Background:

The BYU-Idaho Support Center services the students, staff, and community members for their questions and issues via phone calls, live chats, emails, and walk-ins. These interactions are stored in a database called Genesys. Genesys stores information about the interactions such as the agent that handled the interaction, the call duration, the time taken to complete after call work, whether a call was handled or escalated to another office, hold time, and more. For this analysis, a multiple linear regression will be run to test if there is relationship between call duration, hold time, and after call work time. This test will determine if hold time and call duration can predict ACW time.

After call work is the time that is taken for each agent to write a report on their interaction with details such as how the interaction was handled, what issues the customer had, how the issues were resolved, and other information given. Call duration is measured as how long a specific phone call was from a time that the agent answered the call until the call was ended. Total hold time is defined as the amount of time total that the agent put the customer on hold during the call. All of these variable are observed in minutes.

Data:

The data for this analysis was collected using Genesys and exporting the data to an Excel sheet, then imported to R. The data observed are all of the call interactions from June 1 - 30th of 2026, with 10,425 call interactions total. The calls were then filtered to only view call interactions that had hold times, narrowing down the interactions to 4349 calls observed. The data was then filtered down to interactions that had a duration of less than 90 minutes as well as interactions that had ACW that was less than 11 minutes to reduce extreme outliers. After filtering the data in this way, the total interactions observed was 4,316 calls total.

Six Number Summary of Hold Times:

holds1 <- filter(calldata, `Total Hold` > 0)

holds2 <- filter(holds1, `Total ACW` < 11)

holds <- filter(holds2, `Duration` < 90)

 holds %>%
  summarise(
    min  = min(`Total Hold`), 
    Q1   = quantile(`Total Hold`, 0.25), 
    med  = median(`Total Hold`), 
    mean = mean(`Total Hold`, na.rm = TRUE),
    Q3   = quantile(`Total Hold`, 0.75), 
    max  = max(`Total Hold`)
  ) %>% pander()
min Q1 med mean Q3 max
0.00985 0.2425 0.9922 1.426 1.965 27.87

Based on the six number summary, it is interesting to see that the minimum value for total hold time is 0.00985 minutes, meaning that it is possible that the agent could have put the caller on hold on accident. The mean value for hold time is 1.426 minutes.

Six Number Summary of Total Call Times:

 holds %>%
  summarise(
    min  = min(`Duration`), 
    Q1   = quantile(`Duration`, 0.25), 
    med  = median(`Duration`), 
    mean = mean(`Duration`, na.rm = TRUE),
    Q3   = quantile(`Duration`, 0.75), 
    max  = max(`Duration`)
  ) %>% pander()
min Q1 med mean Q3 max
1.013 7.727 11.04 13.31 16.43 86.57

The mean value for total call duration is 13.31 minutes.

Six Number Summary of ACW Times:

 holds %>%
  summarise(
    min  = min(`Total ACW`), 
    Q1   = quantile(`Total ACW`, 0.25), 
    med  = median(`Total ACW`), 
    mean = mean(`Total ACW`, na.rm = TRUE),
    Q3   = quantile(`Total ACW`, 0.75), 
    max  = max(`Total ACW`)
  ) %>% pander()
min Q1 med mean Q3 max
0 0.8242 1.356 1.66 2.12 10.9

For the six number summary for total After Call Work (ACW), the minimum is 0 minutes, meaning that it is possible that the agent submitted the ACW blank on accident, without filling out any notes.

Mathematical Model:

\[ \underbrace{Y_i}_{\text{ACW in min}} = \overbrace{\beta_0}^{\text{y-int}} + \overbrace{\beta_1}^{\text{slope}} \underbrace{X_{1i}}_{\text{Call Duration}} + \overbrace{\beta_2}^{\text{slope}} \underbrace{X_{2i}}_{\text{Total Hold Time}} + \epsilon_i \quad \text{where} \ \epsilon_i \sim N(0, \sigma^2) \ \text{and} \ \alpha = 0.05 \]

Hypotheses:

For the multiple linear regression, hypotheses are as follows:

1. Overall Model

Null Hypothesis:

Does call duration and/or hold time predict ACW time?

\[ H_0: \beta_1 = \beta_2 = 0 \]

Neither variable, call duration nor hold time, can predict ACW time.

Alternative Hypothesis:

\[ H_a: \beta_1 \neq 0 \text{ or } \beta_2 \neq 0 \]

At least one of the variables (call duration or hold time) can help predict ACW.

2. Call Duration

Null Hypothesis:

\[ H_0: \beta_1 = 0 \]

The call duration does not change ACW.

Alternative Hypothesis:

\[ H_a: \beta_1 \neq 0 \]

The call duration does change ACW.

3. Total Hold Time

Null Hypothesis:

\[ H_0: \beta_2 = 0 \]

The amount of total hold time does not change the ACW.

Alternative Hypothesis:

\[ H_a: \beta_2 \neq 0 \]

The amount of total hold time does change the ACW.

Analysis:

As previously mentioned, for this analysis, a multiple linear regression will be preformed on the data from the BYU-I Support Center. Before the analysis is preformed, assumptions were tested to ensure that a multiple linear regression model was appropriate for the data set.

Assumption Checking:

model <- lm(`Total ACW` ~ `Duration` + `Total Hold`, data=holds)
par(mfrow=c(1,3))
plot(model, which=1:2)
plot(model$residuals, col="hotpink", pch=19)

A Residuals vs. Fitted plot was created to check the assumption that there needs to be constant variance in the data set. There is no funnel shape in the data, meaning that the regression could be well presented as valid and useful for prediction ACW time.

A Q-Q Plot was created to evaluate the normality of error within the data set. There is a small upward pull away from dotted line, hinting that the data might be slightly right skewed. This can be explained because the data is measured in minutes, with numbers that are larger being less represented than numbers that are smaller.

An Index Plot was created to confirm that there are no extreme outliers in the data set and they have been removed through the filtering of the data that was previously done.

Multiple Linear Regression:

model <- lm(`Total ACW` ~ `Duration` + `Total Hold`, data=holds)

pander(model)
Fitting linear model: Total ACW ~ Duration + Total Hold
  Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.102 0.03419 32.23 2.376e-204
Duration 0.0347 0.002295 15.12 2.423e-50
Total Hold 0.06739 0.0121 5.569 2.722e-08

For the testing overall model, the p-value is 2.2e-16, which is less than the alpha level of 0.05, so the null hypothesis can be rejected. This means that call duration or hold time could be useful with predicting ACW time.

For testing to see if duration can be useful to predict ACW, the p-value is 2e-16, less than the alpha level of 0.05, so the null hypothesis can be rejected. This means that the duration could be useful with predicting ACW time.

For testing to see if hold time can be useful to predict ACW, the p-value is 2.72e-08, less than the alpha level of 0.05, so the null hypothesis can be rejected. This means that the hold time could be useful with predicting ACW time.

The Adjusted R-squared value is 0.08019, meaning that the model only explained 8.02% of the variance in the total ACW. This means that there could be other factors that explain ACW time, such as certain agents that take longer to fill out their after call work, time of day, call volumes, and other variables.

Graphics:

ggplot(data = holds, aes(x = Duration, y = `Total ACW`)) +
  geom_point(alpha = 0.3, color = "steelblue") +
  geom_smooth(method = "lm", color = "hotpink", se = TRUE) + 
  theme_minimal() +
  labs(title = "Impact of Call Duration", x = "Duration", y = "Total ACW")

ggplot(data = holds, aes(x = `Total Hold`, y = `Total ACW`)) +
  geom_point(alpha = 0.3, color = "midnightblue") +
  geom_smooth(method = "lm", color = "magenta", se = TRUE) + 
  theme_minimal() +
  labs(title = "Impact of Hold Time", x = "Total Hold", y = "Total ACW")

Interpretation:

Based on the overall model F-test (\(p\)-value \(= 2.2 \times 10^{-16}\), which is less than the significance level of \(\alpha = 0.05\)), we conclude that a statistically significant relationship exists between the predictors and After Call Work (ACW) time. This confirms the visual pattern observed in the scatterplots: as total hold time or call duration increases, ACW time tends to increase as well.

For the individual predictors of call duration and total hold time (\(p\)-values of \(< 2 \times 10^{-16}\) and \(2.72 \times 10^{-8}\), respectively), we reject the null hypotheses and conclude that both variables have a statistically significant, positive relationship with ACW. The data shows right-skewness, as typical calls range between 1 to 17 minutes, though extreme cases lasted up to 90 minutes.

Despite this statistical significance, call duration and hold time together explain only 8.02% of the variation in ACW time (Adjusted \(R^2 = 0.0802\)). Even though a positive relationship exists, these variables alone are poor predictors of how long an agent will spend on ACW. This indicates that other external variables play a key role in determining an agent’s after-call work time.