PPT-Canonical Correlation/Regression

Canonical CorrelationRegression AKA multiple multiple regression AKA multivariate multiple regression Have two sets of variables Xs and Ys Create a pair of canonical variates a 1 X. e AT where is called a Jordan block of size with eigenvalue so 1 Jordan canonical form 122 brPage 3br is upper bidiagonal diagonal is the special case of Jordan blocks of size 1 Jordan form is unique up to permutations of the blocks can have multipl 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 . 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 . Week 1. Data Relationships. Finding a relationship between variables is what we’re looking for when extracting data from sample populations. . Is education better or worst now than before?. Do students learn better with the use of technology in the classroom?. Coefficient. &. Line of Best Fit. . We first need to make . sure the . calculator is . CL. ea. R. . of all . previous content. . We first need to make . sure the . calculator is . CL. ea. R. . 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.. Correlation and regression are powerful tools, but have limitations.. Correlation and regression describe only linear relationship.. Correlation r and the least-squares regression are not resistant. . Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. 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. -2-Note that-1 -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..