You wish to determine if there is a positive linear correlation between the two variables at a significance level of α=0.005. You have the following bivariate data set. x y 49.7 18.9 51.3 23.6 71.2 46.3 53.5 41 45.6 24
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.
| x | y |
|---|---|
| 49.7 | 18.9 |
| 51.3 | 23.6 |
| 71.2 | 46.3 |
| 53.5 | 41 |
| 45.6 | 24 |
H0:
Hα:
Original claim =
- H₀
- H₁
Note: In your calculations, except for the p-value and the graph, round both r and t to 3 decimal places in ALL calculations. What is the
r =
t=
What is the p-value for this correlation coefficient?
p-value = (Round to four decimal places.)
Critical Value = t(0.995,3)=
Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions.
Decision:
Conclusion:
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Null Hypothesis:
Alternative Hypothesis:
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