Definitions
Using a regression line for prediction far outside the range of data is called this.
What is extrapolation?
y – ŷ
What is a residual?
Correlation measures the direction and strength of a linear relationship. It is represented by this letter.
What is r?
The regression line helps us predict the value of y as x changes. The formula for this line is this.
ŷ = a + bx
An outlier that greatly affects the slope and y-intercept of a regression line is called this.
What is influential?
A scatterplot that helps us assess how well a regression line fits the data by showing us the deviation above and below zero. It should show no pattern.
What is a residual plot?
r * (Sy/Sx)
What is slope b?
The correlation coefficient is ALWAYS between these two numbers.
What is -1 and 1?
Identify the slope and y-intercept of the following regression line: ŷ = -33.4 + 0.882(x)
What is -33.4 for y-intercept and 0.882 for slope?
This type of graph shows the relationship between two quantitative variables. The explanatory variable is placed on the x-axis and the response variable on the y-axis.
What is a scatterplot?
This type of variable influences the response of another.
What is an explanatory variable?
ȳ - bx̄
What is y-intercept a?
The closer the correlation is to this number, the weaker the relationship.
What is zero?
Find the prediction of y when x = 90 in the regression line:
ŷ = -33.4 + 0.882(x).
What is 45.98?
In addition to outliers, these three things are used to interpret a scatterplot.
What are direction, form, and strength?
This shows us the fraction of the variation accounted for in the least-squares regression line.
What is the coefficient of determination r2?
This is calculated by summing up ZyZX, dividing that sum by (n-1), then taking the square root.
What is correlation?
Correlation is not resistant. Explain what this means.
Correlation r is strongly affected by outliers.
The formula for standard deviation of the residuals mirrors that of normal standard deviation except for this one thing.
It divides the summation by (n-2) instead of (n-1).
SSE and SST are acronyms for these.
What are Sum of Squared Errors and Total Sum of Squares?
The rate at which the predicted response changes as the explanatory variable changes. It can be positive or negative, which shows in the direction of a line.
What is slope?
1 - (SSE/SST)
What is r2?
List the steps for finding r on your TI-83/84 calculators.
After entering L1 and L2, go to STAT menu, arrow over to CALC, choose 8 for LinReg (a+bx).
The goal of the least-squares regression line is to make the sum of these as small as possible.
What are squared residuals?
This variable is directly responsible for the divorce rate in Finland.
What is the consumption of butter? (Obviously, this is a type of _____________ correlation).