We will use two dimensional scatter plots and three dimensional rotating plots to investigate factors that contribute to taste in Cheddar cheese. The data are courtesy of Statlib at Carnegie Mellon. The data set is described as follows:
Concentrations of the 3 key (as far as flavor goes) ingredients are continuous measurements, and so is the measure of taste. We are interested in understanding the relationship these factors have to taste.
1) Start by producing a scatter plot of 'Taste' (y-axis) against 'Acetic' acid. Cheeses with (higher/lower) levels of acetic acid have higher taste ratings? Is the opposite true, i.e. do higher levels of acetic acid appear to ensure better/worse taste? Describe the relationship between taste rating and acetic acid concentration: is it linear, curvi-linear, increasing, decreasing? Is taste more/less/equally variable for higher levels of acetic acid?
2) Repeat the same questions for plots of 'Taste' against 'H2S'.
3) Repeat the same questions for plots of 'Taste' against 'Lactic'.
4) It seems reasonable to believe that the three ingredients may interact with each other in possibly unpleasant ways. Produce a rotating plot of 'H2S' against 'Acetic' and 'Lactic'. Label points with lower (< 26.5) 'Taste' scores using Edit > Observations > Find, the resulting plot effectively displays 4 dimensions of data! Remove the axes (Axes > Off) and rotate the data. What is the shape of the mass of points (spherical, elliptical, pear, ...)? Are better tasting Cheddars clustered together according to their concentrations of the three chemicals? If so, are there any exceptions to this clustering? If you find exceptions, what are the observation number(s) and taste scores for these observation(s). Situate the axes so the origin is placed at the smallest point (lower left arrow on plot: Axes > At Minima). What concentrations of the three ingredients (high/low/low, etc.) appear to produce the best results?