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Healthcare costs in the United States have been increasing over the years. The g data shows the average cost of healthcare per person for selected years from 1986 to ta from CMS.gov website*)

Healthcare costs in the United States have been increasing over the years. The g data shows the average cost of healthcare per person for selected years from 1986 to ta from CMS.gov website*)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Educational Website Transcription for Health Care Project** **Centers for Medicare and Medicaid Services:** https://www.cms.gov/Research-Statistics-Data-and-Systems/Statistics-Trends-and-Reports/NationalHealthExpendData/Downloads/NHE2014.zip --- ### Questions: **d)** Based on the \( R^2 \) values, which function is the best fit? *Answer:* ________________________________________ **e)** Is this function appropriate? Why or why not? *Answer:* ________________________________________ **f)** If another function is a better fit, which function is it? *Answer:* ________________________________________ Why would this be a better fit? *Answer:* ________________________________________ **g)** Using your chosen function, when would you predict health care costs will hit $9500 per person per year? *Answer:* ________________________________________ **h)** What would each of your functions predict that health care costs would be in 2014? *Answer:* - Linear: ________________________ - Quadratic: ________________________ - Cubic: ________________________ - Quartic: ________________________ **i)** In 2014, health care costs were actually $9523 per person per year. In view of this, what could you say about the ability of your chosen function to predict costs into the future? *Answer:* ________________________________________ **j)** Considering \( R^2 \), model validity, and effectiveness, which function would you recommend as the best fit for the data? *Answer:* ________________________________________
Transcribed Image Text:**Educational Website Transcription for Health Care Project** **Centers for Medicare and Medicaid Services:** https://www.cms.gov/Research-Statistics-Data-and-Systems/Statistics-Trends-and-Reports/NationalHealthExpendData/Downloads/NHE2014.zip --- ### Questions: **d)** Based on the \( R^2 \) values, which function is the best fit? *Answer:* ________________________________________ **e)** Is this function appropriate? Why or why not? *Answer:* ________________________________________ **f)** If another function is a better fit, which function is it? *Answer:* ________________________________________ Why would this be a better fit? *Answer:* ________________________________________ **g)** Using your chosen function, when would you predict health care costs will hit $9500 per person per year? *Answer:* ________________________________________ **h)** What would each of your functions predict that health care costs would be in 2014? *Answer:* - Linear: ________________________ - Quadratic: ________________________ - Cubic: ________________________ - Quartic: ________________________ **i)** In 2014, health care costs were actually $9523 per person per year. In view of this, what could you say about the ability of your chosen function to predict costs into the future? *Answer:* ________________________________________ **j)** Considering \( R^2 \), model validity, and effectiveness, which function would you recommend as the best fit for the data? *Answer:* ________________________________________
### Problem: Healthcare Costs over Time in the United States Healthcare costs in the United States have been increasing over the years. The data below shows the average cost of healthcare per person for selected years from 1986 to 2008. The information is sourced from the CMS.gov website. #### Data Table | Year (x) | Average Cost Per Person | |----------|--------------------------| | 1986 | $1947 | | 1990 | $2843 | | 1997 | $4147 | | 2003 | $6099 | | 2008 | $7909 | #### Tasks **a) Plot the Data (Let 1986 be Year 0)** - **Instructions for Plotting:** You are provided with a graph paper image to plot the given data points. Here, the x-axis represents the year (with 1986 as Year 0, 1990 as Year 4, 1997 as Year 11, 2003 as Year 17, and 2008 as Year 22), and the y-axis represents the cost per person in dollars ($). **b) By Observation** - **Question:** Predict what type of model (linear, quadratic, cubic, or quartic) will best fit the data. **c) Using a Graphing Calculator** - **Task:** Find the R² value for each model (linear, quadratic, cubic, or quartic). Use x=0 for 1986 as the base year. #### Graph Explanation - **Axis Labels:** - The x-axis is labeled "Year." - The y-axis is labeled with dollars ($), representing the cost per person. - **Data Points:** - (0, 1947) - (4, 2843) - (11, 4147) - (17, 6099) - (22, 7909) Evaluate the graph for pattern and trend prediction to determine which model best represents the dataset before calculating the R² values. ##### Additional Notes: - Ensure the plotted points are accurate, adhering to the scaling of the axes. - Compare the fit of different models, observing which trendline aligns most closely with the data points to determine the best fit.
Transcribed Image Text:### Problem: Healthcare Costs over Time in the United States Healthcare costs in the United States have been increasing over the years. The data below shows the average cost of healthcare per person for selected years from 1986 to 2008. The information is sourced from the CMS.gov website. #### Data Table | Year (x) | Average Cost Per Person | |----------|--------------------------| | 1986 | $1947 | | 1990 | $2843 | | 1997 | $4147 | | 2003 | $6099 | | 2008 | $7909 | #### Tasks **a) Plot the Data (Let 1986 be Year 0)** - **Instructions for Plotting:** You are provided with a graph paper image to plot the given data points. Here, the x-axis represents the year (with 1986 as Year 0, 1990 as Year 4, 1997 as Year 11, 2003 as Year 17, and 2008 as Year 22), and the y-axis represents the cost per person in dollars ($). **b) By Observation** - **Question:** Predict what type of model (linear, quadratic, cubic, or quartic) will best fit the data. **c) Using a Graphing Calculator** - **Task:** Find the R² value for each model (linear, quadratic, cubic, or quartic). Use x=0 for 1986 as the base year. #### Graph Explanation - **Axis Labels:** - The x-axis is labeled "Year." - The y-axis is labeled with dollars ($), representing the cost per person. - **Data Points:** - (0, 1947) - (4, 2843) - (11, 4147) - (17, 6099) - (22, 7909) Evaluate the graph for pattern and trend prediction to determine which model best represents the dataset before calculating the R² values. ##### Additional Notes: - Ensure the plotted points are accurate, adhering to the scaling of the axes. - Compare the fit of different models, observing which trendline aligns most closely with the data points to determine the best fit.
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