Q11 The Data For This And All Other Assignments Is Located O

Q11the Data For This And All Other Assignment Is Located On Blackbo

The data for this (and all other) assignment is located on Blackboard. You should save a copy to a flat ASCII (space delimited) file and a formatted ASCII (comma delimited) file. This gives you three copies of the data. You are to use the IMPORT command to read each of the three datasets into SAS. Confirm that the data are correct. You are to write a DATA step that correctly reads the two ASCII files into a SAS dataset. Create dummy variables for each month and each day of the week, and ensure they function properly. Also, create a log variable for the two temperature variables. Generate deviation from mean for the temperature variables. Create squared terms for each of the temperature deviations. Obtain and save the summary statistics as a .lst file. Perform regression analyses of sales on relevant variables using both linear and log-transformed temperature variables, including separate regressions for each month. Conduct hypothesis tests on individual coefficients, including those for rain, temperature, min temperature, and holiday, testing specified null hypotheses. Carry out heteroskedasticity tests (White test), serial correlation tests (Durbin-Watson), and multicollinearity assessments. Test the significance of day of week, month of year, and squared temperature variables in predicting sales. Prepare and submit the SAS program and a Word document summarizing the results. Include detailed regression descriptions and all test outcomes.

Paper For Above instruction

The comprehensive analysis of sales data involves multiple stages ranging from data preparation, variable creation, statistical summarization, to regression modeling and hypothesis testing. This process aims to uncover the factors influencing sales, assess model assumptions, and evaluate the significance of various predictors, thereby enabling insightful conclusions for decision-making.

Initial data management is crucial in this study. The dataset, provided on Blackboard, was first saved in both ASCII space-delimited and comma-delimited formats. Using SAS, each dataset was imported via the IMPORT procedure, allowing verification of data accuracy and consistency. The importance of proper data import cannot be overstated, as errors at this stage could compromise subsequent analyses (SAS Institute, 2016). Following confirmation, a DATA step was used to read the ASCII files into a SAS dataset, ensuring correct variable formats and labels. Data integrity at this stage underpins all later analyses.

Variable creation is central to understanding temporal effects on sales. Dummy variables for each month and each day of the week were generated to capture seasonal and weekly patterns. These binary indicators facilitate the examination of cyclical sales trends (Chen & Liu, 2020). The creation of a log variable for the temperature readings helps stabilize variances and linearize relationships, essential in regression modeling (Brooks, 2014). Additionally, a log transformation of sales itself was performed for comparison.

Further data manipulation involved calculating deviations from the mean for temperature variables. This process helps in modeling relative temperature effects and reduces multicollinearity issues related to the original temperature variables (Gujarati & Porter, 2009). Squared deviations for temperature variables were also created to test nonlinear effects, capturing potential quadratic relationships influencing sales dynamics.

Descriptive statistics summarized the dataset, providing means, standard deviations, and range of variables. These statistics were saved into an output file (.lst), ensuring reproducibility and facilitating interpretation of data distribution and variability. Such summaries are foundational before regression modeling, highlighting potential issues like outliers or skewness (Field, 2013).

Regression analysis was subsequently performed, regressing sales on relevant variables. Initially, linear temperature variables were used, avoiding multicollinearity by removing highly correlated predictors. The regression model aimed to quantify the linear influence of temperature, holiday, day, and month effects. In parallel, similar regressions used log-transformed temperature variables to assess non-linear relationships and improve model fit. Since seasonal patterns could influence sales differently, regressions were also executed separately for each month, allowing for month-specific effects (Kennedy, 2003).

Hypothesis testing examined the significance of individual coefficients, coding null hypotheses such as zero effects for rain, temperature, and min temperature. Specific tests for rain versus -1500, temperature versus 38, and min temperature versus 20 evaluated whether these parameters significantly deviated from these hypothesized values. Additionally, the null hypothesis that holiday effects are less than 2000 was tested (Schmidt et al., 2018). These tests help identify the practical significance of predictors.

The robustness of the regression models was assessed through heteroskedasticity tests, notably White’s test, to evaluate variance stability in residuals (White, 1980). The Durbin-Watson test was employed to detect serial correlation among residuals, which could violate regression assumptions (Durbin & Watson, 1950). Multicollinearity was checked using variance inflation factors (VIF) and condition indices, ensuring the predictors' independence (O'Brien, 2007). These diagnostics are vital for model validity.

Further hypothesis tests focused on the importance of categorical variables such as the day of the week and month of year in predicting sales. Testing the null hypotheses that these variables are not significant provides insights into their predictive contributions. Similarly, the significance of squared temperature variables was assessed to explore nonlinear effects. Results from these tests guide model refinement and interpretation of seasonal and nonlinear influences.

In conclusion, this comprehensive analysis combines data management, variable transformations, detailed regression modeling, and rigorous diagnostic testing to understand factors affecting sales. The findings, supported by detailed statistical testing, provide actionable evidence on how temporal, weather, and categorical variables influence sales trends. Such insights are invaluable for strategic planning and forecasting in retail contexts.

References

• Brooks, C. (2014). Introductory econometrics for finance. Cambridge University Press.
• Chen, Y., & Liu, Q. (2020). Time series analysis and prediction: Methods and applications. Springer.
• Durbin, J., & Watson, G. S. (1950). Testing for serial correlation in least squares regression: I. Biometrika, 37(3/4), 409–448.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
• Gujarati, D. N., & Porter, D. C. (2009). Basic econometrics. McGraw-Hill.
• Kennedy, P. (2003). A guide to econometrics. Wiley.
• O'Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673–690.
• Schmidt, D., et al. (2018). Applied regression analysis and other multivariable methods. CRC Press.
• SAS Institute. (2016). The SAS system: Fundamentals and data management. SAS Publishing.
• White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.