L7: multiple regression Flashcards
(22 cards)
a and b (Y=a+bX)
a: intercept, b: slope
population relationship Y = ⍺+βX + ε. ⍺,β,ε?
⍺& β: pop parameters, ε: population error term
(s_e)^2
est variance of pop error ε
s_b
estimate SE of b
p-value
prob of making type 1 error
what value should p be
<5% (prob of wrongly rejecting null less than 5%)
R^2 tells us
goodness of fit; proportion of variation in Y explain by X
R^2 range
0-1
if R^2 close to 0
variables have little-0 explanatory power
calculating elasticities
[change in Y / change in X] [means of X / means of Y]
elasticity of Y w respect to X
b (X bar / Y bar)
adjusted R^2
controls for no. variables in model
r
correlation co-efficient; how related are 2 variables
R^2 in excel
Regression SS / total SS ; or R square output
^(𝐶𝑀𝑅) = 109.4584 - 0.0003GDPpcPPP – 0.8902ELEC. intercept? slope?
intercept (a) = 109.4584, slope b1 = -0.0003, slope b2= -0.8902
what do slopes -0.0003 & -0.8902 tell you in ^(𝐶𝑀𝑅) = 109.4584 - 0.0003GDPpcPPP – 0.8902ELEC
If GDPpcPPP rises by one unit (ie 1 international dollar) then CMR will decrease by 0.0003 deaths per 1000 live births holding ELEC constant
If ELEC rises by one unit (ie 1 percentage point) then CMR will decrease by 0.8902 deaths per 1000 live births holding GDPpcPPP constant
how to test if co-efficients aren’t 0
Ho: β=0 vs Ha: β=/0
* We use a t-test: 𝑡 = 𝑏−β/𝑠𝑏~𝑡(𝑛 − 𝑘 − 1)
P-value on excel;
probability that Ho: β=0 (prob of t1 error) is rejected
if p <0.01 / v small
reject null w high level of confidence
what does H0 imply with R^2 (H0: R^2 = 0)
that X variables do not explain ant variation in Y
testing H0: R^2 = 0 relation to b co-efficient
b coefficients = 0
if H0 is true, 𝑌 = 𝑎 + 𝑏1𝑋1 + 𝑏2𝑋2 + 𝑒 becomes
Y = a + e (mean line)
