Exploring Regression and ANOVA

#this post is created as a solution for assignments given on 22/01/2013 in IT & Business Applications Lab, Spring Semester, VGSoM, IIT Kharagpur Class of 2014.

Assignment #1: We believe for one kind of car, groove(Independent Variable) is impacting mileage (Dependent Variable). We have to fit 'lm' and comment on the applicability of 'lm'. 

Solution: 

Steps:

1. Extract the data in a separate .csv file.
2.Assign Groove and Mileage to separate variables and apply Regression on them
3. Find the Residual and draw the Q-Q plot.
Results:


plot(k1,res):

 
Q-Q Norm(res):

 

Q-Q Line(res):

We can see that the generated plot is not scattered enough, so linearity is not applicable in this case.
Assignment #2:
Using data of alpha and pluto, find the following:
1. First find the linear regression:

2.Calculate the residuals:

3.plot(p1,res1):

4. Standard residual:

5.Q-Q Norm(res1):

 6. Q-QLine(res1) :

Assignment #3:
Justify Null Hypothesis using ANOVA:
Answer:

We found from the result that, p=0.687
Using 95% confidence interval, we can see that as p>0.05
So, we can't reject the Null Hypothesis and we accept it.