PPT-4.2 Cautions about Correlation and Regression

Correlation and regression are powerful tools but have limitations Correlation and regression describe only linear relationship Correlation r and the leastsquares regression are not resistant . and regression. Scatter plots. A scatter plot is a graph that shows the relationship between the observations for two data series in two dimensions.. Scatter plots are formed by using the data from two different series to plot coordinates along the . Professor William Greene. Stern School of Business. IOMS Department . Department of Economics. Statistics and Data Analysis. Part . 6 – Regression Model-1. Conditional Mean . U.S. Gasoline Price. The Data. http://. core.ecu.edu/psyc/wuenschk/SPSS/SPSS-Data.htm. Corr_Regr. See . Correlation and Regression Analysis: . SPSS. Master’s Thesis, Mike Sage, 2015. Cyberloafing. = Age. , Conscientiousness. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. ... beware. Definition. Var. (X+Y) = . Var. (X) + . Var. (Y) + 2·Cov(X,Y). The . correlation. between two random variables is a dimensionless number between 1 and -1.. Interpretation. Correlation measures the . Linear Function. Y = a + bX. Fixed and Random Variables. A FIXED variable is one for which you have every possible value of interest in your sample.. Example: Subject sex, female or male.. A RANDOM variable is one where the sample values are randomly obtained from the population of values.. Yuhana Kennedy. July 2011. Hypothesis. The growth of cell phone usage in the U.S. has leveled off due to the fact that even though the U.S. population will continue to increase it does not do so without bound.. Fun facts about the regression line. Equation of regression line: . If we convert our X and Y scores to . z. x. and . z. y. , the regression line through the z-scores is:. Because the means of the z-scores are zero and the standard deviations are 1.. What is Correlation Analysis?. Testing the Significance of the Correlation Coefficient . Regression Analysis. The Standard Error of Estimate . Assumptions Underlying Linear Regression. Confidence and Prediction Intervals. Summary of the measure of the characteristics of individuals in groups.. A descriptive statistic talks about a single characteristics within a given group. Lots of descriptive statistics are summarizing lots of characteristics but all within a given group.. Correlation. A statistical way to measure the relationship between two sets of data.. Means that both things are observed at the same time.. Causation. Means that one thing will cause the other.. You can have correlation without causation. Instructor: Prof. Wei Zhu. 11/21/2013. AMS 572 Group Project. Motivation & Introduction – Lizhou Nie. A Probabilistic Model for Simple Linear Regression – Long Wang. Fitting the Simple Linear Regression Model – . -2-Note that-1r1otal Sum of Squares TSS of the data set asTSSni1Syi-y2note thatTSSSyygression SSR asRSSni1Syi-y2and note that sinceyiwill not be exactly on the regression lineTSSx0000RSSunless the poi Fun facts about the regression line. Equation of regression line: . If we convert our X and Y scores to . z. x. and . z. y. , the regression line through the z-scores is:. Because the means of the z-scores are zero and the standard deviations are 1..