(a) Plot the data. (b) Use exponential regression to construct an exponential model for the income data. (Let t be years since 2003 and H be the median household income in thousand of dollars.) H = 62.520 × 0.967t H = 52.587 × 1.035t H = 49.035 × 1.245t H = 57.370 × 1.010t H = 71.932 × 0.856t (c) What was the yearly percentage growth rate in median family income during this period? (Use the model found in part (b). Round your answer to one decimal place.) %
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.
For this exercise, round all regression parameters to three decimal places.
The following table shows the median income, in thousands of dollars, of American families for 2003 through 2008.
| Year | Income (thousands of dollars) |
|---|---|
| 2003 | 52.68 |
| 2004 | 54.06 |
| 2005 | 56.19 |
| 2006 | 58.41 |
| 2007 | 61.36 |
| 2008 | 61.52 |
(a) Plot the data.
(b) Use exponential regression to construct an exponential model for the income data. (Let t be years since 2003 and H be the median household income in thousand of dollars.)
(c) What was the yearly percentage growth rate in median family income during this period? (Use the model found in part (b). Round your answer to one decimal place.)
%
(d) From 2003 through 2008, inflation was about 3% per year. Did median family income keep pace with inflation during this period?
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