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.
Using a microscope, a researcher observed and recorded the number of bacteria spores on a large sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she recorded is shown in the table below.
|
Hours (x) |
Average Number of Spores (y) |
|
0 |
4 |
|
0.5 |
10 |
|
1 |
15 |
|
2 |
60 |
|
3 |
260 |
|
4 |
1130 |
|
6 |
16,380 |
Using these data, write an exponential regression equation, rounding all values to the nearest thousandth. a. Using your equation, determine the number of spores, to the nearest integer, after 8 hours.
b. The researcher knows that people are likely to suffer from food-borne illness if the number of spores exceeds 100. Using the exponential regression equation, determine the maximum amount of time, to the nearest tenth of an hour, that the meat can be kept at room temperature.
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