Question

1. An equal number of families from eight different cities of various sizes were asked their family incomes and how much ney they spent for food, clothing, and housing per year. The city sizes (x1), average annual family income (2), and average family expenditure (y) are summarized below. (City size in 1000s, family income and expenditure in $100s.) City Size ( 30 50 75 100 150 200 175 120 Income (x2) Expenditure (y):65 77 7980 82 90 84 81 122 230 144 280 278 197 230 190 (a) We first study the relationship between City sizes () and expenditure (y). The following quantities can be easily computed. Σ y-51236; у= 79.75: Σή.-126550: ri = 112.5: Σχι-74445 i. Complete the ANOVA table ModelIANOVA Table SourceDf SS MS F Value P-value Model (1) 4 ( (8) E 2) 73.7253 Tota 003 ii. If model Vi = β0 + β! xi-+티 with 티 ~iid. N(0, σ2) is fit to the data using LS techniques, compute Bo, Bi and their estimated standard errors. iii. Fild the 99% confidence interval for β1 and interpret iv. Given a city that has a population of 100,000 people find the 95% prediction interval for its average family annual expenditure

Answer 1

a) = 355, 5 2530口 the slope the "re?"e%. ion equat ron 04 거 S74 거! 2 4 39 2530 0.1055

nt es cept of the equoion lence,lhe y egr esion uation interval ·Th e 99.1. conf \ dence find SSE -fins t : 从ume So, standard CTy or of esti mata will be n- 3.505 The standard eDYope by

The critical value for 99% confid nee inten ๆ9ゾ ,confiden ce is 3、104. The interval is CO. 0234G0 18 10 54) it show s that We aγe 993 confiden t that tru e siope 'stero li e, in the abov e interv cul The Predicted value for χ,-loo is =') y,= GA. 87754 a, 1055 (100) The citical value A5ence intrvod is 2441, The 95% psc diction interval is. 뀨4275 t2-4-4-7 (3-505) | |t-,+ 25390 구?.4275 ± 912-19 = (C 9.3056, 87-549 4)