Simple linear regression results: Dependent Variable: Head Circumference (inches), y Independent Variable: Height (inches), x Head Circumference (inches), y = 12.493169 + 0.18273245 Height (inches), x Sample size: 11 R (correlation coefficient) 0.91107273 R-sq 0.83005352 Estimate of error standard deviation: 0.095384195
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.
A pediatrician wants to determine the relationship that exists between a
child’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares
(a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.
(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
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