Straight Line Regression Analysis Research Articles

Determination of individual teleroentgenographic characteristics of the lower medial incisors position in Ukrainian young men and young women with orthognathic bite

Ethnic, sexual and age features of the incisors positions point to the need for the development of techniques that allow to determine their individual characteristics, since commonly accepted standards recommended for optimal positioning of incisors can only be used as indicative. The purpose of the study – by studying teleroentgenographic indices and conducting direct stepwise regression analysis in young men and young women of Ukraine with orthognathic bite, to develop and analyze the mathematical models of individual characteristics of the position of the lower medial incisors. With the Veraviewepocs 3D device, Morita (Japan) in 38 young men (17 to 21 years of age) and 55 young women (aged from 16 to 20 years) with occlusion close to orthognathic bite and balanced faces received side teleroentgenograms. Cephalometric analysis was performed using OnyxCeph3TM software. Cephalometric points and measurements were performed according to the recommendations of A.M. Schwarz, J. McNamara, W.B. Downs, R.A. Holdway, P.F. Schmuth, C.C. Steiner and C.H. Tweed. According to the above methods, in the licensed package “Statistica 6.0” using direct straight line regression analysis, the teleroentgenographic characteristics of the position of the lower medial incisors (distance 1l_NB, distance 1l_APog, angle 1l_DOP, IMPA angle, Mand1_NB angle, FMIA angle and Mand1_MeIm angle) were performed. In young men with orthognathic bite of 7 possible models of teleroentgenographic characteristics of the lower medial incisors, 5 were constructed with determination coefficient R2 from 0.694 to 0.849, and in young women, all 7 possible models with determination coefficient R2 from 0.595 to 0.794. In young men most often the regression equations included - the angle ANB and facial vertical index GL_SN_S (by 11.5%); lower face height ANS_ME, face angle NBA_PTGN and distance S_E (by 7.7%). In young women most often the regression equations included – the angle of N_POG (16.7%); Wits indicator (13.9%); inclination angle I (8.3%); H-angle, maxillo-mandibular angle MM and angle of facial axis NBA_PTGN (by 5.6%). Thus, in the work with the help of the method of stepwise regression with inclusion, among Ukrainians of juvenile age, on the basis of features teleroentgenographic indicators, the analysis of reliable models of individual teleroentgenographic characteristics of the position of the lower medial incisors was developed and carried out.

A Japanese-Russian collaborative study on aging and atherosclerosis

In Russia, the average life span is decreasing. This phenomenon has not been previously observed in the western hemisphere during periods of relative peace. Although this trend can be attributed to various causes, the available statistics suggest that approximately 55% of the total mortality in Russia at the present time is due to cardiovascular events. Similarly, cardiovascular events are also increasing in Japan and are associated with changes in eating habits. A Japanese-Russian international collaborative study was therefore initiated to investigate this. Data on 102 normal Russian subjects were obtained from a total of 345 patients treated at the Smolensk State Medical Academy outpatients' clinic. The data on the Japanese patients were collected at Tohoku University, Tohoku Rosai Hospital, and Fukuda Denshi Company. Sixty-seven healthy male Japanese volunteers were compared with 44 healthy male Russian patients. In this study, Vasera VS1000 (Fukuda Denshi, Tokyo) was utilized to measure pulse wave velocity (PWV). Linear regression analysis was performed, and the results showed that brachial-ankle PWV (baPWV) was significantly higher in the Russian compared with the Japanese study group. With regard to aging, PWV was found to increase both in the Japanese and Russian subjects, with a significant increase in the latter group during their 40s compared with the Japanese, and with this tendency being carried forward into the 50s. This may be the principal cause for the higher incidence of cardiovascular events reported among Russians. Furthermore, when a straight line regression analysis was performed, the zero axis intercept in both cases showed almost the same value. These results indicated that the PWV may be almost the same in Japanese and Russian populations at the time of birth. In conclusion, at the time of birth, there is no difference in the atherosclerotic status of Japanese and Russian infants. However, over time atherosclerosis becomes more apparent and progresses significantly in the case of Russian subjects. This finding is observed through the analysis of PWV. The present authors intend to continue their study aimed at preventing the further development of atherosclerosis through medical intervention.

The σc — Vcirc correlation in high and low surface brightness galaxies

We investigate the relation between the central velocity dispersion, σc, and the circular velocity, Vcirc, in galaxies. in addition to previously obtained data, we consider an observationally homogeneus sample of 52 high surface brightness and 11 low surface brightness spiral galaxies. We performed a straight line regression analysis in a linear scale, finding a good fit, also for low σc galaxies, always rejected in the previous studies. Low surface brightness galaxies seem to behave differently, showing either higher values of Vcirc or lower values of σc with respect to their high surface brightness counterparts.

Parallel comparison of chronological risk changes among cancers of the breast, the uterine cervix and the stomach, as tested in 9 female populations of the world from early 1960s to mid 1980s: A stochastic study

The purpose of this study was to investigate comparatively the chronological changes of age-adjusted incidence rate (AAIR) as well as age-specific incidence rate (ASIR) of cancers of the breast (Br), the uterine cervix (Cer) and the stomach (St) from early 1960s to mid 1980s (5 data collections) using the data sets of 9 female populations world wide, the total data set number amounting to 45 per tumor. More specifically, we wanted to see whether or not there was any regular relationship between the differential time trends of the above 3 human neoplasias and their oncogene-tumor suppressor gene balances. Our investigation proceeded in 3 steps as follows: step 1, straight line regression analysis of log AAIR was applied to each of tumor pairs Br(x)-Cer(y), Br(x)-St(y) and Cer(x)-St(y). Step 2, direct successive elimination test (Gauss) of log AAIR was applied to each of 6 tumor pairs (Br-St, Br-Cer, Cer-St, Cer-Br, St-Br and St-Cer) to assess the fitness of a test tumor (x-partaner of fitness test) to either the oncogene type equilibrium model (r=-1.000) or the tumor suppressor gene type equilibrium model (r=+1.000). For each of 6 tumor pairs, the fitness test was repeated 3 times using i) the original data set in the ordinary (x,y) framework, ii) the rect-type data sets in the rect-(x,y) framework, and iii) the para-type data set in the para-(x,y) framework. The fitness of a test tumor (x partner in the calculation) to an equilibrium system was assessed in terms of the correlation coefficient value r within the range of -1.000 to +1.000 (step 3). Staging of the whole carcinogenesis process was attempted for each of 3 human neoplasias using either the ASIR profiles of a high- and low-risk populations, and/or those of early 1960s and mid 1980s. Results of key importance are given as follows: i) Br with rapidly growing cancer risk, Cer with rapidly declining cancer risk and St with slowly declining cancer risk were clearly distinguished from one another by the single regression analysis. ii) The fitness test demonstrated that Br, Cer and St each were found to have one score in the positivity test of oncogene activation (r=-1.000), whereas Br with 4 scores, Cer with 2 scores and St with 3 scores of tumor suppressor gene inactivation (r=+1.000) were found to have differential openness to the fitness test of Gauss for the detection of tumor suppressor gene inactivation. It is indicated that the differential opennesses of a window to tumor suppressor gene inactivation observed in 3 human neoplasias represent a measure of the time-linked aggressiveness of cancer risk. iii) The comparison of 4 ASIR profiles of Br suggested the presence of 3 stages of carcinogenesis progression, of which the 1st stage was tentatively classified as of heredity-dependent origin, and the 2nd and the 3rd stages were classified as of environment-dependent origin. The St ASIR profile represents a fusion product of very minor heredity-dependent stage I and a major environment-dependent stage II. In contrast, the Cer ASIR profile completely lacked a heredity-dependent stage. The integrity of the above findings is discussed in the light of a number of pioneering achievements along the line of the steroid criminal theory of carcinogenesis in humans and in non-human mammals.

The performance and radiation exposure of some neutron probes in measuring the water content of the topsoil layer

The use of neutron scattering technique for determining the soil surface water content is not popular due to the radiation escaping from the soil surface and the large errors in measurement. To compare the radiation exposure and the performance of different techniques statistically, 3 sites were selected. Five different neutron probe models and different adaptors were used with the depth probes. Exposure to neutrons and γ radiations, at various distances from the probes, were determined. In situ calibration curves were determined using different models of depth probes with a Solo surface reflector block, CPN surface adaptor, and different numbers of plastic Teflon parallelepiped, as well as surface Troxler 3401-B probes. Depth neutron probe readings increased with increasing number of Teflon plastic blocks deposited on the soil surface. The intercept of the straight line regression analysis of CR (count ratio, surface count over standard count) u. percentage water content on a volume basis decreased with increasing number of blocks deposited on the soil surface at all sites. The determination coefficient values of any depth probe with a Solo surface reflector or a block of 4·8 cm thickness were higher than those of a Troxler 3401-B surface probe or CPN 503 depth probe with its surface adaptor. The least exposure to radiation was with a depth probe with surface reflectors. This study proves the possibility of measuring the moisture content of the soil surface by using a depth neutron probe with a block laid on the surface, without danger of receiving the threshold dose of radiation.

Mid to late luteal phase steroids in minimal stage endometriosis and unexplained infertility

Serum and peritoneal fluid concentrations of progesterone and 17β-oestradiol were measured during days 20–27 of the luteal phase in 33 women with minimal stage endometriosis and 21 with unexplained infertility. The results were analysed using Student's t-test and straight line regression analysis. In both groups, 17β-oestradiol and progesterone values were several-fold higher than the corresponding serum values and there were significant correlations between the peritoneal fluid and the serum steroid values. In the peritoneal fluid there was a significant reduction in both progesterone and its ratio with 17β-oestradiol in women with minimal stage endometriosis ( P < 0.03, P < 0.04, respectively). The peritoneal fluid levels of 17β-oestradiol in women with minimal stage endometriosis were, however, not significantly altered. Despite the correlations between peritoneal fluid and serum steroid levels, there were no significant changes in the serum concentrations of progesterone, 17β-oestradiol or the ratio of progesterone to 17β-oestradiol in women with minimal stage endometriosis. It is concluded that luteal phase progesterone and its relationship to 17β-oestradiol are subtly altered in infertile women with minimal stage endometriosis compared with women with unexplained infertility. These alterations may be more clearly demonstrated in peritoneal fluid rather than in peripheral blood, possibly because the latter contains steroids which are of non-ovarian origin and are also constantly affected by the liver enzyme activity and enterohepatic circulation of individual subjects.

Applied Regression Analysis and Other Multivariable Methods

1. CONCEPTS AND EXAMPLES OF RESEARCH. Concepts. Examples. Concluding Remarks. References. 2. CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS. Classification of Variables. Overlapping of Classification Schemes. Choice of Analysis. References. 3. BASIC STATISTICS: A REVIEW. Preview. Descriptive Statistics. Random Variables and Distributions. Sampling Distributions of t, ?O2, and F. Statistical Inference: Estimation. Statistical Inference: Hypothesis Testing. Error Rate, Power, and Sample Size. Problems. References. 4. INTRODUCTION TO REGRESSION ANALYSIS. Preview. Association versus Causality. Statistical versus Deterministic Models. Concluding Remarks. References. 5. STRAIGHT-LINE REGRESSION ANALYSIS. Preview. Regression with a Single Independent Variable. Mathematical Properties of a Straight Line. Statistical Assumptions for a Straight-line Model. Determining the Best-fitting Straight Line. Measure of the Quality of the Straight-line Fit and Estimate ?a2. Inferences About the Slope and Intercept. Interpretations of Tests for Slope and Intercept. Inferences About the Regression Line ?YY|X = ?O0 + ?O1X . Prediction of a New Value of Y at X0. Problems. References. 6. THE CORRELATION COEFFICIENT AND STRAIGHT-LINE REGRESSION ANALYSIS. Definition of r. r as a Measure of Association. The Bivariate Normal Distribution. r and the Strength of the Straight-line Relationship. What r Does Not Measure. Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient. Testing for the Equality of Two Correlations. Problems. References. 7. THE ANALYSIS-OF-VARIANCE TABLE. Preview. The ANOVA Table for Straight-line Regression. Problems. 8. MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS. Preview. Multiple Regression Models. Graphical Look at the Problem. Assumptions of Multiple Regression. Determining the Best Estimate of the Multiple Regression Equation. The ANOVA Table for Multiple Regression. Numerical Examples. Problems. References. 9. TESTING HYPOTHESES IN MULTIPLE REGRESSION. Preview. Test for Significant Overall Regression. Partial F Test. Multiple Partial F Test. Strategies for Using Partial F Tests. Tests Involving the Intercept. Problems. References. 10. CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL. Preview. Correlation Matrix. Multiple Correlation Coefficient. Relationship of RY|X1, X2, !KXk to the Multivariate Normal Distribution. Partial Correlation Coefficient. Alternative Representation of the Regression Model. Multiple Partial Correlation. Concluding Remarks. Problems. References. 11. CONFOUNDING AND INTERACTION IN REGRESSION. Preview. Overview. Interaction in Regression. Confounding in Regression. Summary and Conclusions. Problems. References. 12. DUMMY VARIABLES IN REGRESSION. Preview. Definitions. Rule for Defining Dummy Variables. Comparing Two Straight-line Regression Equations: An Example. Questions for Comparing Two Straight Lines. Methods of Comparing Two Straight Lines. Method I: Using Separate Regression Fits to Compare Two Straight Lines. Method II: Using a Single Regression Equation to Compare Two Straight Lines. Comparison of Methods I and II. Testing Strategies and Interpretation: Comparing Two Straight Lines. Other Dummy Variable Models. Comparing Four Regression Equations. Comparing Several Regression Equations Involving Two Nominal Variables. Problems. References. 13. ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA. Preview. Adjustment Problem. Analysis of Covariance. Assumption of Parallelism: A Potential Drawback. Analysis of Covariance: Several Groups and Several Covariates. Comments and Cautions. Summary Problems. Reference. 14. REGRESSION DIAGNOSTICS. Preview. Approaches to Diagnosing Problems in Data. Residual Analysis: Detecting Outliers and Violations of Model Assumptions. Strategies of Analysis. Collinearity. Scaling Problems. Diagnostics Example. An Important Caution. Problems. References. 15. POLYNOMIAL REGRESSION. Preview. Polynomial Models. Least-squares Procedure for Fitting a Parabola. ANOVA Table for Second-order Polynomial Regression. Inferences Associated with Second-order Polynomial Regression. Example Requiring a Second-order Model. Fitting and Testing Higher-order Model. Lack-of-fit Tests. Orthogonal Polynomials. Strategies for Choosing a Polynomial Model. Problems. 16. SELECTING THE BEST REGRESSION EQUATION. Preview. Steps in Selecting the Best Regression Equation. Step 1: Specifying the Maximum Model. Step 2: Specifying a Criterion for Selecting a Model. Step 3: Specifying a Strategy for Selecting Variables. Step 4: Conducting the Analysis. Step 5: Evaluating Reliability with Split Samples. Example Analysis of Actual Data. Issues in Selecting the Most Valid Model. Problems. References. 17. ONE-WAY ANALYSIS OF VARIANCE. Preview. One-way ANOVA: The Problem, Assumptions, and Data Configuration. for One-way Fixed-effects ANOVA. Regression Model for Fixed-effects One-way ANOVA Fixed-effects Model for One-way ANOVA. Random-effects Model for One-way ANOVA. -comparison Procedures for Fixed-effects One-way ANOVA. a Multiple-comparison Technique. Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares. Problems. References. 18. RANDOMIZED BLOCKS: SPECIAL CASE OF TWO-WAY ANOVA. Preview. Equivalent Analysis of a Matched-pairs Experiment. Principle of Blocking. Analysis of a Randomized-blocks Experiment. ANOVA Table for a Randomized-blocks Experiment. Models for a Randomized-blocks Experiment. Fixed-effects ANOVA Model for a Randomized-blocks Experiment. Problems. References. 19. TWO-WAY ANOVA WITH EQUAL CELL NUMBERS. Preview. Using a Table of Cell Means. General Methodology. F Tests for Two-way ANOVA. Regression Model for Fixed-effects Two-way ANOVA. Interactions in Two-way ANOVA. Random- and Mixed-effects Two-way ANOVA Models. Problems. References. 20. TWO-WAY ANOVA WITH UNEQUAL CELL NUMBERS. Preview. Problem with Unequal Cell Numbers: Nonorthogonality. Regression Approach for Unequal Cell Sample Sizes. Higher-way ANOVA. Problems. References. 21. THE METHOD OF MAXIMUM LIKELIHOOD. Preview. The Principle of Maximum Likelihood. Statistical Inference Using Maximum Likelihood. Summary. Problems. 22. LOGISTIC REGRESSION ANALYSIS. Preview. The Logistic Model. Estimating the Odds Ratio Using Logistic Regression. A Numerical Example of Logistic Regression. Theoretical Considerations. An Example of Conditional ML Estimation Involving Pair-matched Data with Unmatched Covariates. Summary. Problems. References. 23. POLYTOMOUS AND ORDINAL LOGISTIC REGRESSION. Preview. Why Not Use Binary Regression? An Example of Polytomous Logistic Regression: One Predictor, Three Outcome Categories. An Example: Extending the Polytomous Logistic Model to Several Predictors. Ordinal Logistic Regression: Overview. A Simple Hypothetical Example: Three Ordinal Categories and One Dichotomous Exposure Variable. Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables. Summary. Problems. References. 24. POISSON REGRESSION ANALYSIS. Preview. The Poisson Distribution. Example of Poisson Regression. Poisson Regression: General Considerations. Measures of Goodness of Fit. Continuation of Skin Cancer Data Example. A Second Illustration of Poisson Regression Analysis. Summary. Problems. References. 25. ANALYSIS OF CORRELATED DATA PART 1: THE GENERAL LINEAR MIXED MODEL. Preview. Examples. General Linear Mixed Model Approach. Example: Study of Effects of an Air Polluion Episode on FEV1 Levels. Summary!XAnalysis of Correlated Data: Part 1. Problems. References. 26. ANALYSIS OF CORRELATED DATA PART 2: RANDOM EFFECTS AND OTHER ISSUES. Preview. Random Effects Revisited. Results for Random Effects Models Applied to Air Pollution Study Data. Second Example!XAnalysis of Posture Measurement Data. Recommendations about Choice of Correlation Structure. Analysis of Data for Discrete Outcomes. Problems. References. 27. SAMPLE SIZE PLANNING FOR LINEAR AND LOGISTIC REGRESSION AND ANALYSIS OF VARIANCE. Preview. Review: Sample Size Calculations for Comparisons of Means and Proportions. Sample Size Planning for Linear Regression. Sample Size Planning for Logistic Regression. Power and Sample Size Determination for Linear Models: A General Approach. Sample Size Determination for Matched Case-control Studies with a Dichotomous Outcome. Practical Considerations and Cautions. Problems. References. Appendix A. Appendix B. Appendix C. Solutions to Exercises. Index.

Body fat distribution and cardiovascular risk in middle-aged people in Southern Italy

Skinfold thickness, % body fat content, body mass index, systolic and diastolic blood pressure, plasma glucose, serum cholesterol and triglycerides have been measured in 132 middle-aged men (mean age 39.8 ± 9.9, range 20–59 yr) and in 114 middle-aged women (mean age 39.1 ± 9.3, range 20–59 yr). Anthropometric data were related to blood pressure and biochemical parameters by using a straight-line regression analysis. Body mass index, % body fat content, subscapular and suprailiac skinfold thickness, consideral as indicative of splanchnic fat distribution, were positively correlated to blood pressure, plasma glucose, cholesterol and triglycerides. Triceps skinfold thickness, an index of peripheral fat distribution, showed weaker or no correlation with these parameters. These preliminary observations in the Neapolitan area support the hypothesis that, in addition to body mass index and % body fat content, preferential splanchnic fat distribution is associated with cardiovascular risk factors.

Identification and description of the momentum effect in studies of learning: An abstract science concept

AbstractSeveral studies of the validity of the intensive time series design have revealed a post‐intervention increase in the level of achievement data. This so called “momentum effect” has not been demonstrated through the application of an appropriate analysis technique. The purpose of this study was to identify and apply a technique that would adequately represent and describe such an effect if indeed it does occur, and to use that technique to study the momentum effect as it is observed in several data sets on the learning of the concept of plate tectonics. Subsequent to trials of several different analyses, a segmented straight line regression analysis was chosen and used on three different data sets. Each set revealed similar patterns of inflection points between lines with similar time intervals between inflections for those data from students with formal cognitive tendencies. These results seem to indicate that this method will indeed be useful in representing and identifying the presence and duration of the momentum effect in time series data on achievement. Since the momentum effect could be described in each of the data sets and since its presence seems a function of similar circumstances, support is given for its presence in the learning of abstract scientific concepts for formal cognitive tendency students. The results indicate that the duration of the momentum effect is related to the level of student understanding tested and the cognitive level of the learners.

Calculator program yielding confidence limits for least squares straight line regression analysis

Calculator program yielding confidence limits for least squares straight line regression analysis