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Value of Beta 1 tells you "if the value of x goes up by one unit, you expect y to go up by a certain (slope) amount"
Not causation, correlation |
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Beta not
does not mean a whole lot oftentimes |
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| Partial regression coefficients |
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They are the change in y expected when u change the x 1 unit, all others held constant
Beta 1 hat, beta 2 hat... |
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y-y hat
how much you missed it by
Method of least squares adds them all up and creates one unique line |
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Residual distributed normal
Independent (If you have cross sextional data)
mean = 0, constant variance (in between those 2 bars) |
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x values are correlated
can cause problems
don't assume they are and then throw them out
If the sign is backwards (-) means they may be tied together
Will have to illiminate one and keep the others
If you leave it, it inflates the standard error of the estimate |
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| Standard error of the estimate |
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how accurate your model is, st. deviation of residuals
Want to be small |
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| Heteroscedasticity (homoscedasticity) |
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| building the best model you can with the fewest variables you can. You want a good model with 3 than a slightly better model with 5. You run a risk of the variables not being really good when you add ones that help slightly |
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| coefficient of determination, tells you how much of the variablility of the y value has been explained by knowing x value. If it is .7, this means that 70% variability of the y values is explained by knowing the x, want to be closer to 1 since that means you are explaining more of the data |
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| standard error of the estimates (standard deviation of residuals |
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| t-tests on each coefficient |
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| Null hypothesis: Beta=0 (reject if p-value less than alpha) |
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| Confidence interval on Beta |
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shows 95% confident between 2 points
Predict only in range of X's in model (extrapolation) extrapolation = ou outside the value of possible x's |
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| Prediction interval for one specific observation (not for the mean) |
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| will be wider interval when you do it on the mean, it will be smaller |
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What to see if its a straight line
If not they are not correlated. If they follow a pattern and its not linear, they could still be x^2 or x^3 |
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| Correlations of Y and X's |
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| want to be close to 1 or -1, sign means slope is up or down, also use to see if there is multicollinarity. Even if it is low by itself, it is possible that it may be correlated with the other residuals from the other variables. May be significant with more variables |
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| want to check normality, as long as it is not bimodal that's good, you can also see outliers. Do not delete otliers. Would have to convince yourself that it is not part of the population you intend in you data |
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| Plot of standardized residuals vs standardized Y's |
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| Want to see if the residuals are constant. Should be between the 2 horizontal lines. Build 2 models if need be |
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| used for qualitative data. 1 less than the number of categories you have. If you have 5, ucan only use 4. Comparing what would happen if you were in the category with the ones in your base model. Some may fail out if they are not significant |
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say a non linear scatter plot, need x^2 or x^3 logs
lg:its not x goes up some % and y goes up some % |
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| taking varible in data (dependent) to see if sales this month is correlated to past months. Lag 1 is one period back. Lag 2 is 2 months back |
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| Regression on time series variable |
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| Time series: data collected over a certain time frame. There is an order of what data came first. Intervals have to be the same siz. You are extraplating. Historical datat does not always mean future data. Therefore do not extrapolate too far |
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| Long term, more than a year (t)=time variable=is used to find trent |
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| short term! based on seasons within a given year. Is there differences in months? In quaters? Most companies have seasonality is some form or another. AC repair, retail. Use dummy variables to see which ones are significant |
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| residuals are independent of each other. Used with lagged variables |
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| smoothes the data based on past history. Stock market often uses this |
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