3. Explain how to predict y-values using the equation of a regression line.

Verified step by step guidance

1. Understand that the equation of a regression line is typically written as $y=b0+b1x$, where $b0$ is the y-intercept and $b1$ is the slope of the line.
2. Identify the value of $x$ for which you want to predict the corresponding $y$-value. This $x$ is the independent variable or predictor.
3. Substitute the chosen $x$-value into the regression equation in place of $x$.
4. Perform the arithmetic operations: multiply the slope $b1$ by the $x$-value, then add the y-intercept $b0$ to this product.
5. The result of this calculation gives the predicted $y$-value, which is the estimated value of the dependent variable based on the regression model.

Key Concepts

Regression Line Equation

The regression line equation is typically written as y = mx + b, where y is the predicted value, x is the independent variable, m is the slope, and b is the y-intercept. This equation models the relationship between variables and is used to estimate y for given x values.

Slope and Intercept Interpretation

The slope (m) indicates the rate of change in y for each unit increase in x, showing the strength and direction of the relationship. The intercept (b) represents the predicted value of y when x is zero, providing a starting point for predictions.

Using the Equation for Prediction

To predict y-values, substitute the given x-value into the regression equation and solve for y. This process allows estimation of the dependent variable based on the independent variable, assuming the linear relationship holds.