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| Analysis of the equational relationship between X and Y. Regression SS/Total SS |
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| has a t distribution which standardizes its value to see if it is significantly different from 0. When the p-value of the slope is greater than the level of significance, one should assume the correlation coefficient will e close to 0. |
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| R, indicates nature and strength of the linear relationship variables |
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| Coefficient of determination |
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| R2, the ration of explained variation in Y to the total variation. |
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| minimizes the squared vertical distances between the points and the regression line resulting in the line of best fit. |
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will be smaller for better predictive equation. if the override value of y varies widely about the regression line, the standard error of the slope will be large.
Square root of the MS residual |
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| is the study of the nature and degree of the relationship between variables. A correlation coefficient of +1 or -1 means x and y are perfectly, linearly related. An r value of 0 indicates absolutely no relationship |
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| is using Xs beyond the range of the given Xs to predict Y. THis can cause large errors in prediction. Relationship of slope to the correlation coefficient. signs are the same. |
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| when Xs are highly correlated-this gives redundant information. |
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| non-constant variance in the residuals |
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| constant variance in the residuals |
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| atypical values in a data set (anomalies) |
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| CURVILINEAR patterns or LOGARITHMIC relationships |
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| Multiple regression analysis includes |
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| one dependent variable and more than one independent |
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| tries all combinations of variables and produces the best predictors in order of their predictive power. |
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| Artificially inflated R-squared occurs when.. |
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| there are too many predictors and not enough samples. |
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| you should have at least 10 times the number of observations as predictor variables. |
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| should produce a nearly straight line without outliers. |
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| T distribution vs. F Distribution |
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| T is usedto test the individual coefficients where F tests the overall or "global" model. |
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| are the differences in the observed value of Y at a given X and the predicted value. Absolute values between 2 and 3 are usually just suspicious while those over the absolute value of 3 are severe. |
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| should fall within +/-3 in order to be considered normal values. |
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| Transform Y and/or X when... |
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| any of the assumptions are violated |
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| In simple linear regression the use of regression lines is to ... |
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| predict the average value of y that can be expected to occur at a given value of x. |
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| A high correlation between x and y.. |
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| does NOT prove that x causes y |
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dependent variable plotted..
independent variable plotted... |
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vertical axis
horizontal axis |
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| If the confidence interval on the slope contains 0... |
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| there is no significant relationship between x and y |
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| you CANNOT assume that the slope is also positive. |
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| The slope of the regression line represents... |
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| the amount of change that is expected to take place in y when x increases by one unit. |
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| using values beyond the range of the given Xs to predict Y |
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| if null hypothesis is rejected... |
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| there is a relationship between x and y. |
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| if no correlation between two variables... |
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| the regression line will be horizontal |
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| A large value for the slope does not necessarily imply a large value for the... |
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| Test the individual coefficients to see which Xs are good predictors. |
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| only test these if the overall model had at least one good predictor. |
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| A we add more predictors... |
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| When you re-run a model after taking out the poor predictor variables... |
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| you have reduced the model |
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| When choosing between two models, both with good predictors for y... |
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| choose the one with the smallest standard error. |
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| Check the correlation matrix to make sure the X variables... |
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| are not correlated with each other |
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| check the signs of the coefficients... |
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| to make sure they are logical. |
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| Never say x causes y unless it was... |
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| Qualitative variables in multiple regression are called.. |
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| dummy variables. do not interpret their coefficients |
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| If there is a curve in the scatter diagram for any x,y chart or the residuals use... |
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| a quadratic equation... use x and x^2 |
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| If you think two x variables may work together at different levels to affect y... |
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| then try an interaction term. |
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| Only interpret the coefficients of... |
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| good predictors and first order terms. First order terms are linear terms. |
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| Squared Xs and interacted Xs are called... |
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| The us of regression lines is to.. |
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| predict the average value of y that can be expected to occur at a given value of x. |
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| The study of the equational relationship between variables is called... |
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