
Refer to problem 14.27. Suppose, when testing for the appropriateness of the fitted model, the standard deviations are:Sa1 5 0.90 Sa2 5 0.35 Sa3 5 0.2a. What conclusions can you make?b. Discuss how to proceed if forecasting is still your main objective.
Refer to problem 14.27. The three most recent values are:Y17 5 12 Y18 5 14 Y19 5 19 Forecast the values for the next year and the following year.
A third-order autoregressive model is fitted to an annual time series with 19 values and has the following estimated parameters and standard deviations:a0 5 10.20 a1 5 1.80 a2 5 0.99 a3 5 0.21 Sa1 5 0.25 Sa2 5 0.40 Sa3 5 0.09 At the 0.05 level of significance, test the appropriateness of the fitted
You are given an annual time series with 50 consecutive values and asked to fit a fifth-order autoregressive model.a. How many comparisons are lost in the development of the autoregressive model?b. How many parameters do you need to estimate?c. Which of the original 50 values do you need for
Refer to the data of problem 14.17 on page 566 concerning overseas arrivals.a. Forecast overseas arrivals for 2016 and 2017 using the Holt–Winters method with U 5 0.30 and V 5 0.30.b. Repeat (a) with U 5 0.70 and V 5 0.70.c. Repeat (a) with U 5 0.30 and V 5 0.70.d. Compare these forecasts with
Refer to the data of problem 14.13 on page 565 concerning female average weekly earnings in Australia.a. Forecast the average weekly earnings in May and November 2017 using the Holt–Winters method with U 5 0.30 and V 5 0.30.b. Repeat (a) with U 5 0.70 and V 5 0.70.c. Repeat (a) with U 5 0.30 and
Refer to the data of problem 14.15 on page 566 concerning total exports from Malaysia.a. Forecast total exports for 2013 using the Holt–Winters method with U 5 0.30 and V 5 0.30.b. Repeat (a) with U 5 0.70 and V 5 0.70.c. Repeat (a) with U 5 0.30 and V 5 0.70.d. Which of these sets of forecasts
Refer to the data of problem 14.11 on page 564 concerning gross domestic product. a. Forecast gross domestic product for 2017 and 2018 using the Holt–Winters method with U 5 0.30 and V 5 0.30.b. Repeat (a) with U 5 0.70 and V 5 0.70.c. Repeat (a) with U 5 0.30 and V 5 0.70.d. Which of these sets
Given the following series from n 5 10 consecutive time periods:335 332 325 312 298 275 267 245 223 213 use the Holt–Winters method (with U 5 0.20 and V 5 0.20) to forecast the 11th to 14th periods.
Given the following series from n 5 10 consecutive time periods:152 146 148 135 130 124 120 113 110 104 use the Holt–Winters method (with U 5 0.30 and V 5 0.30) to forecast the 16th to 20th periods.
Consider an annual time series with 20 consecutive values. If the smoothed level for the most recent value is 50.8 and the corresponding trend level is 7.2:a. What is your forecast for the coming year?b. What is your forecast five years from now?
The following table displays the amount of emergency food aid provided to developing countries from 1995 to 2012(measured in $US million). < FOOD_AID >a. Plot the data.b. Calculate a linear trend forecasting equation and plot the results.c. Calculate a quadratic trend forecasting equation and plot
Data for overseas arrivals (immigration) into Australia from 1991 to 2015 are presented below.a. Compare the first differences, second differences and percentage differences to determine the most appropriate model.b. Calculate the appropriate forecasting equation.c. Forecast migration for 2016 and
A time-series plot often helps you to determine the appropriate model to use. For this problem, use each of the time-series presented in the following table. a. Plot the observed data (Y ) over time (X ), and plot the logarithm of the observed data (log Y ) over time (X ), to determine whether a
Use the Malaysian total export data from problem 14.5 to answer the following question.a. Plot the data.b. Calculate a linear trend forecasting equation and plot the trend line.c. Calculate a quadratic trend forecasting equation and plot the results.d. Calculate an exponential trend forecasting
The data in the following table represent the consumer price index (CPI) for Australia from the September quarter 2006 to the September quarter 2011. a. Plot the data.b. Calculate a linear trend forecasting equation and plot the trend line.c. Calculate a quadratic trend forecasting equation and
Female average weekly earnings from November 2006 to November 2016 are presented below.a. Plot the data.b. Calculate a linear trend forecasting equation and plot the trend line.c. Calculate a quadratic trend forecasting equation and plot the results.d. Calculate an exponential trend forecasting
The following data represent welfare expenditure as a percentage of GDP for New Zealand from 1971 to 2001.
Gross domestic product (GDP) is a major indicator of the nation’s overall economic activity. It consists of personal consumption expenditures, gross domestic investment, net exports of goods and services, and government consumption expenditures. The gross domestic product (in $US millions of
The generosity of social security is often expressed as a percentage of average weekly labour market earnings and called a replacement rate. The following is the replacement rate for unemployment benefits in Australia from 1967 to 2007.
The linear trend forecasting equation for an annual time series containing 40 values (from 1969 to 2008) on real net sales (in billions of constant 1998 dollars) is:Yi = 1.2 + 0.5Xi ˆa. Interpret the Y intercept b0.b. Interpret the slope b1.c. What is the fitted trend value for the tenth year?d.
The linear trend forecasting equation for an annual time series containing 20 values (from 1992 to 2011) on real total revenues(in millions of constant 1996 dollars) is:Yi = 23.2 + 4.8Xi ˆa. Interpret the Y intercept b0.b. Interpret the slope b1.c. What is the fitted trend value for the fifth
The following data represent CO2 emissions per capita in Australia from 2000 to 2014.a. Plot the data.b. Fit a 3-year moving average to the data and plot the results.c. Using a smoothing coefficient of W 5 0.50, exponentially smooth the series and plot the results.d. What is your exponentially
The following data represent the assumed cost of a 375-gram jar of Vegemite from 1995 to 2008.
The data in the following table represent total exports for Malaysia (in millions). < MALAY_X >a. Plot the time series.b. Fit a 3-year moving average to the data and plot the results.c. Using a smoothing coefficient of W 5 0.30, smooth the series exponentially and plot the results.d. Repeat (c)
The following data represent unemployment rates for male youths aged 15–19 in New Zealand from 2000 to 2016a. Plot the time series.b. Fit a 3-year moving average to the data and plot the results.c. Using a smoothing coefficient of W 5 0.50, smooth the series exponentially and plot the results.d.
You are using exponential smoothing on an annual time series concerning total revenues (in millions of constant 1995 dollars).If you use a smoothing coefficient of W 5 0.20 and the exponentially smoothed value for 2006 is E2006 5 (0.20)(12.1)+ (0.80)(9.4):a. What is the smoothed value of this
Consider a 3-year moving average used to smooth a time series that was first recorded in the year 1955.a. Which year serves as the first centred value in the smoothed series?b. How many years of values in the series are lost when calculating all the 5-year moving averages?
If you are using exponential smoothing for forecasting an annual time series of revenues, what is your forecast for next year if the smoothed value for this year is$12 million?
An experiment was conducted to study the extrusion process of biodegradable packaging foam (data extracted from W. Y.Koh, K. M. Eskridge and M. A. Hanna, ‘Supersaturated split-plot designs’, Journal of Quality Technology, 45, January 2013, 61–72). Among the factors considered for their effect
The owner of a moving company typically has his most experienced manager predict the total number of labour hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of
The percentage of youth not in employment, education or training (NEET) is of greater policy significance than simply looking at unemployment rates. We hypothesise that NEET is influenced by the average age at which females are having their first child and their school life expectancy. Data is
In the past, countries have tended to follow different economic development strategies. One group tended to favour protectionist theories largely based on the infant industry argument, aimed at reducing imports and substituting them with domestic production. Another group (mostly East Asian
A lecturer believes that students majoring in economics get higher wages than other graduates. To test his theory he selects a sample of 10 past students and collects their wage(in dollars) and weighted average mean of their grades, and includes a variable that equals 1 if the student majored in
Starbucks Coffee Co. uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that Starbucks needed to improve its package sealing process, an experiment was conducted to determine the factors in the bag-sealing equipment that might
An economist wishes to examine the relationship between robberies, literacy and unemployment for a number of countries – robberies = b0 + b1 literacy rate + b2 unemployment rate.
Professional basketball has truly become a sport that generates interest among fans around the world. More and more players venture to the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA
Academics have noticed that attendance at lectures has declined over the last decade or so. A marketing lecturer decides to collect data on 12 students’ lecture attendance over a 13-week session. She believes that attendance is related to the distance a student has to travel to campus (in km) and
What process should you follow to determine which variables should be included in a multiple regression?
Under what circumstances would you include an interaction term in a multiple regression? How would you interpret its coefficient?
Why and how do you use dummy variables?
How do you test for collinearity?
How do the coefficients of partial determination differ from the coefficient of multiple determination?
What is the difference between R2 and adjusted R2?
How does testing the significance of the entire multiple regression model differ from testing the contribution of each independent variable?
How does the interpretation of the slope coefficients differ in multiple regression versus simple regression?
Refer to problem 13.8 on page 510. Perform a multiple regression analysis and determine the VIF for each explanatory variable in the model. Is there reason to suspect the existence of collinearity?
Refer to problem 13.7 on page 510. Perform a multiple regression analysis and determine the VIF for each explanatory variable in the model. Is there reason to suspect the existence of collinearity?
Refer to problem 13.6 on page 510. Perform a multiple regression analysis and determine the VIF for each explanatory variable in the model. Is there reason to suspect the existence of collinearity?
Refer to problem 13.5 on page 509. Perform a multiple regression analysis and determine the VIF for each explanatory variable in the model. Is there reason to suspect the existence of collinearity?
Refer to problem 13.4 on page 509. Perform a multiple regression analysis and determine the VIF for each explanatory variable in the model. Is there reason to suspect the existence of collinearity?
If the VIF is equal to 6.2, what does this indicate?
If the coefficient of determination between two independent variables is 0.50, what is the VIF ?
If the coefficient of determination between two independent variables is 0.35, what is the VIF ?
The director of a training program for a large insurance company has the business objective of determining which method is best for training underwriters. The three methods to be evaluated are classroom, online and courseware app. The 30 trainees are divided into three randomly assigned groups of
In problem 13.7 on page 510, you used GDP per capita and CPI to estimate the percentage of very happy people in a country. Develop a regression model to predict the happiness percentage using GDP per capita, CPI and the interaction of GDP per capita and CPI.a. At the 0.05 level of significance, is
In problem 13.5 on page 509, you used GDP and population density to estimate CO2 emissions. Develop a regression model that includes GDP, population density, and the interaction of GDP and population density to predict CO2 emissions.a. At the 0.05 level of significance, is there evidence that the
In problem 13.8 on page 510, you used radio and newspaper advertising to predict product sales. Develop a regression model that includes radio advertising and newspaper advertising and the interaction between radio and newspaper advertising.a. At the 0.05 level of significance, is there evidence
In problem 13.4 on page 509, a financial planner used unemployment rates and share market returns to predict retirement rates in OECD countries. Develop a regression model that includes unemployment rates, share market returns and the interaction between unemployment rates and share market
In problem 13.6 on page 510, you developed a multiple regression model to predict wine quality for red wines. Now, you wish to determine whether the type of wine – white (0) or red (1) – has an effect on wine quality. These data are organised and stored in < VINHO_VERDE_RED_AND_WHITE >.Develop
A traffic engineer wants to predict the number of road accidents at intersections in a major urban area. He believes the main determinants are volume of traffic and whether or not the intersection has traffic lights. Traffic lights have the dummy value 1 and no traffic lights the value 0. A sample
A real estate association in Melbourne would like to study the relationship between the size of a family house (measured by the number of rooms) and the selling price of the house (in thousands of dollars). Two different neighbourhoods are included in the study, one on the east Dandenong side (=
The manager of a music production house wants to predict CD sales on the basis of the amount spent on advertising and whether the music had air-time on popular radio during the preceding week (no air-time = 0 and air-time = 1).a. Explain the steps involved in developing a regression model for these
Suppose X1 is a numerical variable and X2 is a dummy variable and the following is the regression equation for a sample of n = 35 is:a. Interpret the meaning of the slope for variable X1.b. Interpret the meaning of the slope for variable X2.c. Suppose that the t statistic for testing the
In problem 13.8 on page 510, you used radio and newspaper advertising to predict product sales. Using the computer output from that problem:a. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of
In problem 13.6 on page 510, a wine expert used alcohol content and chlorides to predict wine quality. Using the computer output from that problem:a. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis
In problem 13.7 on page 510, you used GDP per capita and CPI to estimate the percentage of very happy people in a country. Using the computer output from that problem:a. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression
In problem 13.4 on page 509, a financial planner used unemployment rates and share market returns to predict retirement rates for OECD countries. Using the computer output from that problem:a. At the 0.05 level of significance, determine whether each independent variable makes a significant
In problem 13.5 on page 509, you used GDP and population density to estimate CO2 emissions. Using the computer output from that problem:a. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these
The following is the ANOVA summary table for a multiple regression model with two independent variables.
The following is the ANOVA summary table for a multiple regression model with two independent variables.If SSR(X1) = 45 and SSR(X2) = 25:a. Determine whether there is a significant relationship between Y and each of the independent variables at the 0.05 level of significance.b. Calculate the
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