ŷ = a + bx, where ŷ = predicted y, x = explanatory variable, a = y-intercept, b = slope.

$b = r \frac{s_y}{s_x}$, where r = correlation coefficient, sy = standard deviation of y, sx = standard deviation of x.

a = ȳ - bx̄, where ȳ is the mean of y and x̄ is the mean of x.

$R^2 = \frac{Variance \ of \ y - Sum \ of \ Squared \ Residuals}{Variance \ of \ y}$

$s = \sqrt{\frac{\sum(y - \hat{y})^2}{n-2}}$

The line that minimizes the sum of the squared residuals.

The difference between the observed (actual) y-value and the predicted (ŷ) value.

The predicted change in the response variable (y) for every one-unit increase in the explanatory variable (x).

The predicted value of the response variable (y) when the explanatory variable (x) is zero.

The proportion of the variability in the response variable (y) that is explained by the linear relationship with the explanatory variable (x).

Measures the typical distance of the data points from the LSRL.

Squaring residuals gives more weight to larger errors and prevents positive and negative residuals from canceling each other out, resulting in a more accurate model.

R² = 1 means there is a perfect linear fit; all data points fall exactly on the regression line.

We lose two degrees of freedom when we estimate the slope and the y-intercept.

Providing context ensures that the interpretation is relevant and meaningful within the specific scenario of the problem. It connects the statistical result to the real-world situation.

Computer printouts provide key statistics such as the slope, y-intercept, R-squared, and standard deviation of the residuals, aiding in the interpretation and analysis of the regression model.