X 7 5 2 8 4 Y 8 8 14 6 12
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 processing line can combine unites of inputs(X) to produce units of output(Y) such that there
is a linear relationship between X and Y. Given the values of X and Y as follow:
X 7 5 2 8 4
Y 8 8 14 6 12
(i) Formulate a simple linear regression equation.
(ii) Determine the value of the
(iii) Find the value of the coefficient of determination and interpret your results.
(iv) What will be the output level if the input is 20?
(v) What proportion of the variation in output is not due to X?
(vi) Using α = 0.01 test whether the correlation between X and Y is
correlated.
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