200 150 100 50 -50 -100 -50 50 100 150 Fitted Value Here are the equation and residuals plot for Model II: log(Brain weight) = 0.3457 + 0.007371 Gestation Residuals Versus the Fitted Values (Response is Log (Brain Weight)) 0.50 0.25 0.00 -0.25 -0.50 -0.75 +, 0.5 1.0 1.5 2.0 2.5 Fitted Value Residual Residual
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.
Researchers measured gestation time (in days) and
brain weight (in grams) for a random sample of
23 unborn infants. They fit two possible regression
models to their data.
Here are the equation and residuals plot for Model I:
Brain weight = -78.46 + 0.9176 GestationWhich of the following conclusions is correct?
a) Model I is appropriate, since the relationship between
gestation time and brain weight is linear except for a
couple of points.
b) Model I is appropriate, since the relationship between
gestation time and brain weight appears to be
stronger.c) Model II is appropriate, since the residuals are
smaller.
d) Model II is appropriate, since the relationship
between gestation time and brain weight appears
to be linear.
e) Model II is appropriate, since the relationship
between gestation time and the logarithm of brain
weight appears to be linear.
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