Answered: Q 5. In a marketing research study the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

I just want to know the calculations(not using software or ai) for each step to obtain the answers below.

Answers:

(a) SSR(x1) = 1566.45, SSR(x2|x1)=306.25, SSE(x1,x2)= 94.30

d.f= 1, 1, 13

(b) H0: β2=0, Ha:β2=/0

Decision Rule: Reject if F*>9.07, Accept if F*<=9.07

Test statistic is, F= [SSR(x2|x1)/1]/[SSE(x1,x2)/13] = 306.25/1/94.30/13 = 42.219

Comment: conclude Ha.

P-value: 0+

(c)

Yi hat*= 0.89239X1* + 0.39458X2*

Transcribed Image Text:Q 5. In a marketing research study the relation between brand liking (Y) and moisture content (X1) and sweetness (X2) of the product, the following results were obtained, i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Xi1 4 4 4 4 6 6 6 6 8 8 8 8 Xi2 2 4 2 4 2 4 2 4 2 4 2 Yi 64 73 61 76 72 80 71 83 83 89 86 93 10 4 2 4 2 4 88 95 94 100 10 10 10 Assuming a first-order regression model with two predictor variables, Y₁ = ẞ0+ẞ1Xi1+ B2X12 + Ei, Ei ~ N(0, σ²). i = 1, 2, ..., 16 is appropriate. (a) Obtain the analysis of variance table that decomposes the regression sum of squares into extra sum of squares associated with X₁ and with X2, given X1. (b) Test whether X2 can be dropped from the regression model given that X₁ is retained. Use the level of significance 0.01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? (c) Transform the variables by means of the correlation transformation and fit the stan- dardized regression model.

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