Simple Linear Regression Paper

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Part 11 Regression

Introduction:

Simple Linear Regression:

A simple linear regression uses the presence of a linear relationship to predict the value of a

dependent variable based on the value of an independent variable. The dependent variable is also

referred to as the outcome, target or criterion variable and the independent variable as the

predictor, explanatory or regressor variable. A simple linear regression is also referred to as a

bivariate linear regression or simply as a linear regression.

In order to run a simple linear regression, you require the following:

» One independent variable that is continuous (e.g., height, exam performance, etc.).

» One dependent variable that is continuous (e.g., height, weight, etc.).

Simple linear regression can be used to answer the following problems:

1. Predict new values for the dependent variable given the independent variable

You can use simple linear regression to predict the value of one variable when you know the

value of another variable. The value you are predicting is the dependent variable and the value

you know is the independent variable. For example, you might have last year’s student's mid-

term and final exam results for a biomechanics course. Using this data you construct a linear

regression equation. When this year’s class sits the mid-term biomechanics exam, you use the

linear regression equation to predict their performance in their final exam based on their mid-

term exam results (even though they have not yet sat this final exam).

2. Determine how much of the variation in the dependent variable is explained by the

independent variable

Often, your goal is not to make predictions, but to determine whether differences in your

independent variable can help explain the differences in your dependent variable. This approach

is more common in theory building, where you have proposed that your independent variable can

help explain some of the variation of your dependent variable. Furthermore, you want to be able

to quantify the degree to which your independent variable explains your dependent variable. For

example, how much does the amount of time spent exercising influence cholesterol

concentration (a fat in the blood linked to heart disease)?

Multiple Regression

A standard multiple regression allows you to predict a dependent variable based on multiple

independent variables and is an extension to simple linear regression. The dependent variable is

also referred to as the outcome, target or criterion variable and the independent variables as

predictor, explanatory or regressor variables. This method also allows you to determine the

Part 11 Regression

overall fit (variance explained) of the model and the relative contribution of each of the

predictors to the total variance explained.

Y = b

+ b

+ e

Where β

is the intercept (also known as the constant), β

is the slope parameter (also known as

the slope coefficient) for X

, and so forth, and ε represents the errors. This type of statistical test

relies on the initial assumption that there is, in fact, a linear relationship between each

independent variable and the dependent variable and a linear relationship between the

"composite" of the independent variables and the dependent variable. This assumption can be

examined, as you will do in this guide. Confidence intervals can be calculated for the sample

intercept and slope parameters to estimate the likely range of values that these parameters might

take in the population. Furthermore, predictions can be made based on the regression equation

calculated. You will calculate all these statistical measures in this guide.

What is required

In order to run a multiple regression, you require the following:

1. Two or more independent variables that can be either continuous or categorical (e.g.,

height, exam performance, gender, etc.).

2. One dependent variable that is continuous (e.g., height, weight, etc.).

Multiple regression can be used to answer the following problems:

1. Predict new values for the dependent variable given the independent variables

You can use multiple regression to predict the value of one variable when you know the value of

other variables. For example, you might have individuals' heights, weights, age and gender, and

you want to predict running performance. Using this data you construct a multiple regression

equation, which you then use to predict new individuals' running performance based on their

measured physical properties (i.e., their height, weight, age and gender).

2. Determine how much of the variation in the dependent variable is explained by the

independent variables

Often, your goal is not to make predictions, but to determine how much of the variation in the

dependent variable can be explained by all the independent variables. In addition, you can use

multiple regression to understand the relative, unique contribution of each independent variable

towards this total. For example, you might have individuals' heights, weights, age and gender,

and you want to predict running performance. You want to know how much of the variation in

running performance can be explained by the predictor variables. Additionally, you want to

know the relative contribution of each predictor to the explanation of variance.

Assumptions of the Regression:

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Part 11 Regression Introduction: Simple Linear Regression: A simple linear regression uses the presence of a linear relationship to predict the value of a dependent variable based on the value of an independent variable. The dependent variable is also referred to as the outcome, target or criterion variable and the independent variable as the predictor, explanatory or regressor variable. A simple linear regression is also referred to as a bivariate linear regression or simply as a linear regression. In order to run a simple linear regression, you require the following: » One independent variable that is continuous (e.g., height, exam performance, etc.). » One dependent variable that is continuous (e.g., height, weight, etc.). Simple linear regression can be used to answer the following problems: 1. Predict new values for the dependent variable given the independent variable You can use simple linear regression to predict the value of one variable when you know the value of another variable. The value you are predicting is the dependent variable and the value you know is the independent variable. For example, you might have last year’s student's midterm and final exam results for a biomechanics course. Using this data you construct a linear regression equation. When this year’s class sits the mid-term biomechanics exam, you use the linear regression equation to predict their performance in their final exam based on their midterm exam results (even though they have not ...
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Tags: simple linear regression Dependent Variable independent variable multiple regression null and alternative hypotheses