Business Analysis Statistics Test #2

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?

Accepted Answer

The disparity between medium and high value clients' average purchases varies by area.

Answer

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?

Accepted Answer

A decrease in R-Square

Answer

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.

Accepted Answer

-1.0415

Answer

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?

Accepted Answer

A prediction for an observation that includes the event is higher than for an observation that does not.

Answer

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:

Accepted Answer

An empirical logit trend plot against a predictor variable

Answer

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.

Business Analysis Practice Test

Business Analysis Practice Test

Business Analysis Statistics Test #2