Question

taste	Acetic	H2S	Lactic
12.3	4.543	3.135	0.86
20.9	5.159	5.043	1.53
39	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	3.85	1.29
21	5.242	4.174	1.58
34.9	5.74	6.142	1.68
57.2	6.446	7.908	1.9
0.7	4.477	2.996	1.06
25.9	5.236	4.942	1.3
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	4.7	1.49
18	5.247	6.174	1.63
38.9	5.438	9.064	1.99
14	4.564	4.949	1.15
15.2	5.298	5.22	1.33
32	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

Estimate the equation of the regression line predicting taste score based on all three predictor variables in a single equation.

What taste score would you predict for a cheese whose hydrogen sulfide measurement was 5.0, whose acetic acid measurement was 6.1, and whose lactic acid measurement was 0.90?

What proportion of the variability in taste can be explained by the model using all three predictor variables?

Answer 1

The regression model that we want to estimate is

where is the intercept, are the slope coefficients and is a random error

In Excel, setup the regression using data--->data analysis-->regression

get this

ans: the equation of the regression line predicting taste score based on all three predictor variables in a single equation is

Substituting H2S=5, Acetic=6.1 and Lactic=0.90 in the above equation we get

ans: the predicted taste score would be 10.39

The value of R-square from the output is

This indicates that

ans: 65.18% of the variability in taste can be explained by the model using all three predictor variables.