Business Analysis Statistics Test #2 — Questions and Answers
Question 1: A firm has eight regional branch offices. Customers within each region are coded using the variable name VALUE and are categorized as either "High Value" or "Medium Value." The response variable used in the past year is the total number of purchases made by each client. Assume REGION and VALUE have a substantial interaction. What do you draw from this?
- There are more high value clients in regions with higher average buy levels.
- The disparity between medium and high value clients' average purchases varies by area. (Correct answer)
- There are more medium value clients in areas with higher average buy levels.
- Some regions have more high value consumers than others.
Correct answer: The disparity between medium and high value clients' average purchases varies by area.
A substantial interaction between REGION and VALUE means that the effect of one variable on the response (total number of purchases) depends on the level of the other variable. Specifically, it implies that the difference in average purchases between 'High Value' and 'Medium Value' clients is not constant across all regions. Instead, this disparity varies significantly from one region to another, indicating a complex relationship.
Question 2: An existing multiple linear regression model is modified by removing a non-contributing predictor variable (Pr > |t| =0.658). What will happen as a result?
- No change in R-Square
- A decrease in Mean Square Error
- A decrease in R-Square (Correct answer)
- An increase in R-Square
Correct answer: A decrease in R-Square
R-squared measures the proportion of variance in the dependent variable explained by the independent variables. While R-squared never decreases when a new predictor is added, it will decrease when a predictor is removed, regardless of its significance. Removing any variable, even one with a high p-value, will reduce the total variance explained by the model, albeit minimally if the variable was truly non-contributing.
Question 3: The link between a binary response and an ordinal predictor variable, wrist size, is examined in the LOGISTIC method output that follows. The analyst decides on Large (L) as the reference level using reference cell coding. What is a person with a large wrist size's estimated logit? If one is required, simply click the calculator icon to bring one up.
- 0.5663
- 0.0819
- -3.7727
- -1.0415 (Correct answer)
Correct answer: -1.0415
In logistic regression with reference cell coding, the estimated logit for the reference level is directly represented by the intercept term. When 'Large (L)' is chosen as the reference level, its logit is given by the Intercept estimate from the model output. Therefore, the estimated logit for a person with a large wrist size is -1.0415.
Question 4: In the LOGISTIC process, which of the following best defines a concordant pair of observations?
- In comparison to an observation without the event, an observation with the event has a lower anticipated probability.
- There is an equal chance that one observation will be associated with the occurrence as another.
- The anticipated probability for an observation with and without the occurrence is the same.
- A prediction for an observation that includes the event is higher than for an observation that does not. (Correct answer)
Correct answer: A prediction for an observation that includes the event is higher than for an observation that does not.
In logistic regression, a concordant pair consists of one observation where the event occurred and another where it did not. The pair is concordant if the model's predicted probability of the event for the observation where the event *did* occur is higher than the predicted probability for the observation where the event *did not* occur. This indicates that the model correctly distinguishes between event and non-event cases.
Question 5: You may check for non-linearity in binary logistic regression by visualizing:
- Odds ratio values plotted against a predictor variable in a box.
- An empirical logit trend plot against a predictor variable (Correct answer)
- A plot of projected probability values against a predictor variable using logistic regression.
- Binary response scatterplot vs predictor variable
Correct answer: An empirical logit trend plot against a predictor variable
To check for non-linearity in binary logistic regression, an empirical logit trend plot against a predictor variable is the most effective visualization. This plot transforms the binary response into empirical logits, which should show a linear relationship with the predictor if the model's linearity assumption holds. Deviations from a linear trend in this plot indicate non-linearity, suggesting the need for transformations or polynomial terms.
Question 6: What is the LOGISTIC procedure's default approach to handling observations with incomplete data?
- Only instances with completely populated variables are employed. (Correct answer)
- In order to accommodate for the missing values, parameters are estimated.
- All the data is used to estimate the parameters.
- Missing values are imputed.
Correct answer: Only instances with completely populated variables are employed.
By default, the LOGISTIC procedure in SAS (and many other statistical software packages) handles observations with incomplete data by performing a complete-case analysis. This means that only observations where all variables included in the model have non-missing values are used for parameter estimation. Any observation with even a single missing value for a model variable is excluded from the analysis.
Question 7: By examining the correlation between which function of the input variables, Spearman statistics in the CORR technique are helpful for identifying unnecessary variables.
- Rank-ordered values of the variables (Correct answer)
- Concordant and discordant pairs of ranked observations
- Weighted sum of chi-square statistics for 2x2 tables
- Logit link (log(p/1-p))
Correct answer: Rank-ordered values of the variables
Spearman's rank correlation coefficient assesses the monotonic relationship between two variables. It works by first converting the raw data into ranks and then calculating the Pearson correlation coefficient on these rank-ordered values. This makes it useful for identifying monotonic (but not necessarily linear) associations and thus redundant variables based on their ranked relationships.
Question 8: A logistic regression model's input variable, Region (A, B, or C), is investigated by an analyst. The analyst finds that when Region = A, the likelihood of purchasing a specific item is 1. What issue does this highlight?
- Influential observations
- Collinearity
- Problems that arise due to missing values
- Quasi-complete separation (Correct answer)
Correct answer: Quasi-complete separation
When the likelihood of an event (purchasing an item) is 1 for a specific category of a predictor variable (Region = A), it indicates a problem known as quasi-complete separation. This means that for all observations in that category, the event *always* occurs. In logistic regression, this can lead to infinite parameter estimates and convergence issues, as the model tries to perfectly separate the groups.
Question 9: What disadvantage exists in cleaning up the data (imputation, transformations, etc.) on raw data before partitioning it for accurate assessment as opposed to cleaning up the data after partitioning it?
- The advantages of the purification techniques are not applied to the training (and test) data sets.
- It violates assumptions of the model.
- It requires extra computational effort and time.
- It is impossible to compare the efficacy of various washing techniques. (Correct answer)
Correct answer: It is impossible to compare the efficacy of various washing techniques.
Cleaning data (imputation, transformations) on raw data *before* partitioning it for training, validation, and testing can lead to an overly optimistic assessment of model performance. A significant disadvantage is that it becomes impossible to accurately compare the efficacy of different data cleaning techniques. If the cleaning is done on the full dataset, the validation and test sets are no longer truly independent, making it difficult to assess how well a specific cleaning method generalizes to new, unseen data.
Question 10: To execute an unbiased evaluation during the model building process, an analyst has access to a large enough volume of data to do a 3-way partitioning of the data into training, validation, and test sets. What goal does the test data set serve?
- To offer a fair assessment metric for the finished model. (Correct answer)
- To reduce total sample size to make computations more efficient.
- To build the predictive models.
- To compare models and select and fine-tune the final model.
Correct answer: To offer a fair assessment metric for the finished model.
In a 3-way data partition (training, validation, test), the test data set serves the crucial purpose of providing a final, unbiased assessment of the chosen model's performance. It is held completely separate throughout the model building and selection process, ensuring that the model's reported performance metrics truly reflect its ability to generalize to new, unseen data. This prevents overfitting to the validation set during model tuning.
Question 11: Compared to the SCORE statement in the LOGISTIC procedure, think about scoring fresh observations in the SCORE procedure. Which claim is accurate?
- In contrast to the SCORE procedure, the LOGISTIC procedure's SCORE statement generates both anticipated probabilities and predicted logits.
- Only anticipated logits are returned by the SCORE statement in the LOGISTIC process, while only predicted probabilities are returned by the SCORE procedure.
- The output is the same for both the SCORE process and the SCORE statement in the LOGISTIC procedure.
- In contrast to the SCORE method, the SCORE statement in the LOGISTIC procedure simply gives anticipated probabilities. (Correct answer)
Correct answer: In contrast to the SCORE method, the SCORE statement in the LOGISTIC procedure simply gives anticipated probabilities.
The SCORE statement within the LOGISTIC procedure is designed to output only the predicted probabilities for new observations. In contrast, the standalone SCORE procedure is more versatile and can generate both predicted probabilities and predicted logits. Therefore, if you specifically need only the anticipated probabilities from a logistic model, the SCORE statement in LOGISTIC is sufficient, while the SCORE procedure offers more comprehensive output.
Business Analysis Statistics Test #2
A firm has eight regional branch offices.
Customers within each region are coded using the variable name VALUE and are categorized as either "High Value" or "Medium Value." The response variable used in the past year is the total number of purchases made by each client.
Assume REGION and VALUE have a substantial interaction.
What do you draw from this?