You wish to determine if there is a positive linear correlation between the two variables at a significance level of α=0.05 You have the following bivariate data set. x y 38.1 -966.2 51.5 1343.4 50.7 -1155.5 41.9 239.8 34.6 -873.4 56.7 -667.9 22.2 -365.6 42.8 1866.1 17 514.9 19.5 250.7 60.8 1710.9 31 1167.9 37.1 -401.2 52.9 1893.1 49.1 -926.1 52.5 -2174.5 26 75.6 -17.4 330.8 34 2396.9 45.4 -368.1 34.9 -1034.5 31.7 -462.7 24.1 1565 36.5 1284.3 36.7 -1146.6 53.8 -462.3 28.8 2292.3 30.2 1344.7 47.3 1451.7
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.
You wish to determine if there is a positive
| x | y |
|---|---|
| 38.1 | -966.2 |
| 51.5 | 1343.4 |
| 50.7 | -1155.5 |
| 41.9 | 239.8 |
| 34.6 | -873.4 |
| 56.7 | -667.9 |
| 22.2 | -365.6 |
| 42.8 | 1866.1 |
| 17 | 514.9 |
| 19.5 | 250.7 |
| 60.8 | 1710.9 |
| 31 | 1167.9 |
| 37.1 | -401.2 |
| 52.9 | 1893.1 |
| 49.1 | -926.1 |
| 52.5 | -2174.5 |
| 26 | 75.6 |
| -17.4 | 330.8 |
| 34 | 2396.9 |
| 45.4 | -368.1 |
| 34.9 | -1034.5 |
| 31.7 | -462.7 |
| 24.1 | 1565 |
| 36.5 | 1284.3 |
| 36.7 | -1146.6 |
| 53.8 | -462.3 |
| 28.8 | 2292.3 |
| 30.2 | 1344.7 |
| 47.3 | 1451.7 |
What is the
r =
To find the p-value for a correlation coefficient, you need to convert to a t-score: t=√r2(n−2)1−r2 This t-score is from a t-distribution with n–2 degrees of freedom.
What is the p-value for this correlation coefficient?
p-value =
Your final conclusion is that...
- There is insufficient sample evidence to support the claim the there is a
positive correlation between the two variables. - There is sufficient sample evidence to support the claim that there is a statistically significant positive correlation between the two variables.
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