Simple Linear Regression and Correlation ppt课件


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简略标题:Simple Linear Regression and Correla




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Simple Linear Regression and Correlation ppt课件内容预览:Determine the least squares regression equation,and make point and interval estimates for the dependent variable.Determine and interpret the value of the:Coefficient of correlation.Coefficient of determination.Construct confidence intervals and carry out hypothesis tests involving the slope of the regression line.Chapter 15- KeyTermsDirect or inverse relationshipsLeast squares regression modelStandard error of the estimate,sy,xPoint estimate using the regression modelConfidence interval for the meanPrediction interval for an individual valueCoefficient of correlationCoefficient of determinationChapter 15- KeyConceptRegression analysis generates a “best-fit”mathematical equation that can be used in predicting the values of the dependent variable as a function of the independent variable.pptDirect vs InverseRelationshipsDirect relationship:As x increases,y increases.The graph of the model rises from left to right.The slope of the linear model is positive.Inverse relationship:As x increases,y decreases.The graph of the model falls from left to right.The slope of the linear model is negative.Simple Linear RegressionModelProbabilistic Model: yi =b0+b1xi +eiwhere yi =a value of the dependent variable,yxi =a value of the independent variable,xb0=the y-intercept of the regression lineb1=the slope of the regression lineei =random error,the residualDeterministicModel:=b0+b1xi whereand is the predicted value of y in contrast to the actual value of y.Determining the Least Squares RegressionLineLeast Squares RegressionLine:Slopey-interceptSimple Linear Regression: AnExampleProblem 15.9:For a sample of 8employees,a personnel director has collected the following data on ownership of company stock,y,versus years with the firm,x.x 612146913159y 300 408 560 252 288 650 630 522(a) Determine the least squares regression line and interpret its slope.(b) For an employee who has been with the firm 10years,what is the predicted number of shares of stock owned?An Example,cont.An Example,cont.Slope:y-Intercept:So the “best-fit”linear model,rounding to the nearest tenth,is:An Example,cont.Interpretation of the slope: For every additional year an employee works for the firm,the employee acquires an estimated 38.8shares of stock per year.If x1=10,the point estimate for the number of shares of stock that this employee owns is:Interval Estimates Using the RegressionModelConfidence Interval for the Mean of yplaces an upper and lower bound around the point estimate for the average value of y given x.Prediction Interval for an Individual yplaces an upper and lower bound around the point estimate for an individual value of y given x.To Form IntervalEstimatesThe Standard Error of the Estimate,sy,xThe standard deviation of the distribution of thedata points above and below the regression line,distances between actual and predicted values of y,residuals,of eThe square root of MSE given byANOVAEquations for the IntervalEstimatesConfidence Interval for the Mean of y
课件关键字:Simple Linear Regression and C。

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