Consider an experiment in which a medical researcher wants to determine if there
ID: 3180122 • Letter: C
Question
Consider an experiment in which a medical researcher wants to determine if there is a relationship in Y (pulse rate) and X1(cholesterol level), X2(weight), and X3?(age) of an individual.A sample of 50 people is taken and SSE = 25 and SST = 35.
1. First order linear model
df for Error =
df for model =
2. Second order linear model
df for Error =
df for model =
3. Second order linear model with interaction
df for Error =
df for model =
4. For testing the model, what is the correct conclusion?
A. The model is useful.
B. The model is not useful.
C. The result is inconclusive.
D. There is not enough information to draw a conclusion.
Explanation / Answer
Answer:
given sample size n=50
1. First order linear model
Y=b0 + b1*X1 +b2*x2 + b3*x3 +error
df for Error =n-1-k= 50-1-4= 45
df for model =k=4
2. Second order linear model
if we assume, Y=b0 + b1*X1 +b2*x2 + b3*x3 +b1*X1^2 +b2*x2^2 + b3*x3^2 +error
df for Error =49-7=42
df for model =7
3. Second order linear model with interaction
if we assume, Y=b0 + b1*X1 +b2*x2 + b3*x3 +b1*X1^X2 +b2*x2^X3 + b3*x3^X1 +e
df for Error =42
df for model =7
4. For testing the model, what is the correct conclusion?
We need to test for it significant using F-test.
given, SSE = 25 and SST = 35,
so SSR= SST-SSE= 10
If we consider multiple linear regression of 1st order,
we find MSE= SSE/df = 25/45 = 0.556
MSR= SSR/df= 10/4 = 2.5
F-stat= MSR/MSE = 2.5/.556 = 4.505
P-value based on F-table= 0.0038<0.05
reject H0 & conlcude that
Regression is USEFUL!