Statistics Unit 5

How do you interpret r value?

There is a (w, m, s), (pos, neg), linear relationship between x and y

what is a weak correlation?

less than 0.5

what is a moderate correlation?

0.5 to 0.8

what is a strong correlation?

0.8 to 1

what is a residual?

actual - predicted

extrapolation

using model to make predictions outside range of data

Slope interpretation

On average, for every increase in one x, we predict the y to (inc, dec) by slope units

Y-int interpretation

When x variable is 0, we predict the y variable to be y-int

what point will the LSRL always go through?

x bar, y bar

how can you find b?

b = r(Sy / Sx)

all influential points are outliers…

but NOT all outliers are influential

what is an example of an outlier that is not influential?

an outlier in the same direction of the trend

When a residual plot has a pattern…

a linear model will be a BAD fit

coefficient of determination

R²

percent variation in the y can be explained by linear relationship between y and x

R² formula

R² = 1 - (SSResid / SSTotal)

S_e

measures a typical amount of variability in the vertical distances from the y to the regression line