(Medicare). The annual expenditures for Medicare (in billions of dollars) by the US Government for selected years since 1980 are shown in Table 4. Let x represent the years since 1980. (Use 4 decimal places in all answers.) Table 4: Medicare Expenditures Year Billion $ 1980 37 1985 72 1990 111 1995 181 2000 197 2005 330
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.
(Medicare). The annual expenditures for Medicare (in billions of dollars) by the US Government for selected years since 1980 are shown in Table 4. Let x represent the years since 1980. (Use 4 decimal places in all answers.)
Table 4: Medicare Expenditures
| Year | Billion $ |
| 1980 | 37 |
| 1985 | 72 |
| 1990 | 111 |
| 1995 | 181 |
| 2000 | 197 |
| 2005 | 330 |
A. Find the exponential regression model for the data.
M(x) =
B. What is the r2 value for this model?
r2 =
C. Extimate (to the nearest billion) the expenditures in 2008?
The Medicare expenditures in 2008 were about $
billion.
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