Keeping water supplies clean requires regular measurement of levels of pollutants. To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water. Nitrates 75 100 125 150 200 500 600 1400 1600 2400 Absorbance 5.1 7 14.4 28.8 44 99.2 150 189.2 202.4 236.4 Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. (a) Find the correlation rr.
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.
Keeping water supplies clean requires regular measurement of levels of pollutants. To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water.
| Nitrates | 75 | 100 | 125 | 150 | 200 | 500 | 600 | 1400 | 1600 | 2400 |
| Absorbance | 5.1 | 7 | 14.4 | 28.8 | 44 | 99.2 | 150 | 189.2 | 202.4 | 236.4 |
Chemical theory says that these data should lie on a straight line. If the
(a) Find the correlation rr.
r =
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