Home   Description Purchase Tutorials Download   Support Compare   Videos  What's New?     


  Order WINKS Now 



 This is one in a series of tutorials using examples from WINKS SDA Software

Tutorial Menu
TexaSoft Home
More About WINKS


New -- Kwikstat
Data Generator
Generate data sets with continuous, categorical, grouped and correlated data. Great for creating data sets for examples and for quality assurance testing. Data sets are created in standard .CSV format so they can be opened in most statistical programs such as SAS, SPSS, WINKS and into spreadsheet programs such as Microsoft Excel. Order now.


WINKS Statistical Software Manual

These WINKS statistics tutorials explain the use and interpretation of standard statistical analysis techniques for Medical, Pharmaceutical, Clinical Trials, Marketing or Scientific Research. The examples include how-to instructions for WINKS SDA Version 6.0 Software. Download evaluation copy of WINKS.


Simple Linear Regression

This is one in a series of tutorials using examples from WINKS SDA.

Definition: Used to develop an equation (a linear regression line) for predicting a value of the dependent variables given a value of the independent variable. A regression line is the line described by the equation and the regression equation is the formula for the line. The regression equation is given by:

Y = a + bX

where X is the independent variable, Y is the dependent variable, a is the intercept and b is the slope of the line.

Assumptions: For a fixed value of X (the independent variable), the population of Y (the dependent variable) is normally distributed with equal variances across Xs.

Related statistics: The correlation coefficient, r, measures the strength of the association between X and Y.

Test: A test that of the slope of the regression line is 0 is used to determine if the regression line shows an statistically significant linear relationship between X and Y. The hypotheses for this test are:

H0: slope = 0
Ha: slope <> 0

A low p-value for this test (less than 0.05) means that there is evidence to believe that the slope of the line is not 0, or that there is a statistically significant linear relationship between the two variables.

Note: This test is equivalent to the test rho = 0 in the correlation procedure.

Location in WINKS: Simple linear regression is located in the Regression and Correlation procedures menu.

Graphs: Graphs produced with the simple linear regression procedure are:

1. Scatterplot with fitted regression line.

2. Residuals by the independent variable.

3. Residuals by run order.

Examination of the graphs is useful to visually verify that the relationship is linear and that there is no pattern to the residuals. If there is a pattern to the residuals, remedial methods may need to be taken for the analysis. Reference: Neter, Wasserman and Kutner.

Example: Use the Simple Linear Regression procedure to calculate a prediction equation for HP given the WEIGHT of a car using the CAR database. The partial results are:

 Dependent variable is HP, 1 independent variables, 38 cases.

Variable Coefficient St. Error t-value p(2-tail)
Intercept 3.4983434 7.3194069 .4779545 0.6326
WEIGHT 34.314394 2.4839847 13.814253 0.000

R-Square = 0.8413      Adjusted R-Square = 0.8369

Analysis of Variance Table
Source Sum of Sqs d.f. Mean Sq F p-value
Regression 21768.755 1 21768.775 190.8336 0.000
Error 4106.593 36 114.07203
Total 25875.368 37

A low p-value suggests that the dependent variable HP may be linearly related to independent variable(s).

Pearson's r (Correlation Coefficient)= 0.9172    R-Square=.8413

The linear regression equation is:

  HP = 3.498343 + 34.3144 * WEIGHT

Test of hypothesis to determine significance of relationship:
  H(null): Slope = 0 or H(null): r = 0 (two-tailed test)

  t = 13.81 with 36 degrees of freedom p = 0.000

The following plots show the linear relationship and the randomness of the residuals.


Warning: Using the regression equation to predict values of the dependent variable outside the range of the independent variable is not recommended since you have no evidence that the same linear relationship exists outside the observed range.

Related Topics: Correlation, multiple linear regression, polynomial regression.

Simple Linear Regression - Exercise

Data: A random sample of 14 elementary school students is selected, and each student is measured on a creativity score (x) using a well-defined testing instrument and on a task score (y) using a new instrument. The task score is the mean time taken to perform several hand-eye coordination tasks. The data are:

AE		28			4.5
FR		35			3.9
HT		37			3.9
IO		50			6.1
DP		69			4.3
YR		84			8.8
QD		40			2.1
SW		65			5.5
DF		29			5.7
ER		42			3.0
RR		51			7.1
TG		45			7.3
EF		31			3.3
TJ		40			5.2

Answer these questions:

1. Calculate the regression equation for this data, and enter it here:

  Y =

2. Is the relationship between tasks score and creativity score statistically significant?

3. What statistic do you base your answer on?

4. Look at a scattergram of Creativity by tasks. Does the relationship look linear?

5. Look at a plot of residuals. Do the residuals look random?

6. Do you think the task score does a good job of estimating the student's creativity score. Why?

Do this analysis NOW using WINKS

Analyze Data With WINKS

Click to order WINKS.
Best value for an easy to use and extensive statistical program."
Basic edition starts at $99.
Student editions also available.

"Winks is an excellent basic program that runs well on my laptop.  I find that I use it more than SAS"  - Dr. Jim Dickson, Iowa State University

  • Statistical Software designed for your needs -- Medical, Clinical Trials, Dissertation, Thesis, Business, Marketing, Agriculture, Forestry, Science and Research.

  • WINKS is an economical, reliable and simple to use statistical analysis tool designed to help students and researchers get the statistical answers they need quickly and without hassle.

  • It contains a wide range of statistical tests including many handy features not found in programs such as SPSS or SAS -- for example, easy analysis from summary data (as well as from raw data), nonparametric multiple comparisons, APA standard analysis write-up suggestions and more.

  • Newest additions to WINKS (ver 6.05) includes Grubbs Test for outliers  and Tukey Test for outliers, Kwikstat Data Generator evaluation edition, multiple comparisons in 2xc and rx2 crosstabulation (Chi-Square) analysis)  & Permutations and combinations calculator

  • Statistical test such as t-tests (paired t test, independent group t test/unpaired t test), ANOVA, regression, correlation, repeated measures, logistic regression, times series analysis, chi-square, Bland-Altman, Kruskal-Wallis, Mann-Whitney and much more.

  • Friendly interface with easy Excel-like data handling & graphs (reads and writes Excel files.)

  • FAST delivery to you when you order now

  • Print a brochure (pdf format)

  • Recent updates include

    • Added ability to calculate new column of z-scores for numeric variables.
    • Increased maximum groups to 40 for one-way ANOVA and one-way repeated measures (40 repeats).
    • Added editor option to create indicator variables from categorical variables.
    • Added Outcomes and Probabilities module that calculates combinations and permutations.
    • Added Grubbs & Tukey tests for outliers.
    • Added Multiple Comparisons of Proportions to Crosstabulations procedures for 2xc or rx2 tables
    • Updates are free to current users.

Read more about WINKS features.

Download WINKS Evaluation Version Now


For more information... we recommend:

  • WINKS -- a simple to use and affordable statistical software program that will help you analyze, interpret and write-up your results. Download a free trial copy.

  • Additional statistics tutorials.

  • Against All Odds VIDEOS - Now in VHS or DVD formats Teaching Videos from Annenberg/PBS Click here for info

  • BeSmartNotes Reference sheets for SAS, SAS ODS, SPSS and WINKS  - Click here for info. (www.besmartnotes.com)

  • Statistical Analysis Quick Reference Guidebook: With SPSS Examples is a practical "cut to the chase" handbook that quickly explains the when, where, and how of statistical data analysis as it is used for real-world decision-making in a wide variety of disciplines. It contains examples using SPSS Statistics software. In this one-stop reference, the authors  provide succinct guidelines for performing an analysis, avoiding pitfalls, interpreting results, and reporting outcomes. Paperback. Sage Publishers ISBN: 1412925606 Order book from Amazon

| Send comments | Tutorial Index | WINKS Software | BeSmartNotes |



Statistical Software
Reliable. Relevant. Affordable.
Data analysis software that's easy to use.

| Top of document | Tutorial Index | TexaSoft Homepage | Send comments |
Copyright TexaSoft, 2004-2007