Linear RegressionReporters:Cabantac, MarthaCortez, Leah-FaithJose, FatimaPapellares, AndraSalvacion, DanielleVitug, Maynard

•Simple linear regression is the most commonly used technique for determining how the dependent variable is affected by independent variable.

Simple linear regression is used for three main purposes:1. To describe the linear dependence of

one variable on another

2. To predict values of one variable from values of another, for which more data are available

3. To correct for the linear dependence of one variable on another, in order to clarify other features of its variability.

Requirements for Regression

•It is assumed that both variables are measured at the interval level

•Regression assumes a straight-line relationship.

•Sample members must be chosen randomly to employ tests of significance.

•To test the significance of the regression line, one must also assume normality for both variables or else have a large sample.

You should use a Regression when:•You are looking for a relationship between

two samples, one sample from each of a dependent variable and an independent variable.

•You believe the relationship might be modeled by a straight line

•The data are related.

Do not use this test when:

•You want to compare frequency distributions

•You cannot identify a dependent variable and an independent variable

A scatter plot is the appropriate graph to show the relationship between two variables. In the case of a regression, the independent variable is on the horizontal axis, and the dependent variable is on the vertical axis.

Formula for Linear Regression

•a = Y intercept•b = slope of X

STEP by STEP Guided Practice

HeightX

WeightY X2 Y2 XY

A 49 81 2401 6561 3969

B 50 88 2500 7744 4400

C 53 87 2809 7569 4611

D 55 99 3025 9801 5445

E 60 91 3600 8281 5460

F 55 89 3025 7921 4895

G 60 95 3600 9025 5700

H 50 90 2500 8100 4500

N = 8 ∑X= 432 ∑Y= 720 ∑X2 =23,460 ∑Y2 =65,002 ∑XY=38, 980

Table 1. Table for Height-Weight

Step 1. Calculate the mean of X and Y

Step 2. Calculate SSX, SSY and SP

Step 3. Determine the Regression Line

Step 4. Determine correlation and coefficient of determination and non determination

A value of r close to +1 or -1 indicates a strong linear association.

Step 5. Calculate SSTOTAL, SSREG and SSERROR

Step 6. Calculate the regression mean and error mean square

Step 7. Calculate F and compare the critical value from Table of critical values for the F distribution (see attached table)

Hθ = Height has no significant relationship with the amount of variance in weight.

Hα = Height has a positive relationship with the amount of variance in weight

Step 8. Construct a summary table.

Source of Variation SS df MS FRegression 75.75 1 75.75 3.60Error 126.25 6 21.04

Total 202.00 7

RESEARCH PROBLEM

Test Weighing

X

DeuteriumY X2 Y2 XY

A 1498 1509 2244004 2277081 2260482B 1254 1418 1572516 2010724 1778172C 1336 1561 1784896 2436721 2085496D 1565 1556 2449225 2421136 2435140E 2000 2169 4000000 4704561 4338000F 1318 1760 1737124 3097600 2319680G 1410 1098 1988100 1205604 1548180H 1129 1198 1274641 1435204 1352542I 1342 1479 1800964 2187441 1984818J 1124 1281 1263376 1640961 1439844K 1468 1414 2155024 1999396 2075752L 1604 1954 2572816 3818116 3134216M 1722 2174 2965284 4726276 3743628N 1518 2058 2304324 4235364 3124044

N = 14 ∑X= 20288 ∑Y= 22629 ∑X2 = 30112294 ∑Y2 = 38196185 ∑XY= 33619994

•F = 961252 54886

F = 17.51361003 or 17.514

df reg = 1df error = 12α = .05Fcv = 4.75Hθ = There is no significant relationship between the

values of breast milk output obtained by the Test Weighing and by the Deuterium.

Hα = There is a positive relationship between the values of breast milk output obtained by the Test Weighing and by the Deuterium.

THANK YOU