A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Lovers 8 3 1 3 6 3 4 8 GPA 2.1 2.7 3.2 2.6 2.8 3.1 2.9 2.2 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are: `H0: ` ? r ρ μ == 0 `Ha:` ? r μ ρ ≠≠ 0 The p-value is: (Round to four decimal places) Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is u
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 study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below.
| Lovers | 8 | 3 | 1 | 3 | 6 | 3 | 4 | 8 |
|---|---|---|---|---|---|---|---|---|
| GPA | 2.1 | 2.7 | 3.2 | 2.6 | 2.8 | 3.1 | 2.9 | 2.2 |
- Find the
correlation coefficient : r=r= Round to 2 decimal places. - The null and alternative hypotheses for correlation are:
`H0: ` ? r ρ μ == 0
`Ha:` ? r μ ρ ≠≠ 0
The p-value is: (Round to four decimal places) - Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
- There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers.
- There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate.
- There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers.
- There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful.
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