Question

The AAA Club of a small town Emergency Road Service (ERS) to its members. By tracking the weather conditions the Club can divert resources from other Club activities to the ERS for projected peak days. This will lead to better services for Club members and also greatly reduces stress on the Club staff. So they want to determine if the number of calls the Club will receive in a day is predictable from the weather forecast given on the previous day. A sample gives the following data: Temperature (F: X | 03020 2010 40 Number of Calls: Y1 1167981 We are interested in fitting the following simple linear regression model:X-XB+ ε a) Calculate X'X, (X'X)1 and X'Y and then calculate the least squares estimates of Bo and β b) Calculate the variance-covariance matrix of b, and use it to perform a t-test to test the null hypothesis that p-0. Use a 0.05 Use the matrix approach to calculate the following: c) Calculate a 95% confidence interval for the mean of Y when X= 25. d) Calculate a 95% prediction interval for an individual new value of Y when X= 25.

Answer 1

Solution:

Given that,

Slut en a) Calculation ofx'X also calculation ofLeast S9uare P and um 凵m Sum of ProductS Ć.SP〉=-a20 S P 一0.22 ㄚ ㄧ -0.QQX_t 11-y

b. Variance - covayiance matix of 6 ani nll yPothests Suum D Mean Source D F s2uares sguareseatistic P-Valye Regress ion 48-4 000 8.uooo 201667 o.ouo an d 11 Residua1 betuween y an 9.600D |ヌ·11000 To tal (betideen 5S.oo 6o00 i an lowePPey stand SE t4.6 3 79 그4 | o.ooo Io.ooo61 -o.え2 |u.oug|-4.49 |-o-3rbol_o.o83-o-913ri ㅛ.01090 | 1.0000 3 6 oo 990 7 a g

sum of Lx-x bary. = 1000 s-standard eYoY of regress ion s = 1.55 a, So, 5.9 - a-.18 (o-6785) 4-39 to 7-4, d) 95% Prediction fetenal for an neu value Y h X5: o a ndividva vediction Interval = 거거

Standard erYoY o t On 5.9 +--3.דד 2.13 to 9.6 Than k Ye an lk