Linear Regression Hyp testing

Question 1

Normal hypothesis test SLR (5 steps)

Answer 1

1. H0: B1=0 (slope is 0) vs Ha (can be upper, lower or two tailed)
2. define alpha and get crit value t* using table and alpha
3. get test stat with t = b1/SEb1
4. compare t to t* to see if you reject
5. conclusion

Question 2

ANOVA test for SLR (4 things to know)

Answer 2

Note: can only be 2 tail but you dont double bc ANOVA

1. start by filling out the table. Remember that MS = SS/DF. DF1 is always 1, DF2 is always n-2 , and total DF is always n-1 (n-2 +1 = n -1)
2. Also know that SSM/SST = r^2
3. Know that F = t^2

Question 3

Multiple Linear Regression (3 things to know)

Answer 3

1. We have 2 or more X’s (explanatory variables) that are independent.
2. Model becomes y = B0 + B1x1 +B2x2 +B3x3….BiXi + Ei.
3. Confidence intervals are done one line at a time so its the same as SLR, DF = (n - k) where K is the number of variables including y

Question 4

MLR ANOVA

Answer 4

mostly the exact same as with SLR, but DF are different:

DF1 = K-1
DF2 = N -K
DF3 = DF1 +DF2