Fitted values are values that are predicted or estimated by a statistical model. In other words, fitted values are the predicted values that the model provides for a given set of input data.

One example of fitted values is in regression analysis. For instance, let’s say we are trying to model the relationship between a person’s age and their income. We collect data on a sample of individuals, including their ages and their incomes. We then use a linear regression model to fit a line to the data, which will predict the income of an individual based on their age. The fitted values in this case would be the predicted income for each individual in the sample based on their age.

Another example of fitted values is in time series analysis. For instance, let’s say we are trying to forecast the sales of a particular product over the next year. We collect data on the sales of the product over the past few years, and we use a time series model to fit a curve to the data. The fitted values in this case would be the predicted sales for each time period in the forecast.

In both of these examples, the fitted values are the predicted values that are generated by the statistical model based on the input data. These values can then be used to make predictions or estimates about future values, or to assess the accuracy of the model.

Fitted values are an important concept in statistical modeling, as they provide a way to make predictions or estimates based on a given set of input data. By using a statistical model to fit a line or curve to the data, we can generate fitted values that can help us understand the relationship between the input variables and the output variable, and make more accurate predictions about future values.

In the first example of regression analysis, the fitted values can help us understand the relationship between a person’s age and their income. For instance, we may find that the fitted values show a positive relationship between age and income, such that as a person’s age increases, their income also increases. This information can be useful for making predictions about the income of individuals in the future, or for making decisions about hiring and salary based on an individual’s age.

In the second example of time series analysis, the fitted values can help us understand the relationship between the sales of a product over time. For instance, we may find that the fitted values show a seasonal pattern in the sales, such that the sales are higher during certain times of the year and lower during others. This information can be useful for making predictions about the future sales of the product, or for making decisions about inventory and production based on the forecasted sales.

Overall, fitted values are an important tool for making predictions and estimates based on a given set of input data. By using statistical models to fit a line or curve to the data, we can generate fitted values that can help us understand the relationship between the input variables and the output variable, and make more accurate predictions about future values.