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Following the theoretical lecture on meat quality evaluation, we will now show several examples.

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The presentation is part of Module 4: Precision Livestock Farming, which is a part of the ISAGREED project.

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This presentation was supported by the Erasmus+ KA2 Cooperation Partnerships Grant

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"Innovation of the content and structure of study programs in the field

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of management of animal genetic and food resources using digitalization."

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As already mentioned in the theoretical lecture, it is important to determine the fat and muscle content in the carcass.

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Various instrument methods are used for this purpose; injection probes are often used,

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such as the fat o meter, which you can see in the first picture.

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Using this device, the back fat thickness and the Musculus longissimus dorsi muscle thickness

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were determined in 20 pig carcasses.

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At the same time, the lean meat content was determined by dissection of the same carcasses.

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The input data is shown in this table.

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Our task will be to find out whether the back fat thickness and the muscle thickness correlate with the lean meat content and,

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therefore, whether it is possible to use these measured values to predict the lean meat content in the carcass.

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We will solve the task using multivariate correlation and regression analysis.

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In this case, we will choose the lean meat content as the dependent variable;

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the independent variables will be the measured characteristics,

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i.e., the back fat thickness and the muscle thickness.

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Correlation analysis will first allow us to assess the relationship between the dependent and two independent variables.

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The strength of this relationship is given by the correlation coefficient,

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denoted by the lowercase letter r, whose absolute value ranges between 0 and 1.

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The higher the value of the correlation coefficient, the stronger the relationship.

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We say that the variables (or traits) are correlated.

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That means if independent variables change, the dependent variable will change as well.

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Subsequent regression analysis will allow us to mathematically describe the detected relationship.

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Here, we see a regression equation where y is the dependent variable; in our case, the lean meat content,

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x1, x2 are the independent variables, the back fat thickness and the muscle thickness,

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and b1, b2 are regression coefficients, indicating the change in the dependent variable,

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when the independent variable changes by one unit.

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The intercept does not have a direct biological interpretation,

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but it is important for the correct mathematical description of the relationship in the equation.

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We can use, for example, the MS EXCEL for these calculations.

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In the sheet where we have already written down the input data, we choose the option Data,

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then select Data Analysis from the toolbar, choose Regression from the menu, and confirm with the OK button.

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In the following dialog window, we enter the data from which we want to calculate the regression.

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As the input area Y, we choose the column where the values of the dependent variable LMP

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(that is the lean meat content) are listed.

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As the input area X, we select and mark both columns with the values of independent variables

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(that is, the measured values of back fat thickness and muscle thickness).

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After confirming with the OK button, the results will be displayed on the new sheet.

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The high correlation coefficient r = 0.82 indicates a close relationship between the lean meat content

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and both independent variables, back fat thickness and muscle thickness.

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The coefficient of determination shows us the proportion of variability

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of the dependent variable explained by the selected regression model.

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The value of 66% is relatively high and shows that the given model was well designed,

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which is also confirmed by the very low significance value of the F statistic.

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To construct the regression equation, we find in the results the values of the necessary parameters,

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the intercept (61.92), and both regression coefficients

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- for the back fat thickness, the regression coefficient is -0.97 (we insert it into the equation as b1)

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and for the muscle thickness, the regression coefficient is 0. 24 (we insert it into the equation as b2).

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Here we already see the whole assembled equation that tells us that

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Lean meat content equals 61,92 – 0,97*back fat thickness + 0,24*muscle thickness.

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By substituting the measured values of back fat thickness and muscle thickness into the regression equation,

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we can theoretically calculate the estimates of the lean meat content for all 20 cases.

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Here, we see a comparison of the estimate and the exact values of the lean meat content in individual carcasses.

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The last column of the table shows the so-called residuals, or the differences

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between the exact and estimated values of lean meat content.

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Positive values mean that our estimate was slightly lower than the exact measured value,

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and vice versa; negative values indicate an overestimation compared to reality.

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Since we have already verified through the analysis that it is possible to estimate

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the lean meat content with relatively high reliability based on

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the measured back fat thickness and muscle thickness, we can move on to task 2.

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Based on the previous calculation, we have to estimate what the lean meat content will be for a carcass,

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for which the following values were measured:

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Back fat thickness equals 15 mm
Muscle thickness equals 62 mm

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We can calculate the lean meat content by substituting the measured values

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into the regression equation and adding up the value of y.

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A lean meat content of approximately 63 % can be expected on this carcass.

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Finally, we will summarize the content of this presentation.

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The multivariate regression analysis was used to estimate lean meat content.

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Back fat and muscle thickness, which can be measured relatively easily, were considered independent variables.

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The assembled regression model with two independent variables

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allowed a very accurate estimation of lean meat content.

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The correlation coefficient equals 0.82; the coefficient of determination equals 0.67 or 67 %.

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However, since this is a statistical analysis,

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verifying the results on a more significant number of observations would be necessary.

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At this moment I would like to thank you for your attention and if you have any questions, use the e-mail listed here.