Solutions Statistics

As cheddar cheese matures, a variety of chemical processes take place. The taste of the matured chee

Question: As cheddar cheese matures, a variety of chemical processes take place. The taste of the matured cheese is related to the concentration of several chemicals in the final product. In a study of cheddar cheese, a sample of cheddar cheese was analysed for the levels of concentration of various chemicals, and also subjected to taste tests. The table below gives the results of the taste test and analysis of the concentrations of three chemicals, Acetic acid, H₂S, and Lactic acid. The output given is the result of a regression analysis for the taste as a function of the concentrations of the chemicals. Decide if there is a significant relationship, and if so, what variables are significant predictors? Give all hypotheses, decisions and conclusions. What is the \[{{R}^{2}}\] value, what is it called, and what does it mean?

Taste	Acetic	H₂S	Lactic
12.3	4.543	3.135	0.86
20.9	5.159	5.043	1.53
39.0	5.366	5.438	1.57
47.9	5.759	7.496	1.81
5.6	4.663	3.807	0.99
25.9	5.697	7.601	1.09
37.3	5.892	8.726	1.29
21.9	6.078	7.966	1.78
18.1	4.898	3.850	1.29
21.0	5.242	4.174	1.58
34.9	5.740	6.142	1.68
57.2	6.446	7.908	1.90
0.7	4.477	2.996	1.06
25.9	5.236	4.942	1.30
54.9	6.151	6.752	1.52
40.9	6.365	9.588	1.74
15.9	4.787	3.912	1.16
6.4	5.412	4.700	1.49
18.0	5.247	6.174	1.63
38.9	5.438	9.064	1.99
14.0	4.564	4.949	1.15
15.2	5.298	5.220	1.33
32.0	5.455	9.242	1.44
56.7	5.855	10.199	2.01
16.8	5.366	3.664	1.31
11.6	6.043	3.219	1.46
26.5	6.458	6.962	1.72
0.7	5.328	3.912	1.25
13.4	5.802	6.685	1.08
5.5	6.176	4.787	1.25