Other
SCA I - Assignment
- Course
- Institution
Assignment
[Show more]
Seller
Follow
photophoto
Content preview
Assignment 2: Linear Regression1. Suppose you want to analyze how the production volume affects energy
consumption in a plant. You record daily data for one work week and
observe the following.
Obs. Volume Consumption
1 5 34
2 8 66
3 4 45
4 7 67
5 6 63
You perform a simple linear regression and your estimate for the in-
tercept is 10 and your estimate for the slope is 7.5. (Note: Estimating
a statistical model on such a small data set typically makes no sense.
However, here it allows us to perform the calculations by hand and
makes the concepts palpable.)
(a) Draw a picture including the observations and the regression line
similar to Figure 3.1. Add residuals and variation. (Hint: You
can draw the regression line and the observations with Excel or
Python and then add residuals and variation by hand.)
(b) Calculate the residual sum of squares (RSS), the total sum of
squares (TSS), R2 , and the residual standard error (RSE). Briefly
interpret each measure.
(c) Suppose you would duplicate your data set such that your new
data set contains each observation twice.
i. What would happen to your coefficient estimates?
ii. What would happen to RSS, TSS,R2 , and RSE?
(Hint: No calculations needed.)
2. You perform a multiple linear regression to predict the profit associ-
ated with different products depending on a product’s quality (X1 ),
a dummy variable indicating if a product is on sale with no sale as
baseline (X2 = 1, if it is on sale and X2 = 0 otherwise ), and the
interaction between quality and sale (X3 = X1 · X2 ). The estimated
coefficients are βˆ0 = 10, βˆ1 = 5, βˆ2 = 3, and βˆ3 = −7.
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller photophoto. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.97. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53340 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now