Problem Solving 1: To monitor and improve its productivity, a company made an investigation and found out that the factor that affects the productivity the most is the absenteeism. The company data analytics department have collected data about the two variables (Productivity and Absenteeism) for the 12 past years as shown in the table below. Now the purpose of the company is to determine, through regression analysis, whether the productivity is statistically affected by the absenteeism level or not. Table – 1 (Problem 1) Questions:
1. Construct a scatter diagram for the data about productivity and absenteeism then interpret the possible relationship that can be found. 2. Construct a simple regression model to predict the annual productivity by the variable Absenteeism. What is the interpretation that can be made based on the regression results?
3. Compute r2 and r for the regression model constructed earlier. What interpretation can be made?
4. Calculate the prediction error for the annual productivity for the years 8, 9, and 10, based on the corresponding regression model constructed previously.
5. For the regression model of the annual productivity by the variable Absenteeism, draw the errors graph and check if the errors respect the regression assumptions or not. Problem Solving 2: The following table represents data on the monthly sales of cellphones and wireless headsets. The company believes that these two products are complementary, which means that the headset sales affect positively the cellphones sales. To confirm this hypothesis, the company will conduct a statistical study based on the data presented in the table below. Table – 2 (Problem 2) Questions:
1. Construct a simple regression model to predict the monthly cellphone sales by the wireless headset sales.
2. Formulate the hypothesis testing framework to test the model for its statistical significance.
3. Construct the ANOVA table for the regression model.
4. Perform the significance test for ? = and what conclusion can be drawn from the obtained results? Problem Solving 3: The following table represents historical data on laptop sales for seven consecutive periods. Table – 3 (Problem 3) Questions:
1. Compute The forecasting of the periods 5,6, and 8 using the Simple Moving Average of order 1, 3, and then 4. 2. Compute The forecasting of the periods 7, and 8 using the weighed moving average of order
2 (the weights are 15 and 5 from most recent period).
3. Compute The forecasting of the periods 6, and 8 using the weighed moving average of order
4 (the weights are 12, 6, 7, and 4 from most recent period). 4. Compute the forecasting of period 7, for demand of computers, using the exponential smoothing with ? = and F4 = 500.
