R Notebook

Question 7.1

In healthcare analytics, forecasting patient admissions using exponential smoothing is vital for resource planning and staff scheduling.

Situation: Forecasting Patient Admissions

Data Needed:

Historical patient admissions data (daily, weekly, or monthly). Seasonal patterns (e.g., flu season). External factors (e.g., public health alerts). Steps:

Collect and preprocess historical data. Choose the type of exponential smoothing model based on data characteristics. Apply the model to generate forecasts.

Choosing α (alpha):

α closer to 0: Gives more weight to historical data. Suitable if admissions are stable with gradual changes. α closer to 1: Gives more weight to recent observations. Suitable if admissions show significant variability or sudden changes. Expected Value of α:

If admissions data is stable, α would be closer to 0, leveraging historical trends. If data is dynamic, such as during an outbreak, α would be closer to 1 to quickly adapt to recent changes. The choice of α should be based on the data’s characteristics and adjusted through experimentation for accuracy.

Question 7.2

library(dplyr) library(tidyr) library(ggplot2)

temps <-read.table("/Users/micahunderwood/Downloads/week_3_Homework-summer/week 3 data-summer/temps.txt", header = TRUE, sep = "\t")

#convert data to long format

temps_long <- temps %>% pivot_longer(cols = -DAY, names_to = "Year", values_to = "Temperature")

#remove x prefix - this was killing me 

temps_long <- temps_long %>% mutate(Year = as.numeric(gsub("X", "", Year)))

temps_long <- na.omit(temps_long)

#create date column

temps_long <- temps_long %>% mutate(Date = as.Date(paste(Year, DAY, sep = "-"), format = "%Y-%d-%b"))

#aggregate data to weekly

temps_long <- temps_long %>% mutate(Week = format(Date, "%Y-%U")) %>% group_by(Week) %>% summarise(Average_Temperature = mean(Temperature))

#weekly time series

temps_ts <- ts(temps_long$Average_Temperature, start = c(1996, 1), frequency = 52)

#HoltWinters

hw_model <- HoltWinters(temps_ts, seasonal = "multiplicative")

#plot data

plot(hw_model, main = "Exponential Smoothing of Weekly Average High Temperatures (July-October)")

#trend component

trend_component <- hw_model$fitted[, "level"]

#ggplot df

trend_data <- data.frame( Time = time(trend_component), Trend = trend_component )

#plot the shift

ggplot(trend_data, aes(x = Time, y = Trend)) + geom_line() + ggtitle("Trend Component of Weekly Average High Temperatures (July-October)") + xlab("Time") + ylab("Temperature")

#summarize the shift

summary(trend_data$Trend)

Min. 1st Qu. Median Mean 3rd Qu. Max.

59.13 78.21 83.51 84.20 89.56 115.82

#add smoothing line

According to my work, weekly average temperatures would indicate that there most likely is not a significant shift in the end of summer. An uptick in the line would indicate there is.

Question 8.1

In healthcare analytics, a linear regression model is suitable for predicting hospital readmission rates. Reducing readmission rates improves patient outcomes and reduces costs. By identifying key factors, healthcare providers can implement targeted interventions.

Situation: Predicting Hospital Readmission Rates

Predictors:

1. Patient Age: Older patients often have higher readmission rates.

2. Length of Stay (LOS): Longer hospital stays might indicate more severe health issues.

3. Number of Previous Admissions: Frequent hospital visits suggest a higher risk of readmission.

4. Discharge Diagnosis: Certain diagnoses, like heart failure, are linked to higher readmissions.

5. Follow-up Care: Quality of follow-up care can significantly impact readmission rates.

Application:

• Objective: Identify significant predictors of hospital readmissions and quantify their impact.

• Data Collection: Historical data on patient demographics, hospital stays, diagnoses, and follow-up care.

• Model Training: Fit a linear regression model to predict readmission rates.

• Implementation: Identify at-risk patients and develop interventions.

Using linear regression, healthcare providers can proactively reduce readmission risks and improve patient care.

Question 8.2

library(MASS)

data <- read.table("http://www.statsci.org/data/general/uscrime.txt", header=TRUE)

#fit linear model

model <- lm(Crime ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 + Wealth + Ineq + Prob + Time, data=data)

#model summary

summary(model)

new_data <- data.frame( M = 14.0, So = 0, Ed = 10.0, Po1 = 12.0, Po2 = 15.5, LF = 0.640, M.F = 94.0, Pop = 150, NW = 1.1, U1 = 0.120, U2 = 3.6, Wealth = 3200, Ineq = 20.1, Prob = 0.04, Time = 39.0 )

#predict crime rate

predicted_crime <- predict(model, newdata = new_data) predicted_crime

155.4349

Our model has predicted 155 crimes per 100,000 people.

The multiple R-squared value is 0.8031, and the adjusted R-squared value is 0.7078, indicating that about 70.78% of the variability in crime rates can be explained by the predictors we used above.