Chi-Square

One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

1. Run a chi-square test to determine if an individual’s defect rate is independent of their years since training?
   Regression Section
   The management of Beta Technologies, Inc., is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees. The Excel worksheet: Beta Technologies contains their data. Annual Salary is the dependent variable.
2. Is there a significant difference in average annual salary for men and women? Use Simple Linear Regression to answer this question.
3. Excluding the gender variable: Generate a scatter diagram matrix of the remaining variables in the data set.
4. Excluding the gender variable: Generate a correlation matrix of the remaining variables in the data set.
5. Excluding the gender variable: Determine the best " simple linear regression " equation to explain annual salary.
6. Use all of the independent variables in the data set (including gender) to generate a multiple linear regression equation to explain annual salary. Do not use either stepwise or best subsets to determine your model. Include a check for collinearity using VIF.
7. Based on your interpretation of the multicollinearity checks and significance of the beta coefficients from the output with all of the independent variables in the model, make any changes that you deem necessary and rerun the regression model until you are satisfied with the results.
8. Generate a prediction using your equation generated in the previous question for the following person: A female, Age 37, 10 years prior experience, 5 years with the company, and 6 years of education. Use all variables that apply. Include both a Confidence interval and a Prediction interval for your prediction.
   For your final regression equation that you generated after making all of your changes: use residual analysis to check for violations of the following assumptions associated with your regression equation.
9. Normality of the error terms
10. Autocorrelation of the error terms
11. Constant Variance of error terms
12. Use Stepwise to generate multiple regression results. Start with all independent variables in the data.
13. Use Best Subsets to generate multiple regression results. Start with all independent variables in the data set. Use the option that generates only (1) best equation for each variable model.
14. Create a quadratic term for the "beta experience" independent variable. Run a regression model with the beta-experience independent variable and the beta-experience-squared independent variable as the independent variables.
15. Use your quadratic regression equation to make a prediction for an employee that has 5 years of beta-experience.
    Time Series Section
    The NASDAQ stock market includes small and medium sized companies, many of which are in high-tech industries. Because of the nature of these companies, the NASDAQ tends to be more volatile than the Dow Jones industrial Average or the S & P 500. The worksheet Moving Average in the workbook Time series contains the data for 20 weeks. Values are in dollars.
16. Use the charting function in Excel to plot the original time series and a 3 period equally weighted moving average that could be used for smoothing on the same chart. Size the chart so that it is approximately 3 inches by 5 inches and has the legend on the bottom.
17. Use the charting function in Excel to plot the original time series and a 3 period unequally weighted moving average that could be used for prediction on the same chart. Use the following weights: 0.5, 0.3, 0.2, with the most recent data weighted the most. Size the chart so that it is approximately 3 inches by 5 inches and has the legend on the bottom.
18. Use the Excel Worksheet: Exponential Smoothing: to construct and compute an exponentially smoothed forecast. Set up the worksheet so that the weight (W) can be changed and that the MAD is computed automatically. Use the first value for the NASDAQ (2007) as the first smoothed value. Start your computation of MAD with the second forecasted value (16-Jan). Set the weight (W) to 0.8.
    Seasonal Problem
    Metro Food Vending operates vending machines in office buildings, the airport, bus stations, colleges, and other businesses and agencies around town and operates vending trucks for building and construction sites. The company believes its sandwich sales follow a seasonal pattern. It has accumulated the following data for sandwich sales per season during the past four years. The data is contained in the worksheet Seasonal indices.
19. Set up the Excel work sheet to determine the seasonal indices for each season.
20. Use a 3 period (year), equally weighted, moving average model to forecast Total Sales for year 2004. Set up the Excel worksheet to forecast demand for each season for 2004.

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Solution: The downloadable solution consists of 13 pages, 346 words and 17 charts.
Deliverable: Word Document