Describe the relationship between the variables in terms of direction, form and strength.
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.
Describe the relationship between the variables in terms of direction, form and strength.
![**Scatterplot Analysis: Winning Times Over the Years**
The scatterplot depicts the trend in "winning time" over the years, with data points represented as blue dots. The x-axis is labeled "year," spanning from 1950 to 2010, and the y-axis is labeled "winning time," ranging from 27 to 29.6.
### Key Features:
- **Trend Line:** A solid line of best fit is included on the plot, indicating a downward trend in winning times over the observed years.
- **Equation:** The equation of the line is given as:
\[
y = 93.7342 - 0.033x
\]
This suggests a negative correlation, where winning time decreases as years increase.
- **Correlation Coefficient (r):** The value is -0.843, indicating a strong negative correlation between year and winning time.
- **Coefficient of Determination (r²):** The value is 0.71, suggesting that about 71% of the variability in winning times can be explained by the year.
This plot effectively visualizes how performance, as indicated by winning times, has improved over the years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd96c8471-e503-4f49-becc-a1612b09a72f%2Fdba919d8-6a4d-40a4-8892-8d75b25ec6dd%2Fb3iw1tf_processed.jpeg&w=3840&q=75)
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