Week 10 Flashcards
What is a linear relationship?
A relationship between two variables, where increase in one variable is accompanied by a specific increase or decrease in another variable.
What kind of equation would you use to express a linear relationship?
A linear equation.
What formula can express the relationship between X and Y?
Y = bX + a
linear equation
What does b represent in a linear equation?
The slope.
What is slope? (maths)
The slope determines how much the Y variable changes when X is increased by one point.
What does the a represent in a linear equation?
The Y-intercept.
What is the Y-intercept? (maths)
The value of Y when X is zero (where the line on the graph intercepts with the Y-axis).
What is the formula used to find the slope (b)?
b = SP/SSₓ
Sum of products divided by the sum of squared deviations for X
What is the formula used to find the Y-intercept (a)?
a = Mᵧ - b(Mₓ)
Mean of Y scores minus the product of slope times the mean of X scores
What is regression? (statistics)
The statistical technique for finding the best-fitting straight line for a set of data.
What are the two formulas for total squared error/sum of squared residual?
- SSresidual = Σ(Y- ŷ)²
2. SSresidual = (1-r²)SSᵧ
What is the alternative formula for slope (b)?
b = r(sₓ/sᵧ)
What is ŷ?
The predicted value of Y.
What is the formula for the standard error of estimate? (for Y scores)
Standard error of estimate = √SSresidual/(n-2)
What does the standard errors of estimate measure? (Y scores)
The standard distance between the predicted Y values on the regression line and the actual Y values in the data.
