Statistics May 2nd
Statistics May 2nd BusAdm 210-401
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This 2 page Class Notes was uploaded by Tyler espinoza on Wednesday May 4, 2016. The Class Notes belongs to BusAdm 210-401 at University of Wisconsin - Milwaukee taught by Payesteh Sayeed in Spring 2016. Since its upload, it has received 12 views. For similar materials see Introduction to Management Statistics in Business at University of Wisconsin - Milwaukee.
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Date Created: 05/04/16
Least Squares Regression Y=Response variable; X=Explanatory variable Most if not all will be used with a scatterplot Scatter plot review Shows relationship between two quantitative variables Interpret scatter Form: linear, curved, or no pattern Direction: positive or negative Strength: how closely do the points fit form The regression line A line that describes the response variable changes as explanatory variable X changes. Use regression line to find prediction of Y given X Least square idea Y=Observed; Y-ŷ=distance; ŷ=predicted so Regression X is minimal distance from Y Below is resulting Square Line Ŷ=Bo+B1X How To find Sy B1=r Sx r=correlation Sy=Standard Deviation of Response variable Sx= Standard deviation of Explanatory Bo=meany-b1*meanx mean y& mean X are sample means of Y and X Facts about LSR the distinction between explanatory and response variable is essential. The LSR always passes through the point (meanX, MeanY) R^2 in Regression Measures proportion of total variation Y 0<r^2<1 R2=r2, when we have more than 1 explanatory variable. R if you remember is the correlation between the two points. R^2=1 perfect fit, passes through all the points on the line. R^2=0 means no fit. Points scattered and no correlation Formal name called Coefficient of Determination R^2 is a measure of how successful the regression was in explaining the response. For example, if the correlation is .8245 we need to square that. It would mean that we were successful in explaining that 82% of regression Inference We want to extend our analysis to include infrences in order to get them we need to meet a few conditions 1.) Sample treated as an SRS from population 2.) Mean response µy has relationship with X 3.) µy=Bo+Bx 4.) Standard deviation is same for all of X 5.) Response y varies normally around population regression line. Estimate Parameters Population regression line as Bo+Bx. Bo+Bx are your parameters. Confidence Interval At level C Confidence Interval for slope B1; b1± t*SEb1 T* is critical value of t distance with df=n-2. That has area C between –t* and t* The margin of error is m=t* SEb1 S 2 SEb1= √Ʃ(X−MeanX)
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