Refer back to Example 5.31. Two cars with six-cylinder engines and three with four-cylinder engines are to be driven over a 300-mile course. Let X1, . . . X5 denote the resulting fuel efficiencies (mpg). Consider the linear combination Y = (X1 + X2)/2 - (X3 + X4 + X5)/3 which is a measure of the difference between fourcylinder and six-cylinder vehicles. Compute P(0 <= Y) and P(Y > 2). [Hint: Y 5 a1X1 1 . . . 1 a5X5, with a1 = 1/2 ,…, a5 = -1/3.]
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.
Refer back to Example 5.31. Two cars with six-cylinder
engines and three with four-cylinder engines are to be driven
over a 300-mile course. Let X1, . . . X5 denote the resulting
fuel efficiencies (mpg). Consider the linear combination
Y = (X1 + X2)/2 - (X3 + X4 + X5)/3
which is a measure of the difference between fourcylinder
and six-cylinder vehicles. Compute P(0 <= Y)
and P(Y > 2). [Hint: Y 5 a1X1 1 . . . 1 a5X5, with
a1 = 1/2 ,…, a5 = -1/3.]
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