Question

A department store investigated the effects of advertising expenditure on the weekly sales for its men's wear, children's wear, and women's wear departments. Five weeks were randomly selected for each department to be used in the analysis (this makes 15 weeks in total, n). The variables are as follows: y = weekly sales 21 = advertising expenditure 22 = 1 if it is the children's wear department and a 0 otherwise 23 = 1 if it is the women's wear department and a 0 otherwise a) A model with all possible quadratic and interaction terms is fit to the data. Select the appropriate model below that includes all possible quadratic and interaction terms. O ý = Bo + B121 + B222 + B3.13 + B^2} + B5x112 + Box 13 +372112 + B8X123 û = Bo + Bixi + B222 + B323 + B4x7 0 g = Bo + BT + Body + B323 + B4z7+ Ba T2 + B6E723 O ý = Bo + B121 + B222 + B3.13 + B4x3 + Boazx1 + Box 13 +372221 + B82213 b) Fill in the missing entries in the ANOVA table below. Source df S M S Regression 8 3.168 Error 6 9.464 Total 14 c) Is there evidence to support that the model is significant? Test using a = 0.05. 1. H : B =...=Bg vs HQ : At least one B differs from 0. 2. Test statistic: F= 3. Critical value: Fa= 4. Conclusion: Ho (Type either Reject or Fail to reject) There evidence that the part of the model which concerns the departments is significant. (Type either is or is not)

Answer 1

Model with interaction alle possible quadratich term as Toption @ G = BofB, X, FB, 24 e Rudz + B, ah2 + 2+ मनपा & Banaz PM 15 To bull table we find some calculation from lable. Regression df = 8 = 1 100001 1 9is no opasameless sung Square dueto essar a 9.464 the mean sum of square 9,464 essardt MSE z 91469 1.5773 & given that a MSR – 31168 MSE SSR/Rogression at 3,168 115773 ONNI sunto square due to Regression (SSR) 23,168X1.577 & SSR z 8X3,168X1,5773 SSR = 39,9750 total sum of squase = SSRASSE

CONST MSR z total sum of square. - SSR & SSE z SSRt 9.464 x 39,9750 a - 39.9750 9464 = 4.99.60 - 49.4390 Completed. ANOVA tables source of. I ss I MSS 2 Evalue, Regression a 39.9750 14.9968 3,168 Error T6 9,464 1.5773 T Fly G9.439 some bo 22105 no B, zB ₂ - - - B8 @ test Statistics a f = MSR - 3:168 Bolis MSE (²) critical value = 4,1468 Do net Reject no because TE-Calculated fabulated There are insufficient evidence that the part as the model thich concerns the departments is significante