7.1 Introduction to Linear Regression Flashcards
A) What is the purpose of linear regression?
B) What does variation refer to?
A) To explain the variation in a dependent variable in terms of the variation in a single independent variable
B) Variation is the degree to which a variable differs from its mean value
A. What is the dependent variable? B. What are we trying to find out?
C. What is the independent variable?
A. The dependent variable is the variable whose variation is explained by the independent variable
B. We want to answer the question: What explains fluctuations in the dependent variable?
C. The independent variable is the variable used to explain the variation of the dependent variable
What is the sum of the squared errors (SSE)?
The sum of the squared vertical differences between the estimated and actual Y-values
A. What is the regression line?
B. What does it minimise?
A. It is the line that minimises the sum of the squared differences (vertical distances) between the Y-values predicted by the regression line and the actual Y-values.
B. It minimises the SSE
A. What is simple linear regression referred to as?
B. Why?
The ordinary least squares (OLS) method
The values determined by the estimate regression equation are called least squared estimates
What is the slope coefficient?
It describes the change in Y for a one unit change in X
It can be positive or negative
What does the intercept equation highlight?
That the regression line passes through a point with coordinates equal to the mean of the independent and dependent variables
How do you interpret the slope coefficient and the intercept?
A. The slope coefficient is the amount that the dependent variable will change, given a 1% change in the independent variable
B. The intercept is the value of the dependent variable when the independent variable is zero
What are the four assumptions underlying linear regression?
- A linear relationship exists between the independent and dependent variables
- The variance of the residual terms is constant for all observations (homoscedasticity)
- The residual term is independently distributed
- The residual term is normally distributed
What is heteroscedasticity?
Where the variance of the prediction errors is not constant
Why is independence important?
The residual for one observation is not correlated with that of another observation
If X and Y are not independent, the residuals are also not independent, and our estimates of variance and model parameters will be incorrect
Why is it important that the residual term is normally distributed?
When is non-normal acceptable?
What is the impact of outliers?
When the residuals (prediction errors) are normally distributed, we can conduct hypothesis testing to evaluate the goodness of best fit.
Non-normal is acceptable with a large sample size
Outliers will influence our parameter estimates so that the OLS model will not fit the other observations well
What is the formula for variation in Y? (Y = dependent variable)
How is the slope coefficient calculated?
How is the intercept calculated?
What is the simple linear regression model?
What is the linear equation for the line of best fit?
