Question

(1 point) Find the least-squares regression line ý = bp + biz through the points (-2,0),(2,7),(5,13), (8, 18), (11,27), and then use it to find point estimates y corresponding to r = 4 and 3 = 9. For x = 4, y = For x = 9,4 =

Answer 1

Let the regression equation is,

$\therefore \hat{y}=b_{0}+b_{1}x$

The data are given by

(-2,0),(2,7),(5,13),(8,18),(11,27)

х -2 2 у 0 7 13 18 27 65 ху 0 14 65 144 297 5 x^2 4 4 25 64 121 218 8 11 24 Total 520

$\therefore \sum x=24,\sum y=65,\sum xy=520,\sum x^2=218,N=5$

The coefficients of regression equation is given by,

$\therefore b_{0}=\frac{\sum y\sum x^2-\sum x\sum xy}{N\sum x^2-(\sum x)^2}$

1.60 65 x 218 – 24 x 520 5 x 218 – 242

$\therefore b_{0}=3.28793774$

$\therefore b_{1}=\frac{N\sum xy-\sum x\sum y}{N\sum x^2-(\sum x)^2}$

$\therefore b_{1}=\frac{5\times 520-24\times 65}{5\times 218-24^2}$

$\therefore b_{1}=2.0233463$

The regression equation is given by,

$\therefore \hat{y}=3.28793774+2.0233463x$

For x=4 the predicted value of y is given by,

$\therefore \hat{y}=3.28793774+2.0233463\times 4$

$\therefore \hat{y}=11.3813229$

The predicted value of y is 11.3813229

​​​​​​

For x=9 the predicted value of y is,

$\therefore \hat{y}=3.28793774+2.0233463\times 9$

$\therefore \hat{y}=21.4980544$

The predicted value of y is 21.4980544