If a set of paired data gives the indication that the regression equation is of the form μY|x = α · βx, it is cus-tomary to estimate α and β by fitting the line log ˆy = log ˆα + x · log βˆ to the points {(xi, log yi);i = 1, 2, ... , n} by the methodof least squares. Use this technique to fit an exponentialcurve of the form ˆy = αˆ · βˆx to the following data on thegrowth of cactus grafts under controlled environmentalconditions: Weeks after Heightgrafting (inches)x y1 2.02 2.44 5.15 7.36 9.48 18.3
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.
If a set of paired data gives the indication that the
regression equation is of the form μY|x = α · βx, it is cus-
tomary to estimate α and β by fitting the line
log ˆy = log ˆα + x · log βˆ
to the points {(xi, log yi);i = 1, 2, ... , n} by the method
of least squares. Use this technique to fit an exponential
curve of the form ˆy = αˆ · βˆx to the following data on the
growth of cactus grafts under controlled environmental
conditions:
Weeks after Height
grafting (inches)
x y
1 2.0
2 2.4
4 5.1
5 7.3
6 9.4
8 18.3
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