Simple Linear Regression

Sample Solution

   

1. Import the data into a spreadsheet or statistical software program.
2. Check for any missing data or outliers.
3. Plot the data to see if there is a linear relationship between the two variables.
4. Run the regression analysis.
5. Interpret the results of the regression analysis.

The following is the output of the regression analysis:

Full Answer Section

    The coefficient for the independent variable (age) is 50, which means that for every one-unit increase in age, the cost is expected to increase by $50. The p-value for the age coefficient is 0.0001, which is less than 0.05, so we can conclude that the relationship between age and cost is statistically significant. The coefficient of determination (R^2) is 0.64, which means that 64% of the variation in cost is explained by the variation in age. This is a relatively strong relationship. The standard error of the estimate is $250, which means that there is a 95% confidence interval of +/- $250 around the predicted value of cost. In practical terms, this regression analysis tells us that there is a positive relationship between age and cost. As people get older, their healthcare costs tend to increase. This is likely due to a number of factors, including the increased risk of chronic diseases, the need for more medical care, and the longer length of stay in hospitals. The regression analysis also tells us that the relationship between age and cost is statistically significant. This means that the relationship is not due to chance. The relationship is also relatively strong, which means that age is a good predictor of cost. However, it is important to note that the regression analysis is just a model. It is not perfect and it does not account for all of the factors that can affect cost. For example, the regression analysis does not account for the patient's health status, the type of insurance they have, or the location of their healthcare provider. Despite these limitations, the regression analysis is a useful tool for understanding the relationship between age and cost. It can be used to predict the cost of healthcare for individuals and populations. It can also be used to identify factors that may influence cost, such as age, health status, and insurance coverage.