The population of a country is expected to drop by 30% over the next 50 years as the percent of its citizens that are elderly increases. Projections for the country's population through 2050 are shown in the table. Year, t 2005 2010 2020 2030 2040 2050 Population, P (in millions) 127.8 127.3 124.1 117.6 109.5 100.6 (b) Use the regression feature of a graphing utility to find a linear model for the data. (Round your numerical values to two decimal places.) P = (c) Identify the slope of the model from part (b). (Round your answer to two decimal places.)(d) Use the linear model to predict the population in 2015, 2035, and 2060. (Round your answers to one decimal place.)Are these predictions reasonable?
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.
The population of a country is expected to drop by 30% over the next 50 years as the percent of its citizens that are elderly increases. Projections for the country's population through 2050 are shown in the table.
| Year, t | 2005 | 2010 | 2020 | 2030 | 2040 | 2050 |
|---|---|---|---|---|---|---|
| Population, P (in millions) | 127.8 | 127.3 | 124.1 | 117.6 | 109.5 | 100.6 |
(b) Use the regression feature of a graphing utility to find a linear model for the data. (Round your numerical values to two decimal places.)
(c) Identify the slope of the model from part (b). (Round your answer to two decimal places.)
(d) Use the linear model to predict the population in 2015, 2035, and 2060. (Round your answers to one decimal place.)
Are these predictions reasonable?
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