The table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States t years after 1900. t = time in yearssince 1900 s = cost ofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 (a) Use exponential regression to model s as an exponential function of t. s = 0.587 × 1.409t s = 0.819 × 1.037t s = 0.669 × 1.022t s = 0.991 × 1.978t s = 1.521 × 0.813t (b) What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. (Use the model found in part (a). The actual cost was 25 cents.)
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 table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States t years after 1900.
|
t = time in years
since 1900 |
s = cost of
stamp |
|---|---|
| 19 | 2 |
| 32 | 3 |
| 58 | 4 |
| 71 | 8 |
| 78 | 15 |
| 85 | 22 |
| 95 | 32 |
| 102 | 37 |
| 109 | 44 |
| 116 | 47 |
(b) What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. (Use the model found in part (a). The actual cost was 25 cents.)
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