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Ans Q1:

A) As n is extremely large and n is greater than p inflexible
method will be more preferable and we can apply linear
regression

B) Here n is small and p is extremely large so we should apply flexible
statistical learning method will give better performance than
inflexible method because application of linear regression may not
give us good results here, so applying nonlinear will give better
prediction or inference

C) When relationship of response and predictor is highly nonlinear
inflexible method will decrease bias and increase variance and hens
MSE .application of flexible method will perform well.

D) Here variance is high so we should apply flexible method
because for high flexible approach lead to small variance and
hence small MSE

Ans Q2:

a) This is a classification problem. Here we are interested in
inference.
N=500,p=4
b) Here we are interested in prediction of success or failure of
new product which depends on several factors .this is
regression problem and n=20 and p=13
c) This is regression problem as percent change in US dollar
depend on change in world stock market . here we are
interested in prediction
.n=no of weeks in 2012=52 and p=3

Ans Q3 a)
b)
- As mentioned earlier increase in flexibility(x-axis) lead increase in
bias and decrease in variance which we can see in the graph.
- Bold line represents bias. We can see that bias increases as flexibility
increases.
- Also we can see that variance (light line)decreases as flexibility
increases.
- Dotted line represents plot of training error and flexibility. Here
flexibility increases training error decreases upto a point and then
increases, reason behind this is average sum of square of difference
bias
variance
training error
test error
bayes error
of true and estimated so at some level of flexibility we get best
estimates which shows minimum training error and for other it shows
decrease and increase.
- Big dash line shows curve of bayes error with increase in flexibility.
Bayes error provides lower bound on performance of any model.
Bayes error depends on form of the model and parameters. As
flexibility increases estimated parameters are close to true value and
hence bayes error decreases.
- Small dashed line represents curve of test error with increase in
flexibility. We know that test error is bayes error plus local or
estimation error. Generally quantity to be estimated is different from
estimator and difference between these is called estimation error. We
know that as flexibility increases, closeness of estimates to true value
increases and error decreases. And test error is bayes error plus
estimated error and these both errors decreases with increase in
flexibility and hence test error plot decreases.
Ans Q4:

a) 1.credit car issue: banks gives credits to credit card holder
according to their annual income , how frequently they use
credit card, location or city etc.

goal :how much credit should give to new applicant

response is credit and predictors are annual salary, city in
which he is located, type of job etc..
here we will classify new applicant...