The data shown below consists of the price (in dollars) of 7 events at a local venue and the number of people who attended. Determine if there is significant linear correlation between ticket price and number of attendees. Use a significance level of 0.01 and round all values to 4 decimal places. Ticket Price Attendence 6 113 10 196 14 133 18 192 22 113 26 135 30 111 34 133 38 95 42 149
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.
The data shown below consists of the price (in dollars) of 7
| Ticket Price | Attendence |
|---|---|
| 6 | 113 |
| 10 | 196 |
| 14 | 133 |
| 18 | 192 |
| 22 | 113 |
| 26 | 135 |
| 30 | 111 |
| 34 | 133 |
| 38 | 95 |
| 42 | 149 |
Ho: ρ = 0
Ha: ρ ≠ 0
Find the Linear
r =
Find the p-value
p-value =
The p-value is
- Less than (or equal to) αα
- Greater than αα
The p-value leads to a decision to
- Accept Ho
- Reject Ho
- Do Not Reject Ho
The conclusion is
- There is insufficient evidence to make a conclusion about the linear correlation between ticket price and attendance.
- There is a significant linear correlation between ticket price and attendance.
- There is a significant
negative linear correlation between ticket price and attendance. - There is a significant
positive linear correlation between ticket price and attendance.
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