Question

Sts to ind the variable. 10 To determine whether extra personnel are needed for the day, the owners of a water adventure park would like to find a model that would allow them to predict the day's attendance cach morning before opening based on the day of the week and the weather conditions. The model is of the form where: y daily admissions, r, 1 if weekend, 0 otherwise; z = 1 if sunny, 0 if overcast; rs predicted daily high temperature ("C) After collecting 30 days of data, the following least squares model was obtained: y108 +190r, +210r, + 42x The standard errors of the estimated regression coefficients were s.e.(B 37), s.e.(-43) and s.e.(3s 15). The residual sum of squares was SSE 1000 and R-585. (a) Is there evidence to conclude that this model is useful in the prediction of daily attendance (Test Ho : Bm By--0 at level .05) (b) Is there evidence to conclude that mean attendance is higher on sunny days than on overcast days, all else being equal? Use a t-test which compares the 8, to its standard error. Give mull and alternative hypotheses, value of test statistic, p-value and conclusion at level .01. (c) All else being held constant, how much does attendance increase on average if the temperature increases 12"C? (d) Use the regression equation to predict the attendance on an overcast Saturday when the tem- perature is 21 "C (e) Calculate a 99% confidence interval for B 3

Answer 1

we got f value = 8.8 Cortical value of F(8,25) at 5% = 2.76 Since F walue) >> €14,25) all reject the Ho: B-B2 - B2 and conclude that model is useful. (b) Hoo B250 (coefficient has no effects on attendence) using t-test : Hop ₂0 to $2!: 2104S 4.88 54(2) 43 dfam2= 28 .tfcotical value = 1,701 since values t(30) - reject Ho : BE 0 we canctorsed conclude mean attendance is it on sunny days (0) I temperature is increased by 12°C then attendence increase by fortor 12 x 42 = 504 (since Pro 42 ) (d) we have regression tan -108 ti 190k + 2loods + 4243 ich a temperature &2100 on an overlast Saturday ther attendence = -lop + 190 +220 +42X41 yo 1174 cs Scanned with CamScanner

D0.05 ces confidence interval for si lo Bit stresser & critical value) tala (30-2) = 2.048 .: 190 (140 37 x 2.048 ) (190 I 75.78 ) : (1146.2 , 265.78 CSE