Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 9 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x(b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal).ŷ =  +  x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? YesNo     (d) Solve your answer from part (a) for x (rounded to three digits after the decimal).x =  +  y Do you get the least-squares equation of part (b) with the symbols x and yexchanged? YesNo     (e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d). In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.

Question

Suppose you are given the following (xy) data pairs.

x 1 2 6
y 4 3 9

Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ =  +  x

(b) Now suppose you are given these (xy) data pairs.

x 4 3 9
y 1 2 6

Find the least-squares equation for these data (rounded to three digits after the decimal).
ŷ =  +  x 

(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?

YesNo    


(d) Solve your answer from part (a) for x (rounded to three digits after the decimal).
x =  +  y 

Do you get the least-squares equation of part (b) with the symbols x and yexchanged?

YesNo    


(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (xy). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (yx), (with x and y exchanged)? Explain using parts (a) through (d).

In general, switching x and y values produces the same least-squares equation.Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.    In general, switching x and y values produces a different least-squares equation.

Expert Answer

Want to see the step-by-step answer?

See Answer

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Answer
*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.

Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Recall that we say that a random variable X is in the vector space L^2 if it has finite second momen...

A: Properties of a norm:In order to prove that ||X||2 = √E(X2) is a norm, it must satisfy 3 conditions:...

Q: how many four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is al...

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be...

Q: Let A = {4, 6}, B = {6, 11, 23}, D = {35} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.a) {4, ...

A: Given information:The given events are as follows:A = { 4, 6 }, B = { 6, 11, 23 }, D = { 35 } and th...

Q: I asked this question (If X(n,p) is a binomial random variable with parameters n and p, then why is ...

A:  Here X(n,p) and X(n+1p) are not increasing functions. A binomial function X(n,p) increases when (n+...

Q: Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance com...

A: Given data of 16 claims in percentage of wheat loss to hail  in country.X- represent % of wheat crop...

Q: Now you will compute some probabilities of events that are unions of intervals inside the sample spa...

A: The sample space associated with the Ω=[8,87] is: 

Q: Assume that E and F are independent events.  If PR (E) = 0.7 and Pr (F|E) = 0.6, find Pr(F)

A: Independent events:Two or more events are said to be independent if occurrence of one does not affec...

Q: Approximately 1 in 500 African Americans has sickle cell anemia (National Center for Biotechnology I...

A: Explanation:It is given that 1 in 500 African Americans has sickle cell anemia. Thus, it can be said...

Q: For the experiment of drawing a single card from a standard​ 52-card deck, find ​(a) the probability...

A: Part (a):A standard deck of 52 cards has 4 suits of 13 cards each. In each of the four suits (diamon...