age (years) Cumulative percent sexually active 15 16.6 16 28.7 17 47.9 18 64.0 19 77.6 20 83.0 The population of US citizens aged 20-64, in millions, is shown in the table near the top of the next column. a. Find a logistic function that is best fit for the data, with x equal to the number of years after 1940. Report the best model as f(x) with 3 significant digits. c. Use the model to predict the population in 2023. d. What does the model predict will be the maximum number in this population? e. Is it realistic to assume this population will be limited to the number found in part (d) forever, or to assume this model ceases to be valid eventually?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
| age (years) | Cumulative percent sexually active |
| 15 | 16.6 |
| 16 | 28.7 |
| 17 | 47.9 |
| 18 | 64.0 |
| 19 | 77.6 |
| 20 | 83.0 |
The population of US citizens aged 20-64, in millions, is shown in the table near the top of the next column.
a. Find a logistic function that is best fit for the data, with x equal to the number of years after 1940. Report the best model as f(x) with 3 significant digits.
c. Use the model to predict the population in 2023.
d. What does the model predict will be the maximum number in this population?
e. Is it realistic to assume this population will be limited to the number found in part (d) forever, or to assume this model ceases to be valid eventually?
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