An individual's adjusted gross income is the amount of income that is subject to federal income tax. The following table shows the total adjusted gross income (AGI), in trillions of dollars, reported to the IRS in the given year. Year 2009 2010 2011 2012 AGI (trillions) 7.6 8.1 8.6 9.1 (a) Show that the data are linear. The difference in the total AGI (in trillions) from 2009 to 2010 is , the difference from 2010 to 2011 is and the difference from 2011 to 2012 is . Because these values are all ---Select--- the same different , the function is linear. (b) Let t denote the time in years since 2009, and let A denote the total adjusted gross income. Find a linear model for A as a function of t. A(t) = (c) Identify the slope of the linear model you found in part (b). trillion dollars per year Explain its meaning in practical terms. The slope is the initial amount, in trillion of dollars, of the AGI.The slope is the number of years it will take the AGI to increase by one trillion dollars. The slope is the total amount, in trillion of dollars, AGI was increasing by each month in this period.The slope is the number of months it will take the AGI to increase by one trillion dollars.The slope is the total amount, in trillion of dollars, AGI was increasing by each year in this period.
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.
An individual's adjusted gross income is the amount of income that is subject to federal income tax. The following table shows the total adjusted gross income (AGI), in trillions of dollars, reported to the IRS in the given year.
| Year | 2009 | 2010 | 2011 | 2012 |
|---|---|---|---|---|
| AGI (trillions) | 7.6 | 8.1 | 8.6 | 9.1 |
(b) Let t denote the time in years since 2009, and let A denote the total adjusted gross income. Find a linear model for A as a function of t.
(c) Identify the slope of the linear model you found in part (b).
trillion dollars per year
Explain its meaning in practical terms.
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