Medical professionals need to know the absorption rate of caffeine in the bloodstream. In a study of the relationship between caffeine intake (in milligrams) and absorption (in parts per million) by the bloodstream, scientists computed the regression of caffeine and absorption rate. The 12 volunteers used in the study were given caffeine tablets with as few as 216 mg and as many as 410 mg. Absorption rates ranged from 3600 ppm to 7800 ppm. Some computer output from a regression analysis of these data is shown below. a) What is the equation of the least squares regression line that describes the relationship between caffeine intake and absorption in the bloodstream? Define any variables used in this equation. b) What is the value of the correlation coefficient for caffeine intake and absorption rate? Interpret this correlation. c) Suppose that you want to describe the relationship between caffeine intake and absorption rate only in the range of 250 to 350 milligrams. Does the line shown in the scatterplot still provide the best description of the relationship for the data in this range? Why or why not?
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.
Medical professionals need to know the absorption rate of caffeine in the bloodstream. In a study of the relationship between caffeine intake (in milligrams) and absorption (in parts per million) by the bloodstream, scientists computed the regression of caffeine and absorption rate. The 12 volunteers used in the study were given caffeine tablets with as few as 216 mg and as many as 410 mg. Absorption rates ranged from 3600 ppm to 7800 ppm. Some computer output from a
- a) What is the equation of the least squares regression line that describes the relationship between caffeine intake and absorption in the bloodstream? Define any variables used in this equation.
- b) What is the value of the
correlation coefficient for caffeine intake and absorption rate? Interpret this correlation.
- c) Suppose that you want to describe the relationship between caffeine intake and absorption rate only in the
range of 250 to 350 milligrams. Does the line shown in thescatterplot still provide the best description of the relationship for the data in this range? Why or why not?
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