The U.S. national debt (in billions of dollars) for selected years from 1980 is shown in the following table. Year 1980 1985 1990 1995 2000 2004 Debt 930.2 1945.9 3233.3 4974.0 5674.2 7379.1 (a) Find the least squares regression linear function giving national debt as a function of years since 1980 (x = 0 for 1980). (Round all numerical values to two decimal places.) f(x) = (b) Use the regression line to estimate the national debt in 2005. In 2018. (Round your answers to one decimal place.) 2005 $ billion 2018 $ billion (c) Assume 310 million (0.31 billion) people in the United States in 2018. What is the estimated per capita debt? (Round your answer to the nearest thousand.) $
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 U.S. national debt (in billions of dollars) for selected years from 1980 is shown in the following table. Year 1980 1985 1990 1995 2000 2004 Debt 930.2 1945.9 3233.3 4974.0 5674.2 7379.1 (a) Find the least squares regression linear function giving national debt as a function of years since 1980 (x = 0 for 1980). (Round all numerical values to two decimal places.) f(x) = (b) Use the regression line to estimate the national debt in 2005. In 2018. (Round your answers to one decimal place.) 2005 $ billion 2018 $ billion (c) Assume 310 million (0.31 billion) people in the United States in 2018. What is the estimated per capita debt? (Round your answer to the nearest thousand.) $
The given table is,
| Year | Debt(Y) | |
| 1980 | 930.2 | |
| 1985 | 1945.9 | |
| 1990 | 3233.3 | |
| 1995 | 4974 | |
| 2000 | 5674.2 | |
| 2004 | 7379.1 | |
| Total | 24136.7 |
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