Question

Creative Confectioners is planning to introduce a new brownie. A small-scale “taste test” was conducted to assess consumers’ preferences (Y) with regard to moisture content (X1) and sweetness (X2). Data from the taste test may be found in the file Dat9-15.xls on your data disk.

a. Prepare a scatter plot of moisture content versus preference. What type of relationship does your plot suggest?

b. Prepare a scatter plot of sweetness versus preference. What type of relationship does your plot suggest?

c. Estimate the parameters for the following regression function:

Ŷi = b0 + b1X1i + b2X12i + b3X2i + b4X22i

What is the estimated regression function?

d. Using the estimated regression function in part c, what is the expected preference rating of a brownie recipe with a moisture content of 7 and a sweetness rating of 9.5?

 

 

Answer 1

Moisture	Sweetness	Preference
2.5	4.0	69
3.0	4.5	73
3.5	5.0	72
4.0	5.5	75
4.5	6.0	74
5.0	6.5	78
5.5	7.0	80
6.0	7.5	81
6.5	8.0	82
7.0	8.5	85
7.5	9.0	88
8.0	9.5	85
8.5	10.0	84
9.0	10.5	81
9.5	11.0	76
10.0	11.5	74

(a)

(b)

 

	Moisture	Mois.^2	Sweetness	Sweet.^2	Preference
	2.5	6.25	4.0	16.0	69		SUMMARY OUTPUT
	3.0	9.00	4.5	20.3	73
	3.5	12.25	5.0	25.0	72		Regression Statistics
	4.0	16.00	5.5	30.3	75		Multiple R	0.893971305
	4.5	20.25	6.0	36.0	74		R Square	0.799184694
	5.0	25.00	6.5	42.3	78		Adjusted R Square	0.726160946
	5.5	30.25	7.0	49.0	80		Standard Error	2.878724434
	6.0	36.00	7.5	56.3	81		Observations	16
	6.5	42.25	8.0	64.0	82
	7.0	49.00	8.5	72.3	85		ANOVA
	7.5	56.25	9.0	81.0	88			df	SS	MS	F	Significance F
	8.0	64.00	9.5	90.3	85		Regression	4	362.779902	90.69497549	10.94417527	0.000789615
	8.5	72.25	10.0	100.0	84		Residual	11	91.15759804	8.287054367
	9.0	81.00	10.5	110.3	81		Total	15	453.9375
	9.5	90.25	11.0	121.0	76
	10.0	100.00	11.5	132.3	74			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
							Intercept	49.3996427	12592855.33	3.92283E-06	0.99999694	-27716652.32	27716751.12	-27716652.32	27716751.12
	7.0	49.00	9.5	90.3	90.962		X Variable 1	13.78883871	7891351.39	1.74734E-06	0.999998637	-17368742.3	17368769.88	-17368742.3	17368769.88
							X Variable 2	-1.477543501	0	65535	0	-1.477543501	-1.477543501	-1.477543501	-1.477543501
							X Variable 3	-4.703331954	8537780.806	-5.50885E-07	0.99999957	-18791543.06	18791533.65	-18791543.06	18791533.65
							X Variable 4	0.688327815	0	65535	0	0.688327815	0.688327815	0.688327815	0.688327815

(c)

 

(d)

90.961