Tree growth A 1996 study examined the growth ofgrapefruit trees in Texas, determining the average trunkDiameter (in inches) for trees of varying Ages: Age (yr) 2 4 6 8 10 12 14 16 18 20Diameter (in.) 2.1 3.9 5.2 6.2 6.9 7.6 8.3 9.1 10.0 11.4 a) Fit a linear model to these data. What concerns do youhave about the model?b) If data had been given for individual trees instead ofaverages, would you expect the fit to be stronger, lessstrong, or about the same? Explain.
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.
Tree growth A 1996 study examined the growth of
grapefruit trees in Texas, determining the average trunk
Diameter (in inches) for trees of varying Ages:
Age (yr) 2 4 6 8 10 12 14 16 18 20
Diameter (in.) 2.1 3.9 5.2 6.2 6.9 7.6 8.3 9.1 10.0 11.4
a) Fit a linear model to these data. What concerns do you
have about the model?
b) If data had been given for individual trees instead of
averages, would you expect the fit to be stronger, less
strong, or about the same? Explain.
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