Question
Which two quantitative variables would show that a straight line will be produced on a scatterplot?
Answers
GPT-4o mini
In a scatterplot, a straight line is typically produced when there is a **linear relationship** between two quantitative variables. Specifically, if you have:
1. **Independent Variable (Predictor)**: This is the variable that you manipulate or use to predict another variable. It’s often plotted on the x-axis.
2. **Dependent Variable (Response)**: This is the variable that you measure or observe to see how it changes in response to the independent variable. It’s typically plotted on the y-axis.
Examples of pairs of quantitative variables that can show a straight line in a scatterplot include:
- **Height and Weight**: Assuming a specific population, height could predict weight, showing a linear correlation.
- **Study Hours and Exam Scores**: More study hours may correlate with higher exam scores, demonstrating a linear relationship.
For the scatterplot to exhibit a straight line, the relationship between these variables should be consistent, meaning that as the independent variable increases, the dependent variable typically increases (or decreases) at a constant rate. This results in a linear trend.
1. **Independent Variable (Predictor)**: This is the variable that you manipulate or use to predict another variable. It’s often plotted on the x-axis.
2. **Dependent Variable (Response)**: This is the variable that you measure or observe to see how it changes in response to the independent variable. It’s typically plotted on the y-axis.
Examples of pairs of quantitative variables that can show a straight line in a scatterplot include:
- **Height and Weight**: Assuming a specific population, height could predict weight, showing a linear correlation.
- **Study Hours and Exam Scores**: More study hours may correlate with higher exam scores, demonstrating a linear relationship.
For the scatterplot to exhibit a straight line, the relationship between these variables should be consistent, meaning that as the independent variable increases, the dependent variable typically increases (or decreases) at a constant rate. This results in a linear trend.