Question

7. Consider the following pairs of observations. 4 3 5 7 2 6 20 12 10 12 19 7 X 1 Y 3 17 60 a. Calculate the least squares line. b. Determine a 95% confidence interval for the mean value of Y using X-6. Determine a 95% prediction interval for the Y value using X-6.

I keep running into a brick wall on this. I need to show my work and formulas, but got lost. Please help.

Answer 1

a)

(x-x)(y-y 72.5000 11.0000 22.5000 5.5000 1.5000 42.0000 0.0000 595.0000 750.0000 (y-y) (x-x) S.No 1 2 25.0000 4.0000 9.0000 1.0000 1.0000 16.0000 0.0000 196.0000 252.0000 SSX 210.2500 30.2500 56.2500 30.2500 2.2500 110.2500 0.2500 1806.2500 2246.0000 SSY 1 12 10 12 19 4 2 17 20 140 Total Mean 6.0000 17.5000 sample size: here 17.5000 6.0000 from above 252.0000 750.0000 slope- 2.9762 intercept- 0.3571 hence line equation: 0.357 2.976 x

b)

13.8571 S-SSE/(n-2) error variance σ2- 2.310 std error ơ 1.5197 predcited value at X-6 17.500 s*/(1/n+(xo-XYSx.) std error confidence interval- 0.5373 for 95 % Cl value of t= margin of error E-t std error lower confidence bound-sample mean-margin of error- Upper confidence bound-sample mean+margin of error- 2.447 1.3148 16.19 18.81

c)

predcited value at X-6: s*/(1+1/n+(xo-X)ISJ std error prediction interval: 1.6119 for 95 % CI value of t= margin of error E-t std error lower prediction bound-sample mean-margin of error Upper prediction bound-sample mean-margin of error= 2.447 3.9443 13.56 21.44