Week 3 - Correlation and Linear Relationships Vocab

Correlation coefficient r

Strength and direction of a linear relationship

r range

-1 to 1

r close to 1

Strong positive linear relationship

r close to -1

Strong negative linear relationship

r close to 0

Little to no linear relationship

r equals 1

Perfect positive linear relationship

r equals -1

Perfect negative linear relationship

Positive correlation

As x increases y tends to increase

Negative correlation

As x increases y tends to decrease

No linear correlation

No clear straight line pattern

Outlier effect on r

Can significantly distort r

Correlation and causation

Correlation does not imply causation

Correlation

Variables are related

Causation

One variable causes change in another

No correlation

No apparent linear relationship

No correlation and other relationships

A nonlinear relationship may still exist

Quantitative variables

Numerical variables that can be measured or counted

Linear relationship

Relationship with a general straight line pattern

Scatter plot

Shows the relationship between two quantitative variables

Scatter plot point

One x y pair

Horizontal axis

Explanatory variable x

Vertical axis

Response variable y

Explanatory variable

Variable used to explain or predict

Independent variable

x variable

Response variable

Variable being predicted or explained

Dependent variable

y variable

Positive scatter plot

Points rise left to right

Negative scatter plot

Points fall left to right

No linear association graph

Points show no clear upward or downward pattern

Least squares regression line

Line used to predict y from x

Regression equation

y hat = b(0) + b 1x

Predicted value in equation is?

y hat

Observed value

Actual recorded value

Predicted value

Estimated value from the regression equation

y-intercept

b(0)

Meaning of b zero

Predicted y when x equals 0

Slope

b(1)

Meaning of b one

Predicted change in y for each 1 unit increase in x

Positive slope

Predicted y increases as x increases

Negative slope

Predicted y decreases as x increases

Slope of -0.27

y decreases 0.27 units per 1 unit increase in x

Regression prediction

Estimate not certainty

Regression line and means

Always passes through x bar, y bar

Point of means

x bar, y bar

Find predicted value

Substitute x into the equation