Business Analysis Statistics Test #4 — Questions and Answers
Question 1: A data collection with numerous variables that lack values is used to create a prediction model. What two issues might this model have? (Select two.)
- There will be a high rate of collinearity among input variables.
- Complete case analysis means that fewer observations will be used in the model building process. (Correct answer)
- New cases with missing values on input variables cannot be scored without extra data processing. (Correct answer)
- The model will likely be overfit.
Correct answer: Complete case analysis means that fewer observations will be used in the model building process.
When a dataset has numerous missing values, two significant issues arise for predictive modeling. Firstly, if a complete case analysis (listwise deletion) is employed, many observations will be discarded, leading to a substantial reduction in the effective sample size available for model building. Secondly, any new cases with missing values on the input variables cannot be directly scored by the model unless specific preprocessing steps, such as imputation or deletion, are applied to handle those missing values consistently with how the model was trained.
Question 2: A logistic regression model is fitted by an analyst to determine whether a client will default on a loan or not. Agents, who each service 15-20 clients, are one of the predictors in the model. Model convergence is not achieved. The analyzed data is printed by the analyst, along with the breakdown of defaulted loans by agent. View a sample of the output below: What is the main cause of the model's inability to converge?
- There are too many observations in the data.
- There is collinearity among the predictors.
- There are missing values in the data.
- There is quasi-complete separation in the data. (Correct answer)
Correct answer: There is quasi-complete separation in the data.
The main cause of the logistic regression model's inability to converge, especially when examining defaulted loans by agent, is likely quasi-complete separation in the data. This occurs when one or more predictor variables (like 'Agent') perfectly or nearly perfectly predict the outcome (loan default) for a subset of observations. For instance, if all clients of a specific agent either defaulted or never defaulted, the model's algorithm cannot find a finite maximum likelihood estimate for that agent's coefficient, leading to convergence failure.
Question 3: A multiple linear regression model already exists with the addition of a non-contributing predictor variable (Pr > |t| =0.658). What will happen as a result?
- An increase in R-Square (Correct answer)
- No change in R-Square
- A decrease in Mean Square Error
- A decrease in R-Square
Correct answer: An increase in R-Square
In multiple linear regression, adding any predictor variable to the model, regardless of its statistical significance, will always result in an increase or no change in the R-squared value. R-squared measures the proportion of variance in the dependent variable explained by the independent variables, and adding more variables can only account for more (or the same amount of) variance. While an insignificant predictor might not improve the model's predictive power meaningfully, it will still technically contribute to the R-squared calculation, causing it to rise.
Question 4: Choose the LOGISTIC procedure model statements that are equal. (Select two.)
- Mode1 Purchase * Gender | Age | Region;
- Mode1 Purchase * Gender|Age|Region @2;
- Mode1 Purchase * Gender|Age|Region @1; (Correct answer)
- Mode1 Purchase * Gender Age Region; (Correct answer)
Correct answer: Mode1 Purchase * Gender|Age|Region @1;
In SAS's LOGISTIC procedure, the `MODEL` statements `Mode1 Purchase * Gender|Age|Region @1;` and `Mode1 Purchase * Gender Age Region;` are equivalent. The `|` (bar) operator with `@1` (at-sign 1) in the first statement expands to include only the main effects of Gender, Age, and Region. The second statement explicitly lists these main effects. Both syntaxes result in a model that includes only the individual contributions of Gender, Age, and Region to predicting Purchase, without any interaction terms.
Question 5: A linear model includes the following features: a subordinate variable (y) a continuous predictor variable set of three (x1-x3) an individual category predictor variable (c1with 3 levels) Which SAS module does this model fit?
- Proc glm data=sasuser.mlr;class c1 x1 x2 x3;model y=c1 x1-x3 /solution;run;
- Proc glm data=sasuser.mlr;model y=c1 x1-x3 /solution;run;
- Proc glm data=sasuser.mlr;class c1;model y=c1 x1-x3;run;
- Proc glm data=sasuser.mlr;class c1;model y=c1 x1-x3 /solution;run; (Correct answer)
Correct answer: Proc glm data=sasuser.mlr;class c1;model y=c1 x1-x3 /solution;run;
The correct SAS `PROC GLM` statement for this model is `Proc glm data=sasuser.mlr;class c1;model y=c1 x1-x3 /solution;run;`. The `CLASS` statement is crucial for correctly identifying `c1` as a categorical predictor, ensuring SAS creates appropriate dummy variables for its three levels. The `MODEL` statement then specifies `y` as the dependent variable and includes the categorical `c1` along with the continuous predictors `x1` through `x3`. The `/SOLUTION` option requests the display of the parameter estimates for all model effects.
Question 6: The data 13, 15, 16, 17, 19, and 20's median are as follows:
- 30/1
- 30/2
- 33/2 (Correct answer)
- 34/2
Correct answer: 33/2
To find the median of a dataset, first arrange the numbers in ascending order: 13, 15, 16, 17, 19, 20. Since there is an even number of observations (six), the median is the average of the two middle values. The third value is 16 and the fourth value is 17. Therefore, the median is (16 + 17) / 2, which equals 33/2.
Question 7: When taken from: the total of the absolute deviations is at its minimum.
- Median (Correct answer)
- Mode
- Mean
- None of the above
Correct answer: Median
The total of the absolute deviations from a central point is minimized when that central point is the median of the data. This is a unique mathematical property of the median, making it the measure of central tendency that best represents the 'middle' in terms of minimizing absolute differences to all data points. In contrast, the mean minimizes the sum of squared deviations.
Question 8: If a series' maximum value is 25, and its range is 15, then the series' maximum value is:
- 5
- 10 (Correct answer)
- 20
- 30
Correct answer: 10
The range of a series is calculated as the difference between its maximum and minimum values. Given that the maximum value is 25 and the range is 15, we can determine the minimum value by subtracting the range from the maximum value. Therefore, the minimum value is 25 - 15, which equals 10.
Question 9: A debate competition with 10 competitors had a rank correlation coefficient of 0.6, according to the calculations. Later on, it was found that the difference in some participants' ranks was actually 8 instead of 3. How to calculate the right correlation coefficient:
- 0.751
- 0.854
- 0.933 (Correct answer)
- 0.652
Correct answer: 0.933
To correct the rank correlation coefficient, we first find the original sum of squared differences (Σd²) that yielded ρ=0.6 for n=10, which is Σd²=66. The error implies that an incorrect difference of 8 was used, and the actual difference should have been 3. Thus, we adjust Σd² by subtracting the squared incorrect difference (8²=64) and adding the squared correct difference (3²=9), resulting in a corrected Σd² of 66 - 64 + 9 = 11. Plugging this into the Spearman's formula, ρ = 1 - (6 * 11) / (10 * (10²-1)) = 1 - 66/990 = 0.933.
Question 10: The dispersion is referred to as follows if all exam scores tend to cluster around the mean:
- Normal
- Small (Correct answer)
- Symmetrical
- Large
Correct answer: Small
When all exam scores tend to cluster closely around the mean, it indicates that there is very little variability or spread among the scores. This phenomenon is referred to as small dispersion, meaning the data points are tightly grouped and do not deviate significantly from the central tendency. Conversely, large dispersion would imply scores are widely spread out.
Question 11: Find the set's mode (8, 5, 7, 10, 15, 21, 5, 7, 2, 5)
- 5 (Correct answer)
- 10
- 25
- 20
Correct answer: 5
The mode of a set of data is the value that appears most frequently. In the given set (8, 5, 7, 10, 15, 21, 5, 7, 2, 5), the number 5 occurs three times, which is more than any other number. Therefore, 5 is the mode of this dataset.
Business Analysis Statistics Test #4
A data collection with numerous variables that lack values is used to create a prediction model.
What two issues might this model have? (Select two.)