AHIC Regression: Slope and Intercept in Linear Regression

Flashcards cover key concepts: regression purposes, simple linear regression, intercept and slope meanings, OLS fitting, slope/intercept calculation, scatter plots, and interpretation guidelines from the lecture.

What are the three main purposes of regression analysis described in this lecture?

Description (understand relationships between variables), Estimation (estimate a dependent variable from independent variables), and Prediction (predict outcomes from a set of predictors).

What is simple linear regression?

A regression approach focusing on the relationship between a single independent variable x and a single dependent variable y, modeled with a straight line.

In the simple linear regression equation y = a + b*x, what does a represent?

The intercept (y-axis intercept), the value of y when x = 0 (often not meaningful if x cannot be 0).

In the simple linear regression equation y = a + b*x, what does b represent?

The slope (regression coefficient), indicating how much y changes per unit change in x.

From the height-weight example, what does the slope tell us?

For each additional inch of height, weight is expected to increase by 3.43 pounds.

Why might the intercept be not meaningful in the height-weight example?

Because height of 0 inches or negative weight are not realistic; interpretation should focus on the observed data range.

What method is most commonly used to fit a regression line?

Ordinary Least Squares (OLS), which minimizes the sum of squared vertical deviations from the data points to the line.

How is the slope b calculated in ordinary least squares?

b = sum[(xi - xbar)*(yi - ybar)] / sum[(xi - xbar)^2], using the means xbar and y_bar.

How is the intercept a calculated after determining b?

a = ybar - bxbar; substitute into y = a + bx.

What is the purpose of a scatter plot in regression analysis?

To visually inspect whether there is a linear relationship between the independent variable and the dependent variable.

In regression, how are x and y typically designated?

x is the independent variable and y is the dependent variable.

What should you do if the scatter plot does not indicate a linear direction?

Consider not pursuing linear regression or explore non-linear models.

What does the regression coefficient indicate about changes in y?

It indicates how much y changes for a one-unit change in x; interpretation depends on the units of x and y.

What is the objective of ordinary least squares with respect to the distances from data points to the line?

To minimize the sum of squared vertical deviations from the data points to the regression line.

Which reference is cited for simple linear regression in the lecture?

Altman and Krzywinski, Simple Linear Regression, Nat Methods 2015.

What is the equation of the linear regression line and what do y and x denote?

y = a + b*x; y is the dependent variable and x is the independent variable.