Line of Best Fit—Regression Line A number of studies have shown lichens (certain plants composed of an alga and a fungus) to be excellent bioindicators of air pollution. The article “The Epiphytic Lichen Hypogymnia Physodes as a Bioindicator of Atmospheric Nitrogen and Sulphur Deposition in Norway” gives the following data X=NO3 in g/m3 Y=lichen (% dry weight) X .05 .10 .11 .12 .31 .37 .42 .58 .68 .68 .73 .85 .92 Y .48 .55 .48 .50 .58 .52 1.02 .86 .86 1.00 .88 1.04 1.70 1. What is the equation of the least squares regression line? 2. What does the y-intercept of the equation represent, in context of this problem? 3. What does the slope of the line represent, in context of this problem? 4. Predict lichen for an NO3 deposition of .5.
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.
DJ #8-1: Calculating a Line of Best Fit and Making a prediction
Line of Best Fit—Regression Line
A number of studies have shown lichens (certain plants composed of an alga and a fungus) to be excellent bioindicators of air pollution. The article “The Epiphytic Lichen Hypogymnia Physodes as a Bioindicator of Atmospheric Nitrogen and Sulphur Deposition in Norway” gives the following data
X=NO3 in g/m3
Y=lichen (% dry weight)
|
X |
.05 |
.10 |
.11 |
.12 |
.31 |
.37 |
.42 |
.58 |
.68 |
.68 |
.73 |
.85 |
.92 |
|
Y |
.48 |
.55 |
.48 |
.50 |
.58 |
.52 |
1.02 |
.86 |
.86 |
1.00 |
.88 |
1.04 |
1.70 |
1. What is the equation of the least squares regression line?
2. What does the y-intercept of the equation represent, in context of this problem?
3. What does the slope of the line represent, in context of this problem?
4. Predict lichen for an NO3 deposition of .5.
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