4. Exploring Relationships in Data Free Online FlashCards

What distinguishes quantitative from categorical variables?

A quantitative variable records numerical measurements with meaningful, consistent differences; a categorical variable records labels or groupings.

How are variables placed on a scatterplot?

Place the explanatory variable on the horizontal axis and the response variable on the vertical axis; label both axes and include units.

What does the sample correlation coefficient r measure?

The sample correlation coefficient r measures the direction and strength of a linear association between two quantitative variables.

What are the components of ŷ=b₀+b₁x?

In ŷ=b₀+b₁x, ŷ is the predicted response, b₀ is the fitted y-intercept, b₁ is the fitted slope, and x is the explanatory-variable value.

What is extrapolation in regression?

Extrapolation is using a regression model outside the range of x-values used to fit it; such predictions can be misleading because the relationship may change.

What is confounding?

A confounding variable is a third variable that affects both variables and creates or changes their observed association. In the umbrella example, rainy weather is confounding.

How should one quantitative and one categorical variable be compared?

Use side-by-side boxplots, grouped dotplots or histograms, and group means or medians.

What four features describe a scatterplot?

Describe direction, form, strength, and unusual observations such as outliers or influential points.

What is the range and general interpretation of r?

The correlation coefficient must satisfy −1 ≤ r ≤ 1. Values near ±1 indicate strong linear association; values near 0 indicate weak linear association.

What does the coefficient of determination r² represent?

r² is the proportion of response variation accounted for by the linear model in the sample. If r=0.80, then r²=0.64, or about 64%.

How should a regression slope be interpreted?

The slope predicts the average change in y for a one-unit increase in x. In the example, each additional study hour predicts 4.2 more exam-score points on average.

What is a regression residual?

A residual is e=y−ŷ, the observed response minus its predicted value. Positive residuals are above the line; negative residuals are below it.