STAT202 Final

What is F Statistic Explaining

a ratio of explained versus unexplained variance

What results in a large F Statistic

More explained variance compared to unexplained (larger numerator, lesser denominator)

Goal of Anova

determine whether or not the variation in the means is explained versus unexplained

ANOVA Null Framework

μ1= μ2= μ3= μ4

ANOVA Alternate Hypothesis Framework

At least one mean differs

F Statistic Equation

Explained Variance (MSB) / Unexplained Variance (MSE)

What does a rejected null for ANOVA indicate?

At least one mean differs

How can you determine which factor’s means differ in Tukey’s Test?

p<0.05 (alpha)

Nulls for Two Factor ANOVA

H0 (Factor A): A1= A2= A3=A4=A5; H0 (Factor B): B1=B2=B3=B4

How many Test Statistics are Calculated for Two Factor ANOVA

2

ANOVA Interaction Effect Null

H0: All interaction effects are equal to 0

ANOVA Interaction Effect Alternate Hypothesis

H1: Not all interaction effects are equal to 0

What does Linear Regression Test

How one continuous independent variable impacts a continuous dependent variable

Continuous Variables

Quantitative data that can take on any value within a given range, including fractions and decimals (non-negative)

What does the Pearson Correlation Coefficient measure?

The degree of linearity in the relationship between two variables

What are residuals used for?

Estimate the standard deviation between what occurred and what the model predicted would occur

What does R² tell (Coefficient of Determination)

shows the proportion of variation that is explained by regression

Multi- Collinearity

When predictor variables are correlated, this can increase standard error and inflate variance (p value)

How can you identify Multi-Collinearity by comparing R² to Adjusted R²?

If adding a new predictor inflates the p values

Adjusted R²

Adjusts for the number of predictors in a regression model, only increases if a new variable improves the model more than would be expected by chance.

What should be used to identify between two models, which is better at explaining variation?

Adjusted R²

What should variation between residuals of linear regression imitate?

The residuals should form a normal distribution, with more residuals centered around 0, rather than further away.

X axis (horizontal) for Scatterplot of Linear Regression

Independent Variable

In a linear regression model, the independent variable is the

‘predictor’