Business Analytics lab programs Sem 4.pdf
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The document consists of a practical question bank for the B.Com program at Osmania University, focusing on forecasting and predictive analytics. It includes various statistical problems related to regression analysis, such as constructing scatter plots, calculating regression equations, interpreting coefficients, and predicting values based on given data sets. Each unit presents specific data and tasks aimed at assessing students' understanding of analytical methods in business contexts.
Business Analytics lab programs Sem 4.pdf
- 1. Computer Lab - Practical Question Bank FACULTY OF COMMERCE, OSMANIA UNIVERSITY ------------------------------------------------------------------------------------------------------------ B.Com (Business Analytics) CBCS Semester – IV W.E.F.2022-23 Forecasting & Predictive Analytics - Paper: DSC - 403 Time: 60 Minutes Record : 10 Viva-voce : 10 Skill Test : 15 Total Marks : 35 Unit 1: 1. The data given below explain the attitude towards the city and the duration of residence. Respondents 1 2 3 4 5 6 7 8 9 10 `11 12 Attitude towards the city 6 9 8 3 10 4 5 2 11 9 10 2 Duration of Residence 10 12 12 4 12 6 8 2 18 9 17 2 a. Construct a scatter plot. b. Draw the regression line. c. Display the equation of the regression line. d. Display R2 for the equation. e. Estimate the coefficient of determination. 2. Number of profiled customers ( in millions) and Annual Sales in ($Millions) for a Sample of 14 Sunflowers Apparel Stores are given below. Store Profiled Customers(millions) Annual Sales ($ Millions) 1 3.7 5.7 2 3.6 5.9 3 2.8 6.7 4 5.6 9.5 5 3.3 5.4 6 2.2 3.5 7 3.3 6.2 8 3.1 4.7 9 3.2 6.1 10 3.5 4.9 11 5.2 10.7 12 4.6 7.6 13 5.8 11.8 14 3.0 4.1 a. Assuming a linear relationship between the Attitude towards the city and the duration of residence, determine regression equation. b. Determine the regression coefficients b0 and b1
- 2. c. Interpret the meaning of the slope, b1 in this problem. d. Interpret R Square with respect to the data given. e. Estimate the coefficient of determination. 3. In finance, it is of interest to look at the relationship between Y, a stock’s average return and X, the overall market return. The slope coefficient computed by linear regression is called stock’s beta by investment analysis. A beta greater than 1 indicates that the stock is relatively sensitive to changes in the market; a beta less than 1 indicates that the stock is relatively insensitive. Y 10 12 8 15 9 11 8 10 13 11 X 11 15 3 18 10 12 6 7 18 13 For the above data, a. Compute the beta b. Compute standard error c. What is the coefficient of determinant. d. Explain the significance of F. e. Explain the significance of t-statistic f. Test the model to see whether it is significantly less than 1. Use = 0.05 . 4. Campus stores has been selling the Believe It or Not: Wonders of Statistics Study Guide for 12 semesters and would like to estimate the relationship between sales and number of sections of elementary statistics taught in each semester. The following data have been collected. Sales 33 38 24 61 52 45 65 82 29 63 50 79 No. Of Sections 3 7 6 6 10 12 12 13 12 13 14 15 a. Develop the estimating equation that best fits the data both from scatter plot and from data analysis tool. b. Calculate the sample coefficient of determination. c. Draw Residual plots d. Draw normal probability plot and explain the output. e. Estimate the coefficient of determination. 5. Realtors are often interested in seeing how the appraised value of a home varies according to the size of the home. Some data on area ( In thousands of square feet) and appraised value ( in thousands of dollars) for a sample of 11 homes if given below. Area 1.1 1.5 1.6 1.6 1.4 1.3 1.1 1.7 1.9 1.5 1.3 Value 75 95 110 102 95 87 82 115 122 98 90 a. Estimate the Least Squares Regression to predict appraised value from area. b. Predict the value for the size of the home whose area is 1.8. c. What is the standard error of estimate. d. Generally, realtors feel that a home’s value goes up by $50,000 ( 50 thousands of dollars) for every additional 1,000 square feet in area. For this sample, does this relationship seems to hold? Use = 0.05
- 3. e. Predict the value for the size of the home whose area is 2.3 6. Given the following set of data Y 25 30 11 22 27 19 X1 3.5 6.7 1.5 0.3 4.6 2.0 X2 5.0 4.2 8.5 1.4 3.6 1.3 a. Calculate the multiple regression equation. b. Give the values of intercept bo, b1 and b2 values. c. Explain the significance of b0, b1, and b2 values d. Predict Y when X1= 3.0 X2 = 2.7 from the regression equation obtained. 7. Find the multiple linear regression of Y on X1 and X2 Y 11 17 26 28 31 35 41 49 63 69 X1 2 4 6 5 8 7 10 11 13 14 X2 2 3 4 5 6 7 9 10 11 13 a. Find the Multiple regression equation. b. What is R2for this regression? What is your inference? c. What is adjusted R2 for this equation? What is your inference? d. Explain R2and adjusted R2 with reference to the variables and equation. e. Why is adjusted R2different from R2? 8. The following data explains the attitude toward the City of Residence. Sl.No. 1 2 3 4 5 6 7 8 9 10 11 12 Attitude toward the city 6 9 8 3 10 4 5 2 11 9 10 2 Duration of Residence 10 12 12 4 12 6 8 2 18 9 17 2 Importance attached to weather 3 11 4 1 11 1 7 4 8 10 8 5 a. Find the regression equation. Mention the regression coefficients and their significance. b. Test the significance of the overall regression equation. c. What is the standard error of estimate. d. Explain the attitude toward the city in terms of durations of residence and importance attached to weather. e. Compare the regression coefficients and explain which attribute – Duration of residence , Importance attached to weather has more influence on Attitude toward the city.
- 4. 9. We are trying to predict the annual demand for widgets ( DEMAND) using the following independent vairables. Price = Price of Widgets ( in $) Income = Consumer income ( in $) Sub = Price of a substitute commodity (in $) ( A substitute commodity is one that can be substituted for another commodity. For example, margarine is a substitute commodity for butter) The below data is collected form 1982 to 1996. Year Demand Price ($) Income ($) Sub ($) 1982 40 9 400 10 1983 45 8 500 14 1984 50 9 600 12 1985 55 8 700 13 1986 60 7 800 11 1987 70 6 900 15 1988 65 6 100 16 1989 65 8 1100 17 1990 75 5 1200 22 1991 75 5 1300 19 1992 80 5 1400 20 1993 100 3 1500 23 1994 90 4 1600 18 1995 95 3 1700 24 1996 85 4 1800 21 a. Using MS-Excel determine the best fitting regression equation . b. Are the signs (+) and (-) of the regression coefficients of the independent variables as one would expect? Explain briefly. c. State and interpret the coefficient of multiple determination for this problem d. State and interpret the standard error of estimate. e. Using the equation, what would you predict for DEMAND if the price of widgets was $6 consumer income was $1200, and the price of the substitute commodity is $17. 10.Consider a study that examined the business problem facing a concrete supplier of how adding fly-ash affects the strength of concrete. (fly-ash is an inexpensive industrial waste by-product that can be used as a substitute for Portland cement, a more expensive ingredient of concrete. Batches of concrete were prepared in which the percentage of fly-ash ranges from 0% to 60%. Data were collected from a sample of 18 batches and organized. Fly-ash % 0 0 0 20 20 20 30 30 30 Strength 4,779 4,706 4,350 5,189 5,140 4,976 5,110 5,685 5,618 Fly-ash % 40 40 40 50 50 50 60 60 60 strength 5,995 5,628 5,897 5,746 5,719 5,782 5,895 5,030 4,648 a. Draw the scatter plot. b. Draw the regression line.
- 5. c. Display the regression equation d. Display R2 and interpret the result. e. Describe the strength of association between the variables. 11.For the above data a. Find the quadratic regression model for the concrete strength data. b. Explain the linear and quadratic effect of fly-ash on strength of the concrete. c. Explain the test for the significance of the Quadratic Model using F-stat. d. Test the significant difference between the quadratic model and linear model for testing the quadratic effect. e. If you select the 0.05 level significance, then explain the critical values for the t-distribution. 12.A real estate developer studying the business problem of estimating the consumption of heating oil by single family houses has decided to examine the effect of atmospheric temperature and the amount of attic insulation on heating oil consumption. Data are collected from a random sample of 15 single family houses. Heating oil Temperature Insulation 275.3 40 3 363.8 27 3 164.3 40 10 40.8 73 6 94.3 64 6 230.9 34 6 366.7 9 6 300.6 8 10 237.8 23 10 121.4 63 3 31.4 65 10 203.5 41 6 441.1 21 3 323.0 38 3 52.5 58 10 a. Find the multiple regression equation using two independent variables: atmospheric temperature and attic insulation b. For the excel regression model, interpret the results for predicting monthly consumption of heating oil. c. Draw the residual plot for attic insulation. Do you find some evidence of quadratic effect. d. If, then establish the quadratic regression model, by adding a quadratic term for attic insulation to the multiple regression model. e. Test the significance of quadratic effect. 13.The table gives the data of 30 respondents, 15 of whom are brand loyal (Indicated by 1) and 15 of whom are not ( indicated by 0). Loyalty 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Brand 4 6 5 7 6 3 5 5 7 7 6 5 7 5 7 Loyalty 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
- 6. Brand 3 4 2 5 4 3 3 3 4 6 3 4 3 5 1 a. Draw the scatter plot. b. Find the regression equation. c. Interpret R2 d. Interpret adjusted R2 14.The table gives the data of 30 respondents, 15 of whom are brand loyal (Indicated by 1) and 15 of whom are not ( indicated by 0). Attitude toward the Brand, Attitude toward the Product Category, and Attitude toward the Shopping experience are also measured. The objective is to estimate the probability of a consumer being brand loyal as a function of attitude toward the brand, the product category and shopping. Loyalty 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Brand 4 6 5 7 6 3 5 5 7 7 6 5 7 5 7 Product 3 4 2 5 3 4 5 4 5 6 7 6 3 1 5 shopping 5 4 4 5 4 5 5 2 4 4 2 4 3 4 5 Loyalty 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Brand 3 4 2 5 4 3 3 3 4 6 3 4 3 5 1 Product 1 6 5 2 1 3 4 6 4 3 6 3 5 5 3 shopping 3 2 2 4 3 4 5 3 2 6 3 2 2 3 2 a. Plot the scatter plot. b. Find the Regression equation. c. What are the degrees of freedom. d. Explain R2 and adjusted R2. e. Explain the significance of each of the regression coefficients. f. Of the three independent variables, which variable is more significant to predict the brand loyalty. 15.One of the investments considered in The Principled Scenario is the entertainment industry. The table given below presents the yearly US and Canada movie attendance ( in billions) from 2001 through 2014. Year 2001 2002 2003 2004 2005 2006 2007 Attendance 1.24 1.14 1.34 1.39 1.45 1.33 1.52 Year 2008 2009 2010 2011 2012 2013 2014 Attendance 1.42 1.34 1.28 1.44 1.56 1.58 1.62 a. Present the Time Series plot of this data. b. Describe the data. c. Draw the trend line to the data. d. Obtain the regression line to the data e. Obtain the R2 for the data. 16.For the data given above a. Obtain a three year moving average. b. Draw the trend line graph for the 3 year moving average. c. Obtain the regression line and R2. d. Forecast the attendance in the year 2016.
- 7. 17. For the data given below Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Sales ( in billions) 16.6 15.2 13.4 15.5 15.8 16.3 14.5 16.8 19.8 20.5 Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Sales ( in billions) 21 19.2 18.3 21.9 23.1 24.5 28.7 31.9 30 35.1 a. Obtain 5 year moving average b. Draw the trend line graph for the 5 year moving average. c. Obtain the regression line and normal probability plot d. Obtain the line fit plot. e. Forecast the Revenue in the year 2020. 18. According to The Coca-Cola Company’s Website, revenues in 2014 were almost $46 billion. The data given below lists The Coca-Cola Company’s gross revenues (in $billions) from 1998 to 204 are given. Year 1998 1999 1200 2001 2002 2003 2004 2005 2006 Revenue (in $ Billions) 18.8 19.8 20.5 20.1 19.6 21.0 21.9 23.1 24.1 Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 Revenue (in $ Billions) 28.9 31.9 31.0 35.1 46.5 48.0 46.7 45.9 50.1 a. Obtain the linear trend model to forecast the revenues. b. Obtain the quadratic trend model to forecast the revenues. c. Using both the equations obtained, forecast the revenues for the year 2020. d. Do you find any difference in the expected revenues? If explain the reasons and the significance. e. Of both the models, which model can be considered? 19.For the data given above a. Find the Exponential trend model. b. Forecast the revenues for the year 2020. c. Compare the three models Linear Trend Model, Quadratic Trend Model and Exponential Trend model. d. Select the best model for the data given. 20.Find the Euclidean Distance for the following data in Excel. X 1 3 4 7 8 10 15 18 20 21 Y 3 5 8 11 14 19 25 27 30 35 21. Form two clusters for the given 9 elements – 2 3 4 10 11 12 20 25 30
- 8. a. How many combinations of clusters are possible. b. Which cluster is more suitable and Why? c. How many elements are in each of the cluster which is suitable for modelling. 22.From the data Height 121 164 148 186 178 156 179 163 152 131 Weight 53 71 56 79 68 55 67 62 51 48 Height 138 166 189 123 178 161 149 189 176 159 Weight 53 68 83 54 74 58 52 78 67 52 Create a relationship model using the lm() function in R Display the regression model and creating the mathematical equation. 23.For the above data, check the non-linearity between weight and height. 24.For the above data, graphical evaluation of statistical assumptions for regression. 25. From the data “mtcars” data set, which has 32 observations and 11 variables, find the simple linear regression model. 26.Develop the regression model from the data set “state.x77” for applying regression analysis. 27.Check the multi-collinearity assumption using vif( ) function for the above data. 28.Develop the multiple regression model using step wise backward approach from the data set “Longley” 29.Develop best Regression Model using Stepwise Forward Approach using dataset ‘Prestige” available in “car” package of R environment. 30.From the data set “Ratings for Wine” use KNN classifier to build a model for 5 neighbours and validate the data set. 31.From the data set “HouseVotes84” that can be downloaded from https://archive.ics.uci.edu/ml/datasets/congressional+voting+records this data set includes votes for each of the US house of representative. Congressmen on the 16 key notes identified by the CQA. Classify the algorithm using Naïve Baye’s classifier. ( note R does not support missing values. So delete missing values and then Classify in R) 32.From https://archive.ics.uci.edu/ml/datasets/Occupancy+Detection
- 9. apply Naïve Baye’s classifier to detect the Occupancy status. 33.From the dataset https://archieve.ics.uci.edu/ml/datasets/banknote+authentication Appli Naïve Baye’s classifier to detect the bank note authentication. 34.From the data “breast Cancer” data set, build the model to predict if the given tumor is benign or malignant depending upon the value of the Cell.size, Cell.Shape and Cl.thickness using the information available in the data set 35.From the data set Creditcard.csv https://www.kaggle.com/datasets/mlg- ulb/creditcardfraud?select=creditcard.csv use Support Vector Machine to detect the fraud for credit card. 36.From https://archive.ics.uci.edu/ml/datasets/Occupancy+Detection apply Decision Tree to decide the occupancy status. 37.Create the cluster analysis using R package for the following data. 2 4 10 12 3 20 30 11 25 15 Explain the output. 38.From the data “Breast Cancer” data set, determine the utility of cluster analysis. 39.Apply the K-means cluster analysis using 3 clusters for “Breast Cancer” Data set. 40.From the data set “sample.stock.yields.1959.1969” explain the utility of Hierarchical clustering using average method. A firm manufactures four different machine parts A, B, C and D using Copper and Zinc. The requirement of copper and zinc for each part and their availability and the profit earned from each part are given below: Item Requirements Profits(Rs.) Copper Zinc A 5 2 12 B 4 3 8
- 10. C 2 8 14 D 1 1 10 Availability 100 75 41. What is the objective function that we need to optimize. 42. What are the decision variables that determine the objective function. 43.Write the constraints that the solution must satisfy. 44. What are the non-negative constraints. 45. How many of each part should be manufactured in order to maximize the profit. MKV Foods Companyis developing a diet supplement called Hi-Pro. The specifications and the calorie, protein and vitamin content of three basic food are given below: Nutritional elements Units of nutritional elements per 100 gm Basic foods Hi-Pro Specification F1 F2 F3 Calories 350 250 200 300 Proteins 250 300 150 200 Vitamin A 100 150 75 100 Vitamin C 75 125 150 100 Cost per 100 gms (Rs.) 1.50 2.00 1.120 46.What is the objective function that we need to optimize. 47. What are the decision variables that determine the objective function. 48.Write the constraints that the solution must satisfy. 49. What are the non-negative constraints. 50. Determine the quantities of F1, F2, F3 to be used to meet the requirements with minimum cost.