Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=8.2052+0.5693?Y^=8.2052+0.5693X What is the value of ?ˆY^ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. ?ˆ= Interpret the value of ?ˆ. The value of ?ˆ is the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the probability that a crab will be 21.7865 months old. the predicted size of a crab when it is 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months.
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.
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm.
What is the value of ?ˆY^ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places.
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