Conditions
L stands for
Linear. The true relationship between the variables is linear, and the residual plot has no pattern.
Slope Regression Line
A line predicting the approximate relationship between explanatory variable x and response variable y.
Degrees of Freedom
df = n - 2
Mean of Slope
ub = B
Hypotheses
Ho: B = 0 and Ha: B =/= 0, B > 0, or B < 0
I stands for
Independence. Observations are independent (10% population size rule).
Slope Standard Error
A value measuring how much the sample slope is likely to vary from the population slope, part of interval and hypothesis testing.
Residuals
Residual = y - y^
SD of Slope
ob = o / (ox √n)
Area and T-Stat Relationship
invT (area, df) = T-Value
N stands for
Normal. The residual distribution should be normal and show a bell shape if put into a histogram.
Residuals
The difference between the observed and expected value of the response variable, measuring how closely the prediction matches the output.
Pop. Slope Regression
uy = a + Bx
Standard Error of Slope
SEb = s / (sx √n-1)
T-Stat and P-Value Relationship
tcdf(-e99 or t, e99 or t, df) = p-val for one-sided, x2 for two-sided
E stands for
Equal Variances. The residual plot should have random scatter with no fanning or tapering effect.
T-Test Statistic
Measures how many standard deviations away the estimated value of the slope is from the null slope, used for hypothesis testing and intervals
Sample Slope Regression
y^ = a + bx
Slope Independence
#observations < (.1 x total population)
Hypothesis Conclusion
Because the P-val of ___ is >/< ____, we (fail to) reject Ho. There is (not) significant evidence for a (pos/neg) linear relationship between x and y in context.
R stands for
Randomness. The data is derived from a random experiment/selection.
P-Value
A proportion estimating how rare it is to get a sample slope at least as extreme as the one calculated if the null hypothesis is true.
Estimation of Pop. Slope
B = b +/- t * SEb
T-Test Stat from Slope
t = (b-B) / SEb
Interval Conclusion
We are c-lvl% confident that the interval from [lower] to [upper] captures the true slope of the population line between x and y in context.