Business Analysis Statistics Test #1

Question 1

A linear regression's usual formula is Y= beta0+beta1*X+error. Which phrase best encapsulates the presumptions made about the mistakes?

Accepted Answer

The errors are independent, normally distributed with zero mean and constant variance.

Answer

In ordinary least squares (OLS) linear regression, several key assumptions are made about the error term (residuals). These include that the errors are independent, follow a normal distribution, have a mean of zero, and exhibit constant variance (homoscedasticity). These assumptions are crucial for the validity of hypothesis tests and confidence intervals derived from the regression model.

Question 2

Which SAS application will split the original data set into training and validation data sets stratified by county, each comprising 60% of the data?

Accepted Answer

Proc sort data=SASUSER.DATABASE;by county;run;proc surveyselect data=SASUSER.DATABASE samprate=0.6 out=sample outall;strata county;run;

Answer

To perform stratified sampling in SAS, the data must first be sorted by the stratification variable, which in this case is 'county'. The `PROC SURVEYSELECT` procedure is then used to select a sample, with `samprate=0.6` indicating a 60% sample. The `strata county;` statement ensures that the sampling is done independently within each county, and `outall` creates an output dataset containing both selected and unselected observations, allowing for easy creation of training and validation sets.

Question 3

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?

Accepted Answer

Quasi-complete separation

Answer

Quasi-complete separation occurs in logistic regression when a predictor variable or a combination of predictors perfectly predicts the outcome for a subset of observations. If the likelihood of purchasing an item is exactly 1 (or 0) for all observations in a specific region, it means that region perfectly predicts the outcome. This can lead to infinite maximum likelihood estimates for the regression coefficients, causing problems with model convergence and interpretation.

Question 4

The mean incomes of men and women employed by a corporation are compared by an analyst. Variables in the SAS data collection SALARY include: Gender (M or F) Pay (dollars per year) What SAS tools may be used to calculate the p-value when comparing the wages of men and women? (Select two.)

Accepted Answer

Proc ttest data=salary;class gender;var pay;run;

Answer

Both `PROC TTEST` and `PROC GLM` (General Linear Model) can be used to compare the means of two groups. `PROC TTEST` is specifically designed for t-tests, directly comparing means between two classes (gender in this case) for a continuous variable (pay). `PROC GLM` is a more general procedure that can perform ANOVA, which for two groups is equivalent to a t-test, allowing comparison of means of 'pay' across 'gender' categories.

Question 5

Which statistic from a validation sample can be used to choose the model to employ for a binary target variable's prediction?

Accepted Answer

Average Squared Error

Answer

For a binary target variable, the Average Squared Error (ASE) on a validation sample is a common and effective metric for model selection. ASE measures the average of the squared differences between the predicted probabilities and the actual binary outcomes (0 or 1). A lower ASE indicates better predictive accuracy, making it a suitable criterion for choosing the best model among candidates, especially when dealing with probabilities.

Business Analysis Practice Test

Business Analysis Practice Test

Business Analysis Statistics Test #1