part iv significantly different using inferential statistics chapter 15 using linear regression...
TRANSCRIPT
![Page 1: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/1.jpg)
Part IVSignificantly DifferentUsing Inferential Statistics
Chapter 15
Using Linear Regression
Predicting Who’ll Win the Super Bowl
![Page 2: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/2.jpg)
What you will learn in Chapter 15
How prediction works and how it can be used in the social and behavioral sciences
How and why linear regression works predicting one variable from another
How to judge the accuracy of predictions
The usefulness of multiple regression
![Page 3: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/3.jpg)
What is Prediction All About?
Correlations can be used as a basis for the prediction of the value of one variable from the value of another Correlation can be determined by using a set
of previously collected data (such as data on variables X and Y)
calculate how correlated these variables are with one another
use that correlation and the knowledge of X to predict Y with a new set of data
![Page 4: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/4.jpg)
Remember…
The greater the strength of the relationship between two variables (higher the absolute value of the correlation coefficient) the more accurate the predictive relationship
Why??? The more two variables share in common
(shared variance) the more you know about one variable from the other.
![Page 5: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/5.jpg)
The Logic of Prediction
Prediction is an activity that computes future outcomes from present ones What if you wanted to predict college GPA
based on high school GPA?
![Page 6: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/6.jpg)
Scatter Plot
![Page 7: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/7.jpg)
Regression Line
Regression line – reflects our best guess as to what score on the Y variable would be predicted by the X variable. Also known as the “line of best fit.”
![Page 8: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/8.jpg)
Prediction of Y given X = 3.0
![Page 9: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/9.jpg)
Error in Prediction
Prediction is rarely perfect…
![Page 10: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/10.jpg)
Drawing the World’s Best Line
Linear Regression Formula Y=bX + a
Y = dependent variable the predicted score or criterion
X = independent variable the score being used as the predictor
b = the slope direction of the line
a = the intercept point at which the line crosses the y-axis
![Page 11: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/11.jpg)
Hasbro
![Page 12: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/12.jpg)
Slope & Intercept
Slope – calculating b
Intercept – calculating a
![Page 13: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/13.jpg)
Number of Complaints (y) by Reindeer Age (x)
![Page 14: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/14.jpg)
Complaints by Reindeer Age: Intermediate Calculations
![Page 15: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/15.jpg)
SS Reg, SS Error, R2, and Correlation
![Page 16: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/16.jpg)
Chapter 6 16
Now You Try!!
Participant Hours/Week Video Games College GPA
1 3 3.8
2 15 2.1
3 22 2.5
4 30 0.6
5 11 3.1
6 25 1.9
7 6 3.9
8 12 3.8
9 17 1.7
![Page 17: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/17.jpg)
Printout: Slope Int, SS Reg, SS Error
and R2
![Page 18: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/18.jpg)
College GPA by SAT scores
Slope 0.003478 -1.07148Intercept
0.000832 0.957866
Rsquare 0.686069 0.445998
F 17.48335 8dfsSS Regression 3.477686 1.591314
SS Residual
![Page 19: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/19.jpg)
Severity of Injuries by # hrs per week strength
training;
Slope -0.12507 6.847277Intercept
Stand Error 0.045864 1.004246
R2 0.209854 2.181672
7.436476 28SS Regression 35.39532 133.2713
SS Residual
![Page 20: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/20.jpg)
Using the Computer
SPSS and Linear Regression
![Page 21: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/21.jpg)
SPSS Output
What does it all mean?
![Page 22: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/22.jpg)
SPSS Scatterplot
![Page 23: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/23.jpg)
The More Predictors the Better? Multiple Regression
Multiple Regression Formula Y = bX1 + bX2 + a
Y = the value of the predicted score X1 = the value of the first independent variable
X2 = the value of the second independent variable
b = the regression weight for each variable
![Page 24: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/24.jpg)
The BIG Rule…
When using multiple predictors keep in mind... Your independent variables (X1,, X2 ,, X3 , etc.)
should be related to the dependent variable (Y)…they should have something in common
However…the independent variables should not be related to each other…they should be “uncorrelated” so that they provide a “unique” contribution to the variance in the outcome of interest.
![Page 25: Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649efe5503460f94c130c0/html5/thumbnails/25.jpg)
Glossary Terms to Know
Regression line Line of best fit
Error in prediction Standard error of the estimate
Criterion Independent variable
Predictor Dependent variable
Y prime Multiple Regression