Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 10 13 12.74 6 12 8.14 11 14 7.46 6.77 7.11 7.81 8.84 6.09 5.39 6.43 5.72 9 Click here to view a table of critical values for the correlation coefficient.
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.
#### Part (a): Construct a Scatterplot
Choose the correct graph below to represent the dataset provided above:
##### Scatterplot Options:
- **Option A**
- A scatterplot that shows a non-linear, increasing pattern.
- **Option B**
- A scatterplot that shows a positive linear relationship.
- **Option C**
- A scatterplot that depicts a negative linear relationship.
- **Option D**
- A scatterplot that indicates a quadratic relationship with both increasing and decreasing trends.
**Analysis:**
- Carefully observe the pattern in the scatterplot by plotting each \((x, y)\) pair.
- Recognize the overall trend of the data points to choose the scatterplot that best represents the dataset.
**Selection Criteria:**
- Compare the plotted scatterplot with each of the provided options (A, B, C, and D).
- Determine which scatterplot (A, B, C, or D) visually matches the dataset behavior.
By understanding and visualizing the data through scatterplots, one can determine the nature of the correlation between the variables \(x\) and \(y\) in the dataset. This is crucial for higher-level statistical analysis and interpretation.
For further learning, we encourage using statistical software or graphing tools to create scatterplots and analyze datasets for more hands-on experience.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6eeb107-3976-477c-976e-1778ebbdfd8b%2F37eba190-e60b-4428-a838-b1eef7fa8d1a%2Fd344war_processed.png&w=3840&q=75)
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