Stats Unit 3

How to Describe Scatter Plot Relationship

DUFS + CONTEXT

• Direction/Slope (Positive/Negative/None)

• Unusual features (Outliers or Clusters)

• Form (Linear or Non-Linear)

• Strength (How close to the form)

Explanatory Variable

• Used to predict the Input

  • Like a measurement/unit being tested

  • Ex. One rubber Band

• Always the X axis

Response Variable

• Outcome of study

  • what is being tested

  • Ex. Distance

• Always the Y axis

correlation (r)

• Correlation between 2 quantitative variables

• Measures how close the points follow a line

• Strength of linear relationship

r²

• How much of the variation in the response variable (y) is explained by the linear relationship with the explanatory variable (x)

• Interpretation

  • “The percent of the variation in y explained by the linear relationship with x.”

Residual Measurement

• Difference between Actual and Predicted

• Residual= Actual_y -Predicted_y

Extrapolation

• Use of data and linear regression to find something outside of our data

• Must be Cautious

How to find Linear Regression Equation

• Look at data & Identify Explanatory & Response Variable

• Make Explanatory L1

• Make Response L2

• Use LinReg(a+bx) function

Interpret when x=0

• When x=0, the predicted y context is y-int

Interpret x-context

for each additional x-context, the predicted y context increases/decreases by slope

Residual Plots

• Plots used to plot the residuals of data

  • Plotting difference between actual and predicted of the model

• To determine if Linear model is good fit

• If there is a Curved pattern (U-Shaped) then the linear model is likely not best representation

  • ANY U SHAPE, UPWARDS, DOWNWARDS, SIDEWAYS

• If no pattern & random scatter, then it’s a good model

Least Square Regression Line

• Line that minimizes the sum of the squared residuals

Effect on LSLR when adding Horizontal Outlier

Tilt the Line

• Slope always decreases

  • Farther point → greater decrease

• Y intercept increases

  • Farther distance → Greater increase

• Correlation decreases

  • Farther distance → weaker corelation

Effect on LSR when adding Vertical Outlier

Shift the Line up or down

• Slope Doesn’t Change

• Correlation Decreases

  • Farther Distance → Weaker correlation

• Y intercept varies

  • Higher Up shifts graph up → greater y intercept

  • Lower down shifts graph down → smaller y intercept

High Levarage

• Very large or Very small x-values

Important Liner Regression Formulas

Methods to Graph Data

How to Choose Best Regression Model

1. Check Scatterplot for linear pattern (No pattern, random)

2. Check Residual plot for no leftover pattern

3. Check for r² closest to 1