The head width (in) and weight (lb) is measured for a random sample of 20 bears. The data shows that the mean head width is 6.9 inches, mean weight is 214.3 lb, and the correlation r = 0.879 and its p-value is less than 0.0001. The suggested linear regression equation is WEIGHT = -212 + 61.9 WIDTH. (a) How is the best predicted weight value of a given head width found with this data found? (b) For the preceding part, why? (c) Find the best predicted weight given a bear with a head with of 6.5 inches.
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.
The head width (in) and weight (lb) is measured for a random sample of 20 bears.
The data shows that the mean head width is 6.9 inches, mean weight is 214.3 lb, and the
correlation r = 0.879 and its p-value is less than 0.0001. The suggested linear regression
equation is WEIGHT = -212 + 61.9 WIDTH.
(a) How is the best predicted weight value of a given head width found with this data found?
(b) For the preceding part, why?
(c) Find the best predicted weight given a bear with a head with of 6.5 inches.
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