1. Intro to Stats and Collecting Data
Intro to Stats
3:43 minutesProblem 10.3.3
Textbook Question
Coefficient of Determination Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.394. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?
Verified step by step guidance1
The coefficient of determination, denoted as R², is calculated by squaring the linear correlation coefficient r. The formula is:
Substitute the given value of r (0.394) into the formula:
Simplify the expression by squaring 0.394 to find the value of R².
The coefficient of determination, R², represents the proportion of the variance in the dependent variable (e.g., weight) that is predictable from the independent variable (e.g., height).
In practical terms, the value of R² indicates how well the linear regression model explains the variability of the dependent variable. A higher R² value means a better fit of the model to the data.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coefficient of Determination (R²)
The coefficient of determination, denoted as R², quantifies the proportion of variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 indicates no explanatory power and 1 indicates perfect explanation. In practical terms, a higher R² value suggests a better fit of the model to the data.
Recommended video:
Guided course
05:43
Correlation Coefficient
Linear Correlation Coefficient (r)
The linear correlation coefficient, represented as r, measures the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where values close to 1 indicate a strong positive correlation, values close to -1 indicate a strong negative correlation, and values around 0 suggest no linear correlation. The square of r (r²) is used to calculate the coefficient of determination.
Recommended video:
Guided course
05:43Correlation Coefficient
Practical Interpretation of R²
The practical interpretation of the coefficient of determination (R²) provides insights into how well the independent variable(s) predict the dependent variable. For instance, if R² is 0.155, it indicates that approximately 15.5% of the variance in the dependent variable can be explained by the independent variable. This information is crucial for assessing the effectiveness of the model in real-world applications.
Recommended video:
05:22Combinations
2:13mWatch next
Master Introduction to Statistics Channel with a bite sized video explanation from Patrick
Start learning
