For this exercise, round all regression parameters to three decimal places. The table below shows the estimated value C, in dollars, of an 1877 Indian Head Cent (Philadelphia mint mark) in very fine condition t years after 1950. t = time in years since 1950 C = value in dollars 0 25 30 400 45 625 54 1750 60 2000 (a) Use exponential regression to model C as an exponential function of t. C = 32.489 × 1.022t C = 29.490 × 1.076t C = 24.657 × 1.250t C = 18.460 × 0.598t C = 28.981 × 0.268t (b) According to your exponential model, by what percentage does the value of the 1877 cent increase from year to year? (Use the model found in part (a). 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 table below shows the estimated value C, in dollars, of an 1877 Indian Head Cent (Philadelphia mint mark) in very fine condition t years after 1950.
|
t = time in
years since 1950 |
C = value
in dollars |
|---|---|
| 0 | 25 |
| 30 | 400 |
| 45 | 625 |
| 54 | 1750 |
| 60 | 2000 |
(b) According to your exponential model, by what percentage does the value of the 1877 cent increase from year to year? (Use the model found in part (a). Round your answer to one decimal place.)
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