Linear regression and correlation

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Regression Line ◽  
World Population ◽  
Regression To The Mean ◽  
Straight Line ◽  
The Mean ◽  
Line Fitting ◽  
Single Predictor ◽  
Over Time

This chapter addresses the descriptive treatment of linear regression with a single predictor: straight-line fitting, interpretation of the regression line and standard deviation, the confusing phenomenon of “regression to the mean,” correlation, and conducting regressions on the computer. These concepts are illustrated with student discussions and activities. Many examples are of the sort commonly found in statistics textbooks, but the focus here is on how to work the examples into student-participation activities rather than simply examples to be read or shown on the blackboard. Topics include the following relationships: height and income, height and hand span, world population over time, and exam scores.

Breastfeeding Self-Efficacy and Its Relationship with the Perceived Stress and the Breastfeeding Performance in Iranian Mothers with Late Preterm Infants, 2019

2020 ◽  
Author(s):  
Akram Kahforoushan ◽  
Shirin Hasanpour ◽  
Mojgan Mirghafourvand
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Preterm Infants ◽  
Perceived Stress ◽  
Self Efficacy ◽  
Short Form ◽  
Late Preterm ◽  
Late Preterm Infants ◽  
The Mean

Abstract BackgroundLate preterm infants suffer from many short-term and long-term problems after birth. The key factor in fighting these problems is effective breastfeeding. The present study aimedto determine the breastfeeding self-efficacy and its relationship with the perceived stress and breastfeeding performance in mothers with late preterm infants. MethodsIn this prospective study, 171 nursing mothers with late preterm infants born in Alzahra Medical Center of Tabriz, Iran, who met the conditions of this study were selected through convenience sampling. The Breastfeeding Self-Efficacy Scale-Short Form (BSES- SF) was employed to measure breastfeeding self-efficacy and 14-item Perceived Stress Scale (PSS14) was used to measure the perceived stress during 24 hours after giving birth and when the child was 4 months old the breastfeeding performance was measured by the standard breastfeeding performance questionnaire. The data were analyzed by Pearson and Spearman’s correlation tests, independent t-test, one-way ANOVA, and Multiple Linear Regression.ResultsThe mean (standard deviation) of breastfeeding self-efficacy equaled 50.0 (7.8) from the scores ranging between13-65 and the mean (standard deviation) of the perceived stress equaled to 26.5 (8.8) from the scores ranging between 0-56. The median (25-75 percentiles) of breastfeeding performance score in the mothers equaled 2.0 (1.0 to 3.0) from the scores ranging between 0-6. On the basis of multiple linear regression and through adjusting the personal-social characteristic, by increasing the score of the breastfeeding self-efficacy, the perceived stress was decreased to a statistically significant amount (B=-0.1, 95%CI=-0.3 to 0.0), however, there was no statistically significant relationship between breastfeeding self-efficacy and breastfeeding performance (p=0.418). ConclusionDue to the modifiable variability of breastfeeding self-efficacy and its role in perceived maternal stress, the development of appropriate strategies to further increase breastfeeding self-efficacy and provide more support to these mothers and infants is of particular importance.

Testing the Theory in Latin America

2020 ◽  
pp. 121-148
Author(s):  
Nicole Baerg
Keyword(s):  
Latin America ◽  
Standard Deviation ◽  
Developed Countries ◽  
Inflation Expectations ◽  
Theoretical Argument ◽  
Instrumental Variable Analysis ◽  
Economic Output ◽  
Information Precision ◽  
The Mean ◽  
Over Time

This chapter moves from studying developed countries to a sample of countries in Latin America over time. The chapter presents evidence that an increase in the information environment, in terms of its level of precision, exerts an attenuating and significant effect on the mean and standard deviation of forecasters’ inflation expectations, ultimately lowering inflation outcomes. The finding is robust to the inclusion of policy credibility, persistence in inflation, economic output, and month and country effects. When conducting instrumental variable analysis, similarly signed results hold. The main results imply that an increase in information precision helps to lower aggregate levels of inflation and that the channel that this works through is by lowering the weight of prior expectations, as predicted by the theoretical argument. Importantly, the results persist even when considering a sample of countries with relatively variable inflation outcomes and less established (and therefore less credible) economic institutions.

Direct calibration of a totally implantable pulsed Doppler ultrasonic blood flowmeter

1977 ◽  
Vol 232 (5) ◽  
pp. H537-H544
Author(s):  
H. V. Allen ◽  
M. F. Anderson ◽  
J. D. Meindl
Keyword(s):  
Linear Regression ◽  
Abdominal Aorta ◽  
Regression Line ◽  
Volume Flow ◽  
Flow Profile ◽  
Pulsed Doppler ◽  
Velocity Flow ◽  
The Mean ◽  
Best Fit

A totally implantable pulsed Doppler ultrasonic blood flowmeter has recently been developed to provide information on the velocity-flow profile in a vessel as well as its diameter. Volume flow can be indirectly obtained according to the formula: Q = (phi/4)(diam)2-v. In order to determine the accuracy of this estimate, in vivo direct bleedout measurements were performed on the abdominal aorta of six dogs with an overall accuracy in 77 trials of +2.0 +/- 8.7% (mean +/- 1 SD). The best-fit mean linear regression line was found to be: flowmeter output = 1.013-true flow + 5.1 ml/min. The scatter in the flowmeter's accuracy is thought to be due to small variations in the angle of the transducer. The source of the 2% overestimation in the mean accuracy could not be directly attributed to any one condition; the error is sufficiently small that in many cases it can be neglected.

Characterization of a Fibrin Glue-Gdnf Slow-Release Preparation

1998 ◽  
Vol 7 (1) ◽  
pp. 53-61
Author(s):  
Henrich Cheng ◽  
Matt Fraidakis ◽  
Birger Blombäck ◽  
Paul Lapchak ◽  
Barry Hoffer ◽  
...  
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Fibrin Glue ◽  
Trophic Factor ◽  
Adult Rats ◽  
First Order ◽  
First Order Kinetics ◽  
Implantation Sites ◽  
The Mean ◽  
Over Time

One novel method to deliver trophic factor locally in the CNS is to mix it into fibrin glue. In the present studies, [125I]-labeled GDNF-containing fibrin glue balls were used to determine binding and spread of the trophic factor. First, the binding of different concentrations of [125I]-labelèd GDNF in fibrin glue was determined in vitro. Within the six concentrations used (from 200 nM to 0.004 nM, 0 M as control), there was a strong linear correlation between the [125I]-GDNF concentration and the recovered radioactivity (r = 0.992). The mean bound radioactivity in 16 samples with 4 nM [125I]-GDNF was 71262 + 2710 CPM, and accounted for 89.8% of the mean initial count of free [125I]-GDNF (79369 + 3499 CPM). Second, [125I]-GDNF-containing glue balls were implanted into the anterior chamber of adult rats. The implanted fibrin glue balls decreased in size with time, but could still be identified on the irises 2 wk after implantation. Radioactivity was concentrated at the implantation sites in the early stages with a distribution in the surrounding iris tissue, which became separated into focal radioactive spots at the third week. Counts of radioactivity were significantly higher in the [125I]-GDNF glue ball-implanted irises than controls until 14 days after implantation. A study of the [125I] decay over time using least-squares linear regression demonstrated first-order kinetics (r = —0.98, p < 0.02) with k = 0.0091 and T 1/2 = 76 h. Finally, [125I]-GDNF–containing glue balls were implanted in the spinal cord of adult rats. Radioactivity was concentrated at the implantation sites in the early stages and was later distributed more widely in the surrounding thoracic cord. The [125I]-GDNF–containing glue degraded over time and became a porous meshwork with decreasing radioactivity at the later time points. Radioactivity in the spinal cords subjected to implantation of [125I]-GDNF–containing glue balls was higher than in controls for 14 days. Study of the [125I] decay by time with least-squares linear regression demonstrated first-order kinetics (r = -0.97, p = 0.001) with T 1/2 = 75.6 h. We conclude that the trophic factor GDNF becomes bound in the fibrin glue matrix from which it is gradually released. Our results suggest that fibrin glue is an effective substrate for keeping a trophic factor localized in situ for a finite period, protected from the circulation, surrounding aqueous humor or CSF.

scholarly journals Against Common Assumptions, the World’s Shark Bite Rates Are Decreasing

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Erich Ritter ◽  
Raid Amin ◽  
Kevin Cahn ◽  
Jonathan Lee
Keyword(s):  
South Africa ◽  
Human Population ◽  
Regression Line ◽  
Annual Number ◽  
Statistical Software ◽  
Global Trend ◽  
Straight Line ◽  
The Us ◽  
Core Feature ◽  
Over Time

The trends of the world’s top ten countries relating to shark bite rates, defined as the ratio of the annual number of shark bites of a country and its resident human population, were analyzed for the period 2000-2016. A nonparametric permutation-based methodology was used to determine whether the slope of the regression line of a country remained constant over time or whether so-called joinpoints, a core feature of the statistical software Joinpoint, occurred, at which the slope changes and a better fit could be obtained by applying a straight-line model. More than 90% of all shark bite incidents occurred along the US, Australia, South Africa, and New Zealand coasts. Since three of these coasts showed a negative trend when transformed into bite rates, the overall global trend is decreasing. Potential reasons for this decrease in shark bite rates—besides an increase in the world’s human population, resulting in more beach going people, and a decrease of sharks due to overfishing—are discussed.

scholarly journals Controlling for baseline telomere length biases estimates of the rate of telomere attrition

2019 ◽  
Vol 6 (10) ◽  
pp. 190937 ◽  
Author(s):  
Melissa Bateson ◽  
Dan T. A. Eisenberg ◽  
Daniel Nettle
Keyword(s):  
Measurement Error ◽  
Telomere Length ◽  
Statistical Models ◽  
Meta Analysis ◽  
Regression To The Mean ◽  
Inference Models ◽  
Telomere Attrition ◽  
The Mean ◽  
Invalid Inference ◽  
Over Time

Longitudinal studies have sought to establish whether environmental exposures such as smoking accelerate the attrition of individuals' telomeres over time. These studies typically control for baseline telomere length (TL) by including it as a covariate in statistical models. However, baseline TL also differs between smokers and non-smokers, and telomere attrition is spuriously linked to baseline TL via measurement error and regression to the mean. Using simulated datasets, we show that controlling for baseline TL overestimates the true effect of smoking on telomere attrition. This bias increases with increasing telomere measurement error and increasing difference in baseline TL between smokers and non-smokers. Using a meta-analysis of longitudinal datasets, we show that as predicted, the estimated difference in telomere attrition between smokers and non-smokers is greater when statistical models control for baseline TL than when they do not, and the size of the discrepancy is positively correlated with measurement error. The bias we describe is not specific to smoking and also applies to other exposures. We conclude that to avoid invalid inference, models of telomere attrition should not control for baseline TL by including it as a covariate. Many claims of accelerated telomere attrition in individuals exposed to adversity need to be re-assessed.

The Effects of Lifting Frequency on the Dynamics of Lifting

1995 ◽  
Vol 39 (10) ◽  
pp. 650-654 ◽  
Author(s):  
Gary A. Mirka ◽  
Daniel P. Kelaher
Keyword(s):  
Standard Deviation ◽  
Linear Increase ◽  
Time Dependent ◽  
Lumbar Region ◽  
Non Linear ◽  
Trends Over Time ◽  
The Mean ◽  
Over Time

The goal of this study was to quantify the effects of different lifting frequencies (3, 6 and 9 lifts/minute) at different lifting heights (30 and 60 cm) on the kinematics of the lumbar region. Each of these lifting tasks was performed for twenty minutes. The time dependent traces of the both the mean and standard deviation of sagittal acceleration showed subject dependent trends over time. Averaged across time, the results of this study reveal that there is a non-linear increase in the sagittal acceleration with greater frequency of lifting.

scholarly journals Statistical cures and other fallacies

2012 ◽  
Vol 18 (4) ◽  
pp. 387-390 ◽  
Author(s):  
Gary R Cutter
Keyword(s):  
Wishful Thinking ◽  
Percentage Change ◽  
Regression To The Mean ◽  
The Common ◽  
The Mean ◽  
Regression Towards The Mean ◽  
The Impact ◽  
Relapse Rates ◽  
Over Time

Relapse rates and thus the impact of therapies have been decreasing. Why they decline and the impact on our ability to understand which treatments are better require more than simple math. The objective of this review is to discuss the impact of regression to the mean, changes in outcome effects and how we compare outcomes over time and among studies. This paper provides discourse on the topics of regression to the mean, some examples of the pitfalls of changes and some difficulties in the interpretation of the common percentage change in outcomes. The results show that we can often be deceived by what we think we see and they also demonstrate how such confusion evolves in the literature. This article aims to caution against the over-interpretation of changes from baseline, which are helped along by regression towards the mean and other factors. Furthermore, how we interpret changes from baseline requires care and not wishful thinking, coupled with careful digestion of seemingly reasonable explications of results.

scholarly journals Regression to the mean correction for Collision Modification Factors

2021 ◽  
Author(s):  
Bernard James
Keyword(s):  
Standard Deviation ◽  
Road Safety ◽  
Relative Number ◽  
Highway Safety ◽  
Regression To The Mean ◽  
Simple Method ◽  
Highway Safety Manual ◽  
The Mean ◽  
Site Population

Collision Modification Factors (CMFs) are a simple method of representing the effectiveness of road safety treatments. With the release of the Highway Safety Manual (HSM) and the recent launching of a CMF Clearinghouse website, CMFs are likely to become more widely used for estimating the effects of potential road safety treatments. The presence of regression to the mean (RTM) bias has long been shown to affect the accuracy of CMFs that did not account for the RTM in their development. The purpose of this research was to study how the RTM depends on the number of years of data used for selecting high collision sites for treatment and on the relative number of sites selected. From this analysis, a function based on the number of years, percentage of high collision sites selected, and the mean and standard deviation of the site population from which the treated sites are drawn was developed to more accurately estimate the magnitude of the RTM effect. This function can be used to adjust CMFs that do not account for RTM, complementing the procedure developed and used to correct CMFs included in the HSM.

scholarly journals Relationship between Demographic Characteristics, Depression and Insomnia with Restless Legs Syndrome: a Study of Adults Aged 17-70 Years in Yazd 2019

2020 ◽  
Author(s):  
Mohammad Hossein Sorbi ◽  
Ali Issazadegan ◽  
Esmaiel Soleimani ◽  
Hamid Mirhosseini
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Restless Legs Syndrome ◽  
Pearson Correlation ◽  
Demographic Characteristics ◽  
T Test ◽  
Cluster Sampling ◽  
Motor Disorder ◽  
Restless Legs ◽  
The Mean

Introduction: Restless legs syndrome (RLS) is a neurological-motor disorder in which most patients tend to shake their legs during sleep and describe it as an unpleasant feeling. The aims of this study were to determine the prevalence of RLS, its relationship with demographic characteristics, depression, and insomnia and comparison of the mentioned variables in the group with and without RLS.  Methods: This was a case-control analytic study. The sample consisted of 429 adults aged 17-70 years who had referred all the psychiatric and neurological clinics of Yazd (center of Iran) in 2019. Participants were selected by cluster sampling method. Research tools included a demographic questionnaire, the Beck Depression Inventory (BDI-II), Insomnia Severity Index (ISI), and an International Restless Legs Syndrome Questionnaire (IRLSQ). The data were analyzed by SPSS-21, chi-square, Pearson correlation coefficient, independent t-test, and linear regression. Significant level was considered 0.05. Results: The mean and standard deviation of the age of participants was 34.43± 10.82. Furthermore, the mean and standard deviation of the age group with RLS was 36.07± 10.95 while in group without RLS was 33.92± 10.75. Prevalence of RLS in adults was 23.5% (n= 101), in women was 32% (n= 66) and in men was 28.7% (n= 35). The t-test showed patients with RLS had a higher degree of depression and insomnia than those without RLS (p<0.05). Multiple linear regression also showed that insomnia (β= 0.36), age (β= 0.13), and depression (β= 0.15) had a significant effect on RLS score.  Conclusion: The prevalence of RLS among adults in Yazd is high. Severe insomnia, depressed mood, and aging are considered as important factors in predicting this disease. According to what was mentioned early detection, prevention, and treatment of this disorder in adults is necessary.

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