You wish to determine if there is a negative linear correlation between the two variables at a significance level of a = 0.005. You have the following bivariate data set. 25.4 8.1 16 38.1 14.5 37.9 29.7 30.2 2.7
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.
Claim : There is a negative linear correlation between the two variables.
Based on the above claim the null and alternative being tested is ,
Null hypotheses , Ho : ρ = 0.
Alternative hypotheses , H1 : ρ < 0.
The directional of this is left tailed test .
Note : left and right tailed tests both comes under one tailed test.
Original claim : H1 .
It is asked to calculate correlation coefficient , r for the given data set.
It can be easily calculated by using MS_EXCEL.
Please refer the following steps.
- Enter your x and y data in excel.
- Use =CORREL ( array 1 , array2 ) function to calculate r.
it will look like ,
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Now hit on enter to get the correlation coefficient (r) and it is equal to -0.79684 till 3 decimal places it would be -0.797.
Thus , the correlation coefficient (r) for this data set is -0.797.
The formula to calculate t score is ,
Note : n is the numbers in your data set (either in x or y) so it is equal to 5.
Thus , t score = 2.286.
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