Y2, C1 - Regression, Correlation, & Hypothesis Testing Flashcards
What is extrapolation
Making predictions outside of the original data range
What is a regression line
A line of best fit
What is the equation for an exponential line of best fit
y = a * b^x
If y = ab^x, what would the equation of a log graph look like
log y = log a + x log b
Exponential model P = k * b^t
Where x = t and y = log P
Regression line is y = 2 + 0.3x, find k and b
y = 2 + 0.3x
log P = 2 + 0.3t
P = 10^2+0.3t
P = 10^2 * 10^0.3t
P = 100 * 1.995^t
k = 100
b = 1.995
Data coded: y = log t and x = log n
Regression line of y on x is y = -0.301 + 0.6x
Find an equation for t in terms of n in the form t = a * n^k
y = -0.301 + 0.6x
logt = -0.301 + 0.6 logn
logt = -0.301 + logn^0.6
logt - logn^0.6 = -0.301
log(t/n^0.6) = -0.301
t/n^0.6 = 10^-0.301
t = 0.5n^0.6d
What does PMCC stand for
Product Moment Correlation Coefficient
What is the range of values the PMCC can be
-1 <= PMCC <= 1
What is the rule of thumb for strong +ve or strong -ve correlation
r > 0.7
r < -0.7
What type of correlation does the PMCC describe
Linear correlation
What do r and ρ mean in the context of PMCC
r = PMCC of a sample (smaller portion of the whole population)
ρ = PMCC of the whole population
Therefore r is the test statistic, ρ is the population parameter
Example of how the observed PMCC can differ from the true PMCC
Randomly generated numbers would have true PMCC = 0 however observed PMCC would likely be -0.2 < PMCC < 0.2
How do you check the critical values for correlation coefficients?
Check the table in the formula booklet
If I am testing for no correlation with a 10% significance level (two-tailed), what level of PMCC do I look at
5%
0.05
If two things don’t have a significant PMCC value does it definitely mean they don’t have a relationship
NO.
This means they don’t have a linear relationship
They could still have an exponential relationship
