Regression

REGRESSION, quantitative changes in one phenomenon occurring in connection with changes in another phenomenon that is in a correlational relationship with the first. Thus, successive changes in weight in individual parts of a collective that is homogeneous in its basic characteristics (by age, sex, social status, etc.) in connection with successive changes in height in the corresponding parts of it represent the regression of weight by height. The inverse changes are the regression of height by weight. The degree of change (the magnitude of regression) is determined by the regression coefficient: R_x = r * (σ_x / σ_y) and R_y = r * (σ_y / σ_x). In both expressions: r is the correlation coefficient of the studied variation series (see Correlation), and σ_x and σ_y are the standard deviations of the same series (see Variation Statistics). Thus, if the correlation coefficient between height and weight for a certain group of persons is equal to +0.5384, the standard deviation (σ_x) of the variation series representing the height of the same group is equal to 6.7272 cm, and the standard deviation (σ_y) of the weight series is equal to 8.2143 kg, then the regression coefficient of height by weight is equal to: 0.5384 * (6.7272 / 8.2143) = +0.4409 cm, and the regression coefficient of weight by height is equal to: 0.5384 * (8.2143 / 6.7272) = +0.6574 kg. The first number shows that an increase in weight of 1 kg is associated with an increase in height of approximately 0.5 cm; the second number indicates that an increase in height of 1 cm is associated with an increase in weight of 0.66 kg. It should be especially emphasized that when determining the regression coefficient, each standard deviation is taken in its absolute expression (taking into account the size of the intervals of the corresponding variation series).

In addition to the indicated application in the analysis of phenomena, the regression coefficient is very useful in some cases for finding the theoretical values of one of the phenomena depending on changes in the other. For this purpose, equations of the following form are used: X_x = M_x + R_x(Y_x - M_y) and Y_x = M_y + R_y(X_x - M_x). In the first equation, X_x is the sought value of one of the phenomena at a corresponding given value of the second phenomenon (Y_x) and at the arithmetic means M_x and M_y of both studied variation series. The sought value in the second equation is the value of the second phenomenon Y_x at a given size of the first phenomenon (X_x) and at the same arithmetic means. Substituting instead of the algebraic expressions the values corresponding to the above example about height and weight: M_x = 65.65 kg, M_y = 175.32 cm, R_x = +0.6574 kg, and R_y = +0.4409 cm, we will have: X_x = 65.65 + 0.6574 * (Y_x - 175.32) and Y_x = 175.32 + 0.4409 * (X_x - 65.65), whence: X_x = -49.61 + 0.6574 * Y_x and Y_x = 146.13 + 0.4409 * X_x.

If some given values of height (Y₁ = 157.5, Y₂ = 163.5, Y₃ = 169.5, etc.) are substituted into the first equation, we will obtain the following theoretical values of weight: X₁ = 53.9, X₂ = 57.8, X₃ = 61.8, etc. Substituting the given values of weight (X₁ = 48, X₂ = 57, X₃ = 66, etc.) into the second equation, we will obtain the following theoretical values of height: Y₁ = 167.3, Y₂ = 171.3, Y₃ = 175.2, etc. The presented relationships in the sizes of height and weight (and vice versa) should have been observed in the studied mass of persons if the existing dependence between both phenomena were not disturbed by extraneous circumstances.

The geometric mean of both regression coefficients is equal to the correlation coefficient: r = √(R_x * R_y). The standard error of the regression coefficient is equal to m_Rx = m_r * (σ_x / σ_y) and m_Ry = m_r * (σ_y / σ_x), where m_r is the standard error of the correlation coefficient.

P. Kuvshinnikov. REGULATION (of functions), the ability of an organism to change functions in the form of adapting them to definitely changed conditions. The result of such a change in functions is the maintenance of the basic vital activities of the organism at the level necessary for its existence. This special property of organisms to change functions in the presence of altered conditions of existence should be understood not as the exhaustion of the entire reactive capacity of organisms, but as a change in the direction of increasing or decreasing functions, and consequently, reactive capacity under the influence of various kinds of stimuli. Regulation is thus connected with such a state of the organism which is characterized primarily by the preservation of basic functions, allowing the organism to exist without damage. Understanding regulation in this way, one should distinguish between physiological and pathological regulation. In the first case, it is a matter of adaptation to ordinary conditions, and in the second, to special conditions that go beyond the limits of physiological fluctuations. Examples of physiological regulation include fluctuations in the lumen of peripheral vessels under the influence of thermal conditions, which protect the organism from both cooling and overheating. Also included here are: working hypertrophy of skeletal muscles in individuals engaged in physical labor or sports, increased blood flow to working organs, carried out by way of local acidosis as a result of the organ's activity, temporary changes in respiratory and circulatory functions during the transition of an individual from a state of rest to movement, increased secretory activity of glands under the influence of various kinds of stimuli, differences in the secretion of digestive enzymes depending on the type of food, and much more. All functions of the organism are subject to physiological regulation, and the latter occurs constantly and perfectly, since under ordinary conditions it is a matter of accommodation to such fluctuations in the influences of the external and internal environment to which the organism is already phylogenetically adapted. The presence of pathological conditions places regulation in special conditions, mainly in the form of a change in the reactive sensitivity of tissues to ordinary stimuli. As examples of pathological regulation, one could point to the fact of a sharp increase in intracardiac pressure in the cavity of the right ventricle of the heart, signifying a significant increase in the work of the latter in an experiment with artificial gradual narrowing of the lumen of the pulmonary artery, or a change in the frequency and magnitude of respiratory excursions in an experiment with artificial pneumothorax, with the replacement of negative pressure in the pleural cavity with positive, or finally, a similar change in respiratory function during artificial restriction of air access to the trachea. In all three mentioned cases, the conditions are unusual and go beyond the limits of physiological fluctuations; nevertheless, thanks to pathological regulation, the affected basic functions of the organism remain at their previous level for a certain time and up to certain limits: in the first experiment, thanks to the increased work of the right ventricle, the heart manages to push the necessary amount of blood through the narrowed opening per unit of time, and gas exchange in the latter two experiments does not decrease. Pathological regulation differs from physiological, therefore, only in the unusual nature of the conditions of its occurrence, often in the degree of its manifestation, and sometimes in a qualitative change in functions, but in any case, no new functions arise as a result. Thus, the heart, adapting in both physiological and pathological conditions, is capable of producing only one effect—contraction—but the strength and character of the latter are different in different conditions. Similarly, the function of the kidneys in physiological and pathological regulation always remains the same—excretory—but this function changes strongly in terms of the quantity and quality of products removed from the organism. The significance of regulation for the organism is self-evident, just as there is no need to explain the fact that, despite the wide possibilities opened up by the organism's ability for pathological regulation, the latter, just like physiological regulation, has its limits, beyond which a disturbance of basic functions occurs. The mechanism of regulation is different in different cases. First of all, pathological regulation often proves possible only thanks to the presence in organs of the ability for increased work at the expense of their so-called 'reserve forces.' Pathological regulation in such cases boils down to the manifestation of such reserve forces. Thus, the wall of blood vessels is capable of withstanding, if necessary, much greater blood pressure than under ordinary conditions. Bones are likewise capable of greater loads, and muscles, in case of need, can perform significantly greater work compared to that produced by them in the absence of increased demands upon them. The buffer systems of the organism are capable of compensating, if necessary, for significantly greater shifts in the direction of acidosis or alkalosis than is usually necessary for maintaining acid-base balance. A part of an organ, vicariously hypertrophying, as is known, can in many cases take upon itself the function of the whole organ. At the same time, the 'reserve force' of vascular walls is, of course, nothing other than the degree of their elasticity, i.e., the property of the material from which they are built, and just as in technology, when speaking of the elasticity of materials, it is said that the degree of elasticity under such-and-such conditions is higher than the pressure or stretching produced on the object, a similar meaning is invested in the above-mentioned designation. The same applies entirely to the skeletal system. The 'extensibility' of the buffer properties of the blood and tissues, i.e., the ability of the organism to regulate the active reaction of the latter within known limits, is, as is known, determined by the presence of so-called alkaline reserves and the precise setting of the work of the respiratory apparatus (removal of CO₂ by the lungs), and vicarious and compensatory hypertrophy of organs finds its explanation in the fact that 'work and nutrition, nutrition and work are two interpenetrating processes': increased demands provide a stimulus for increased work, and the active state of an organ is accompanied by a shift of the reaction in the direction of acidity, and this latter circumstance increases the arterialization of the given section of the organism. Somewhat greater difficulties are presented by the question of adaptability to increased demands on the heart. Regarding hypertrophy of the heart, one could basically say the same thing as regarding hypertrophy of skeletal musculature, although one has to admit that in all details the mechanism of this phenomenon remains not fully clarified to this day. Of great interest, however, are other kinds of cases—cases of an almost sudden, sometimes sharp increase in the work of the heart. Some authors, in explaining this phenomenon, appeal to the augmenting nerves of the heart, i.e., they admit the possibility of the transmission of stronger impulses to the heart muscle in such cases along the mentioned nerves, but such an interpretation encounters a certain difficulty from the side of the so-called 'all-or-nothing' law (see), according to which an excitable substance in response to any individual excitation gives either a maximum reaction or no reaction at all—a law, admittedly, not yet recognized by everyone. There are more grounds, however, to see the source of the heart's reserve forces elsewhere—in its ability, as needed, to actively lengthen its muscle fibers and thereby increase the energy of contractions. What the mechanism of such lengthening is, is not yet known exactly, but it must be thought to be of a reflex nature. Many other regulatory adaptations are noted for their demonstrably reflex nature. Thus, in the field of the cardiovascular apparatus, in addition to the long-known depressor nerves, the so-called carotid reflex was recently discovered by Hering, leading to a decrease in blood pressure in the arterial system of the greater circulation in the case of an increase in the latter (transmission from the bulbus caroticus through a branch of the glossopharyngeal nerve, the so-called sinus nerve, to the vasomotor center with subsequent dilation of vessels). But the mechanism of regulation by way of reflected action can also be somewhat different, not according to the classical type of reflex with the transmission of excitation through centripetal fibers to the corresponding center, but by way of direct action on the center through the blood. Thus, in the same cardiovascular system, there is a mechanism that carries out autoregulation of the work of the heart in such a way that when the latter is strengthened, the increase in the tone of the vagus nerve center in the medulla oblongata (directly through blood pressure) that grows along with it begins to inhibit the frequency of heart contractions, and when weakened, the decrease in the tone of the same nerve that goes hand in hand with it produces the opposite effect. In the same way, by direct action on the corresponding center through the blood, regulation of a purely chemical nature is carried out in a number of cases. Thus, for example, hyperglycemia in alimentary glycosuria leads to the excitation of the vegetative center involved in sugar metabolism in the medulla oblongata, as a result of which the secretion of insulin by the pancreas increases. But chemical regulation can also occur at the periphery.

Such a regression exists, for example, between the sugar-forming function of the liver and the glycogen-forming function: the process of glycogenolysis, having reached the stage of lactic acid formation, then passes under the influence of a change in the reaction of the medium and the prevalence, depending on this, of one hormone over another, into the reverse process—glycogen formation. The question of the mechanism of autoregulation of various organs and systems of the organism, which is important in both a physiological and pathological respect, is of no small interest in a methodological respect as well, demonstrating the transition of one tendency into another, directly opposite to it. From this side, one principle deserves attention, which primarily relates to the endocrine system, but was extended by Belov to other organs and systems as well and put forward by him as a principle of general physiological significance. This is the law of the so-called parallel-cross conjugation of organs, which consists in the fact that in each pair of directly and immediately connected organs, parallel impulses go from one organ to the other (i.e., an increase in the function of one gives an increase in the function of the other, and conversely, a decrease in the function of one leads to a decrease in the function of the other), and from the second to the first go cross impulses, i.e., its weak activity stimulates, while its increased activity inhibits the conjugated organ. The following examples illustrate this kind of regularity. First of all, the connection between the heart and the medulla oblongata, more precisely, with the center of the vagus nerve located in it, can serve as an illustration: parallel impulses go from the heart to the medulla oblongata (strengthening of heart work—increase in the tone of the vagus nerve; its weakening—decrease in the tone of the vagus nerve); in the opposite direction, cross impulses go (an increase in the tone of the vagus nerve inhibits, while a decrease leads to an increase in heart rate). Another example: the lungs and the medulla oblongata, more precisely, the respiratory center located in it. Excitation of the respiratory center leads to increased ventilation work of the lungs, and conversely, its reduced excitability is accompanied by less work of the lungs. Conversely, energetic work of the lungs, by creating conditions of eupnea, prevents excitation of the respiratory center, whereas insignificant respiratory excursions, causing an accumulation of CO₂ in the blood, result, on the contrary, precisely in the excitation of this center. Consequently, parallel impulses go from the medulla center to the lungs, and cross impulses go from the lungs to the respiratory center. A third example: the pituitary gland (more precisely, its anterior lobe) and the ovaries. Apparently, parallel impulses go from the former to the latter, since extirpation of the anterior lobe of the pituitary gland leads to underdevelopment of the gonads, and prolan gives early maturation of the ovaries; in the opposite direction, there is apparently cross conjugation, judging by the fact that castration gives hypertrophy of the anterior lobe of the pituitary gland. Thus, a connection between organs of the parallel-cross conjugation type undoubtedly exists in the organism within certain limits, and one may only doubt its universality. (By the way, the connection can be not direct, but indirect—through the mediation of a third organ and, in particular, sometimes at a considerable distance from both.) The very mechanism of autoregulation in these cases is as follows. Let us assume that organ A is in a state of hyperfunction. Then, according to the scheme of parallel-cross conjugation, it will send more energetic stimuli to organ B. The latter, in turn, will increase its function and inhibit the first organ. Conversely: hypofunction of A will lead to hypofunction of B, but the latter must stimulate A to increase activity, and thus the system will come to equilibrium. Correspondingly, conditions are provided for the restoration of equilibrium in the case of a primary deviation of organ B both in the direction of hyper- and in the direction of hypofunction (see figure). If this is so, then it means that in the tendency of an organ to deviate in the direction of hyper- or hypofunction, there is also hidden a directly opposite tendency—to its inhibition or stimulation. But the matter would not essentially change with a somewhat different approach to the question, namely from the point of view of the law of van 't Hoff and Le Chatelier put forward by Breitman. Belov's formulation in a number of cases encounters

difficulties, while the law of van 't Hoff and Le Chatelier, as sufficiently well-known in chemistry, hardly needs critical evaluation. According to it, a disturbance of equilibrium in a closed system, which has arisen as a result of the influence on it of any cause in a certain direction, is leveled by the system itself in such a way that a counteraction arises in it in the opposite direction. This law could also be extended to biology. Thus, an increase in the anabolic phase of metabolism—assimilation—leads subsequently to the catabolic phase—dissimilation, and since the assimilatory phase corresponds to a state of rest, and the dissimilatory phase to the work of an organ, or otherwise: the first to inhibition, and the second to excitation, then in other words one could say: the tendency to rest or inhibition subsequently generates a tendency to activity or to excitation, and conversely.

In a certain refraction and modification, the same above-mentioned regularity also finds expression in the long-known law of Hering and Breuer, according to which the stretching of the lungs caused by inhalation gives a stimulus to exhalation, and the collapse of the lungs caused by exhalation is a stimulus to inhalation, as well as in what we know about the alternation of states of hollow organs: filling and stretching of a hollow organ, for example, the urinary bladder, uterus, intestine, causes contraction of its smooth musculature; emptying, on the contrary, relaxes the latter. But the same in essence, again only in a somewhat peculiar refraction, can also be seen in Ukhtomsky's doctrine of the dominant. A dominant is a focus of increased excitability of nerve centers, which gains significance for the work of other centers due to the fact that, by accumulating excitation from the most distant sources, it thereby inhibits the ability of other centers to respond to stimuli that have a direct relation to them. But it is especially interesting that the dominant itself also harbors the opposite tendency to the resolution of excitation and, consequently, to its reduction to nothing by an endogenous path (the process of inhibition as a negative trace after excitation). Thus, the systems of the organism, having been brought out of a state of equilibrium, strive to restore equilibrium in a direction directly opposite to its initial disturbance, i.e., the tendency to excitation potentially contains within itself the opposite tendency to inhibition, and the tendency to inhibition—the tendency to excitation. Until the moment of reaching a certain threshold, however, there is, as expected, a direct negation of its opposite: thus, assimilation for a time inhibits dissimilation, and conversely, and the dominant, concentrating in itself excitation from the remaining areas, for a time prevents the emergence of other, compensating dominants. As for the relationship between the sympathetic and parasympathetic nervous systems in particular, with their sympathicotonia and parasympathicotonia, which under normal conditions are in a state of some dynamic equilibrium and are considered antagonists, certain reservations and limitations are required in this regard. Based on an analysis of blood pressure curves under the action of adrenaline, Dresel established that sympathetic irritation is accompanied by parasympathetic, thanks to which equilibrium is immediately restored (a comparison with a rope that is pulled by two parties of people in opposite directions). The fact is, however, that contrary to the views that recently dominated science, the doctrine of such an absolute antagonism between the two above-mentioned systems cannot be accepted at the present time from either an anatomical or a physiological-pharmacological point of view. Intrasecretory regulation is carried out in two ways: ion-endocrine and neuro-endocrine, and between the endocrine organs themselves, in turn, two kinds of correlation and regulation are admitted: both through the vegetative nervous system and directly through the blood (see Internal secretion).