Ds 312 Fall 21 Excel Assignment 1 Posted On September 27, 20

Ds 312 Fall21 Excel Assignment 1posted On Monday 9272021 At 900 Am

This assignment accounts for 7% of the final grade and involves data analysis and software exercises using Excel. All answers should be typed in a single MS Word document, with relevant Excel outputs, graphs, and tables pasted in the document. Label your answers with the respective question numbers, e.g., 1.1). Do not retype the questions. Save your Excel file with the name “DS312 Excel assignment#1-LastnameFirstname” and keep it for submission if required later. Collaboration, consultation, or assistance from others is not permitted—ask the instructor if you have questions. Late or missed submissions will receive a zero. Submitting only Excel outputs or plots without explanations will be considered incomplete. The evaluation will be based on completeness and correctness of responses.

Paper For Above instruction

This assignment involves a comprehensive analysis of data sets using Excel, focusing on regression analysis, residual diagnostics, confidence intervals, and prediction intervals across multiple contexts. The tasks are designed to assess understanding of statistical concepts and proficiency in applying Excel tools for data analysis.

The first part requires identifying independent and dependent variables, creating scatter plots, performing regression analysis, and evaluating the relationship between variables through residual analysis. These steps foundationally test the ability to interpret relationships between variables and validate model assumptions.

The subsequent questions involve applying regression predictions and inferential statistics to different data sets:

1. For the first data set (GPA and ACT scores), calculations include obtaining point estimates for mean GPA at a given ACT score, constructing confidence intervals for this mean, and prediction intervals for individual students. These tasks demonstrate understanding of estimation and interval construction in regression contexts.
2. For the second data set (Copier Maintenance), similar procedures are performed to estimate average service times, with corresponding confidence and prediction intervals, based on the number of copiers serviced.
3. The third data set (Airfreight Breakage) focuses on predicting the average number of broken ampules based on the number of transfers, including the construction of confidence and prediction intervals for future shipments.

Throughout these tasks, explicit intermediate calculations should be shown, emphasizing the process and understanding underlying the statistical techniques used. The work must incorporate proper statistical assumptions, accurate interpretation of outputs, and clarity in presenting results.

Paper for the Above Instructions

Predicting outcomes and understanding relationships between variables are fundamental objectives in applied statistics. Excel provides a flexible and accessible platform for conducting such analyses, which are critical for making informed decisions in business and scientific contexts.

The initial step in regression analysis often involves determining the roles of variables—identifying which is independent (predictor) and which is dependent (response). For example, in the first data set, the ACT score acts as a predictor of GPA. Establishing this relationship allows for meaningful modeling and prediction. Creating scatter plots assists in visually assessing the form and strength of this relationship—whether linear, nonlinear, or nonexistent. A clear linear pattern indicates that simple regression is appropriate and justifies further analysis.

Regression analysis using Excel’s built-in functions yields a regression equation. This equation quantifies how changes in the independent variable affect the dependent variable. The regression summary output provides coefficients, R-squared, standard errors, and significance levels. The R-squared value indicates the proportion of variance in the dependent variable explained by the model. A high R-squared suggests a strong predictive relationship, while a low value indicates limited predictive power.

However, the validity of the regression model depends on the residuals behaving in accordance with key assumptions—normality, constant variance (homoscedasticity), and independence. Residual analysis involves plotting residuals versus fitted values, histograms, or Q-Q plots, to visually inspect for violations. Any pattern, skewness, or heteroscedasticity necessitates further investigation before relying on the model for prediction.

Estimation of mean outcomes at specific predictor values involves calculating point estimates and corresponding confidence intervals. For example, estimating the mean GPA for students with an ACT score of 30 requires applying the regression equation and calculating the standard error of the mean estimate. Constructing a 98% confidence interval involves the t-distribution critical value, the standard error, and the mean estimate.

Prediction intervals, on the other hand, account for the variability of individual responses. For Mary Jones, who scored 28 on the ACT, a 90% prediction interval for her GPA incorporates the extra uncertainty associated with predicting a single individual’s outcome, which is wider than the confidence interval for the mean.

In the context of the second data set, estimating the mean service time for a given number of copiers serviced (80) and constructing the associated intervals provides practical insights into operational efficiency. Similarly, for the third data set, predicting the mean and individual outcomes for future shipments—like 20 transfers—requires translating regression outputs into usable intervals that account for both model uncertainty and individual variability.

Throughout these analyses, it is crucial to explicitly perform each calculation step—computing means, standard errors, critical values, and the intervals—to demonstrate understanding and ensure accuracy. Proper interpretation of these results in context guides decision-making and showcases mastery of regression diagnostics and inference techniques.

References

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• Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied Linear Statistical Models. McGraw-Hill Irwin.
• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Zimmerman, D. (1998). Business Statistics: A First Course. McGraw-Hill.
• McClave, J. T., & Sincich, T. (2017). Statistics. Pearson.
• Wilkinson, L., & Task Force on Statistical Inference. (2018). Statistical Methods in Psychology. American Psychological Association.
• Heck, R. H., Thomas, S. L., & Tabata, L. N. (2017). Multilevel and Mixed Effects Models. Routledge.
• Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.