Question

An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls. Temperature in degrees Fahrenheit and number of emergency calls are shown.

Temperature (°F)	Number of emergency calls
68	7
74	4
82	8
88	10
93	11
99	9
101	13

a. (9 marks) Compute and interpret the sample correlation coefficient and test the significance of the correlation coefficient at $\alpha$ = 0.05. Discuss your conclusion.

b. (14 marks) Compute the coefficients of regression b₀ ,b₁and test the hypothesis at $\alpha$ = 0.05. Develop the best estimated regression equation to predict the number of emergency calls for the outside temperature of 80 °F . Given S_b0 = 5.331 and S_b1 = 0.06114

c. (2 marks) Do you believe the estimated regression equation would provide a good prediction of the number of emergency calls? Use R² to support your answer and interpret its meaning.

Answer 1

Answer:-

Page one

604.867 82 calculations X: Temperature : Number of emergency Cars X-ž yuy [X-X² (y-7)2 &x-x (4-9) 68 of |-18.429-1857 339.612 8449 34.224 74 4 -12.429 -4.857 154.469 23.592 -4.429 -0.857 1916/2 0.735 3:4796 88 10 1-sol 1.143 2.469 1.306 1•1996 93. 11 6.57 2.143 4.502 14.082 99 9 12.511 0.143 1581041 1.196 rol 13 14:541 4.143 2/2.327 17:163 801367 estal 60s 62 929.714 50.PSY nean 186,429 8.857 43.184 0.020 176.429 a) ben x and y Y 8 = correlation { (x~♡ryný. 51XX)2 564-4)2 176.429 0.8114 929.714 X 50.857 occer 0 past = there is positive, linear correlation between temperature and number of emergency callsi Testing to test Ho: p=0 Wis Hi! Pť test statistic ta r Jn-2 0.811455 3,1041 51-82 F-081142 treitical = tn-2,0)2 = t s, Orosz "(two tailed) = 2.571 feon t table decision: Here to treitical, so we Reject to at 5% L-o.us Conclusion: correlation ceefficient is significent: there is significent relationship between temperature $ number of emergeny calls.

Page two

b) = 0.18977 5:33 compute bo and bi, bj = {(x-7)(49)= 196.43 Elx-72 92girl bo= i - bix= 8.86-(0.18977 X 86.43) = -7.5441 . The best reqression egn is yo 7. 5441 + 0.18979 X if tempes afuse is 800f Cive x =80) then - 29.5441+ 0.18997 (80) 7.6345 peadicted No. of emergency calls is 706378 testing. ;). HO: ⓇOSO nsi Hii po to C eignificant) Cinsignificant] test statistic, ta -7.5447-4156 sbo. treitical = tn 2, alz =ts, 0.05/2 2:57) devision's It < treitical, so we Reject to Conclusion: Bo is not significant Hoibiro Hii Hii Bio test statistic to bi 0.18979 = 3.1039 Sol 0.06114 treiticals tha2, Q12 = 2.54). deusim Here t > treitical, Reject Ho. conclusions seqression coefficient coil is significanti R2-t correlatimes for $114)2 = 0.6584 & There is 65.84% variation in the number of emergency calls that can explained by temperature... 65.84% variation shows in regression model Yes, segrepeion equation peovide good! peedi prediction of the number of د Here emergency calls

Thanks dear student.