[Solved]Given Data Set N Points X1 Y1 X2 Y2 Xn Yn Call Original Dataset Solution Least Squares Q37298644
We are given a data set of n points {(x1,y1),(x2, y2), . . .(xn,yn)}, that we call the original dataset. The solution ofthe least squares regression can be calculated using one of theestimators in Question 1, and it consists of the valuesb0 and b1 in the best fitting line: y =b0 + b1x.
We now apply some transformation to the data. For each answer,make sure you show your calculations and comment on yourobservations.
- In the first case, the values of response variable y aremodified:
z = y + c0
Calculate the new value of slopeb1(1) and interceptb0(1) for the new data set {(x1,z1),(x2, z2), . . .(xn,zn)}, so that we can write the linear regression as z =b (1) 0 + b (1) 1 x. Show that the slope is the same as the slopeobtained from the original dataset, i.e.,b1(1) = b1.
Hint: you shouldexpress the values of b1(1) andb0(1) using one of the estimators fromQuestion 1. We suggest you to use the estimators in Eq. (3).
- Let us now assume that the values of the predictor variable xare modified:
w = c1x + c0.
Calculate the new value of slopeb1(2) and interceptb0(2) for the new data set {(v1,y1),(v2, y2), . . .(vn,yn)}, so that we can write the linear regression as y =b0(2) +b1(2)w, using one of the estimatorsin Question 1. Specify for what values of c0 andc1 we obtain the same slope as in the original dataset,i.e., b1(2) = b1.
estimators of b0 and b1 from Qestion 1referred in this problem:
12 R饱 yi .跑 2 (홈-)-1 ( -) 7n Σ(zi-7)2 1.x : J bi i=1 SD of y where r is the correlation coefficient, defined in your DSC 10 textbook as “the average of the products of the two variables, when both variables are 3 measured in standard units.” Translating the definition of r from words into a mathematical expression gives 8 SD of xSD of y Show transcribed image text 12 R饱 yi .跑 2 (홈-)-1 ( -)
7n Σ(zi-7)2 1.x
: J bi i=1
SD of y where r is the correlation coefficient, defined in your DSC 10 textbook as “the average of the products of the two variables, when both variables are 3 measured in standard units.” Translating the definition of r from words into a mathematical expression gives 8 SD of xSD of y
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Answer to We are given a data set of n points {(x1, y1),(x2, y2), . . .(xn, yn)}, that we call the original dataset. The solution … . . .
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