Question

Question 2

A research firm collected data on a sample of n= 30 drivers to investigate the relationship between the age of a driver and the distance the driver can see. The data is given below:

Age	Distance		Age	Distance
18	510		55	420
20	590		63	350
22	560		65	420
23	510		66	300
23	460		67	410
25	490		68	300
27	560		70	390
28	510		71	320
29	460		72	370
32	410		73	280
37	420		74	420
41	460		75	460
46	450		77	360
49	380		79	310
53	460		82	360

Use SAS to fit a simple linear regression and answer the following questions.

a)  Find the least squares estimate for the regression line Y_i= b₀+ b₁X_i+ e_i.

b) Estimate the standard deviation of the error term e_i

c)   Test the null hypothesis that b₁= 0, using α = 0.05. Is the model useful?

d)   Calculate R²? Explain what this means, and comment on whether or not it suggests the model is good.

e)   Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good.

f)    What would you expect the distance that a 50 year old driver can see to be?

g)   Give a 95% prediction interval for the distance that an individual 50 year old can see.

h)         Give a 95% confidence interval for the mean distance that 50 year olds can see.

Answer 1

Solution . Calculate the table is given question   
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3 023 193 2688 3452 3121 (757682 11389 12258 615 2 2 2 1 3716572 62097 8 9 67210 6293 91823 18188 7 5 5444555 239271 561928788 2 2339 9 2 0122 1 26 229 275 2 y153 75 64 72 87 82 04 1 2 1 1 5 9 04 3 5 8 8 4 1 8 72 64 75 19 45 64 >745 423675271 11618 172 2 2 0362693 654431 112223334456 y 9 2 6 7 7 14572 5 9369511 3321098876 2222211111 555544 260771529 1590 0099 5544 1188 2 4444433333333333 2

Sample size n 3o T423 333 Fsłimated Inex 3.00 68 Sxy Sim 어 Segune due to totul sST- yi-y)2-193666 AG I- 49-76 16 standln EsIimated 어 standard Eht-ton of slope 243

-7.08 Co P-value 0.0000 canty Lou Thru fon We Rject The gicnt Rela honshi befueen dnive oge and distanc coefficient 아 delenMinahon負2 = S28 SST Model -0.8012 x XSsy) belwcen votakleas Values is deses fo ne c (1) Extected distance, funX:50 t=57-18-301 KS‘

ทุ X-50 - 50,5859