Overview
This lecture explains how to use square footage to predict monthly rent for apartments in Queens, NY, using linear regression analysis.
Identifying Variables
- The X variable (explanatory) is square footage.
- The Y variable (response) is monthly rent.
- X is what you use to predict; Y is what you want to predict.
Creating a Scatter Plot
- Square footage is plotted on the X-axis; monthly rent on the Y-axis.
- The scatter plot appears linear, suggesting a linear relationship.
Calculating the Correlation Coefficient (r)
- Enter square footage data in List 1 and rent in List 2 on your calculator.
- Use the calculator's LinReg(a+bx) function under Stat > Calc > Option 8.
- The calculated r value is 0.909, indicating a strong positive linear relationship.
Regression Equation & Prediction
- LinReg(a+bx) provides the regression equation: y = -34.31 + 2.21x.
- This equation fits the data points well and can be used for predictions.
- To predict rent for a 995 sq ft apartment, plug 995 into the equation: y = -34.31 + 2.21(995) = $2164.64.
Key Terms & Definitions
- Explanatory Variable (X) — the input variable used to make predictions (here, square footage).
- Response Variable (Y) — the outcome you want to predict (here, monthly rent).
- Scatter Plot — graph showing relationship between two variables.
- Correlation Coefficient (r) — measures strength and direction of linear relationship between variables.
- Linear Regression — statistical method to model and predict the relationship between two variables.
- Regression Equation — formula predicting Y from X; here, y = -34.31 + 2.21x.
Action Items / Next Steps
- Complete the calculation for predicted rent with other square footage values.
- Review calculator functions: entering data, creating scatter plots, performing linear regression.
- Practice identifying X and Y variables in other prediction problems.