The data set represents several attributes on data breaches across several organizations. It includes 500 observations and 10 variables. The names and descriptions of each variable in the data set is provided below.

- event_ID: used to label each event
- data_type: the type of data breached
- num_people (in millions): the number of people impacted by a data breach, expressed in millions
- num_people_v2: coded version of the variable num_people
- num_records (in millions): the number of records breached, expressed in millions
- per_sensitive: percent of sensitive data breached
- per_sensitive_v2: coded version of the variable per_sensitive
- dys_impact: the length of the negative financial impact from the data breach
- dys_detect: the number of days it takes to detect the breach
- cost_controls (in millions): the amount of money spent on security controls, expressed in millions

1.

Use the best subsets approach to determine which variable(s) would best predict the cost of controls. Please be sure to exclude categorical variables such as event_ID.

**NOTE:** Please note that *predictors* is being used as a placeholder for the actual predictors in your model. In your answer below, make sure you replace all the blanks, such as [1] and [2], with the correct syntax so that the lines of code work. Make sure you also include the variable names of your predictors in place of *predictors*.

bestsubsets = [1]([2]~ *predictors*, data = [3], [4])

[5]([6], [7] = “adjr2”)

2.

The single best **one-variable** model includes which of the following variables?

Group of answer choices data_type

num_people

num_people_v2

num_records

per_sensitive

per_sensitive_v2

dys_impact

dys_detect

3.

The single best **two-variable** model includes which of the following variables?

Group of answer choices data_type

num_people

num_people_v2

num_records

per_sensitive

per_sensitive_v2

dys_impact

dys_detect

4.

The single best **three-variable** model includes which of the following variables?

Group of answer choices data_type

num_people

num_people_v2

num_records

per_sensitive

per_sensitive_v2

dys_impact

dys_detect

5.

The single best **four-variable** model includes which of the following variables?

Group of answer choices data_type

num_people

num_people_v2

num_records

per_sensitive

per_sensitive_v2

dys_impact

dys_detect

6.

Run five separate regression models that represent the five models shown in the best subsets plot in R. Number your models sequentially from Model 1 to 5 based on the number of predictors it includes. Provide the Adjusted R2 values for each of your five models below.

__ Note:__ Please the report the values as displayed in R. Do not round them.

Model 1:

Model 2:

Model 3:

Model 4:

Model 5:

7.

After examining the significance of the predictors in each model and their Adjusted R2, which of the following models provides the best fit for predicting the cost of controls?

Group of answer choices Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

8.

Evaluate Model 5 for multicollinearity and provide the estimates below.

The highest VIF among your predictors is:

The lowest tolerance among your predictors is:

__ Note:__ Please report each of these values as displayed in R. Do not round them.

9.

Based on the results from your calculations for the tolerance, you can conclude that for Model 5 there is:

Group of answer choices a potential concern for multicollinearity.

a serious concern for multicollinearity.

no concern for multicollinearity.

10.

Based on the results from your calculations for the VIF, you can conclude that for Model 5 there is:

Group of answer choices a concern for multicollinearity.

no concern for multicollinearity.

11.

Use R to generate a correlation matrix for the predictors used in Model 5. Based on your results, the strongest correlation can be found between which of the following two predictors?

Group of answer choices num_people

num_records

per_sensitive

dys_impact

dys_detect

cost_controls

12.

The value of the strongest correlation between your predictors is: