712 Linear Regression

linear regression

a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observe data

dependent variable (response variable)

the variable trying to predict or explain

independent variable (predictor variable)

the variable used to predict the dependent variable

predictor

an independent variable that is used to estimate or predict values of the dependent variable

best fitting line (regression line)

A straight line that best represents the data on a scatter plot. It is used to describe the relationship between the dependent and independent variables

slope

the amount by which the dependent variable change for a one-unit change in the independent variable

Y intercept

the value of the dependent variable when the independent variable is zero

coefficient of determination (R²)

a statistical measure that is represents the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to1 and is usually expressed as a percentage

correlation

a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1 where -1 indicates a perfect negative linear relationship, 1 indicated a perfect positive linear relationship, and 0 indicates no linear relationship

multivariate (multiple) linear regression

a type of linear regression where there are multiple independent variables. This is used when the dependent variable is influenced by more than one independent variable

outliers

data points that are significantly different from others

slope equation

y=mx+b

R

the correlation coefficient which measures the strength and direction of the linear relationship between the observed and predicted values of the dependent variable

adjusted R squared

a modified version of R² that adjusts for the number of predictors in the model, providing more accurate measure of model fit hen multiple predictors are used

0.00-0.19

R² value indicating a weak fit

0.20-0.39

R² value indicating a modest fit

0.40-0.59

R² value indicating a moderate fit

0.60-0.79

R² value indicating a strong fit

0.80-1.0

R² value indicating a vert strong fit

unstandardized coefficients (B)

values that represent the change in the dependent variable for a one-unit change in the independent variable

standarized coefficients (Beta)

these coefficients are normalized, allowing to compare the relative importance of different independent variables in the model

standard error (SE)

This measures the accuracy of the coefficient estimates. Smaller standard errors indicate more precise estimates

t-value and p-value

these statistics test whether each coefficient is significantly different from zero. A high t-value and a low p-value (typically less than 0.05) suggest that the corresponding variable significantly contributes to the model

importance of regression analysis

• understanding relationships

• prediction

• decision making

• controlling the confounders: isolation of the effect of each variable accounting for the influence of other factors

relevance to physical therapy

• optimizing treatment plans

• evidence based practice

• resource allocation

• outcome measurement