Correlation + Simple Linear Regression

What does correlation measure?

Strength and direction of a linear relationship between 2 quantitative variables

Range of r?

-1 to 1

r > 0 means?

Positive Linear Relationship

r < 0 means?

Negative Linear Relationship

r = 0 means?

no linear relationship

Does correlation imply causation?

no

Strong correlation range?

Roughly |r| > 0.8

Regression equation

y = b₀ + b₁x

What is the slope?

Predicted change in y for a 1-unit increase in x

What is the intercept?

Predicted y when x = 0.

Interpret slope of 7 in y = -100 + 7x.

For every 1-unit increase in x, predicted y increases by 7.

Interpret intercept of -100 in y = -100 + 7x.

Predicted y is -100 when x = 0

Interpret slope of y in y = -100 + 7x.

For every 1-unit increase in x, predicted y increases by 7.

Interpret intercept of -100 in y = -100 + 7x

Predicted y is -100 when x=0.

What is R²?

Proportion of variability in y explained by the linear relationship with x.

Interpret R² = 0.81.

81% of variability in y is explained by x.

In simple regression, relationship between r and R²?

R² = r²

What does LINE stand for?

• Linear relationship

• Independence

• Normal residuals

• Equal variance

What residual plot pattern suggests nonlinearity?

Curved pattern.

What residual plot pattern suggests unequal variance?

Funnel/tunnel shape

What is extrapolation?

Predicting outside the observed range of x

Why is extrapolation dangerous?

The relationship may not continue outside the observed data