We won't calculate this t value and associated p-value manuallySee table 3 of the Regression for calculation of t and of the p-value.In the last row, we see the t value of -13.49 and a p-value of 0.000.Interpretation: This sample provides overwhelming evidence that there is a negative linear relationshipbetween selling price (y) and odometer reading (x).i.e., It is nearly impossible to obtain sample results like we have if there were no relationship.The "remaining" variation in selling price has a stdev of about $152.Statistically, we have overwhelming evidence from this sample that there is a negativerelationship in which odometer reading can help to predict/explain selling price.s epsilonIn our case,se=Sample Stdev (sy) =y= beta(0) + beta(1) * x+ epsilonHo: beta(1) = 0Ha: beta(1) <> 0t = ( b1- 0 ) / sb1OUTPUT:This relationship with odometer reading accounts for ~ 65% of the variation in selling price.
CLASS NOTES 3-1 page 4SO FAR:REGRESSION ANALYSIS:Step 1Estimate the ModelOutput: Show the model with numeric intercept and coefficients.Step 2Assess the Estimated ModelOutput: Statement about fit (R Sq and std error) and statistical results.NOW:The validity of the statistical tests of regression analysis (t-Tests and F-Tests we'll do in multiple regression)depend upon several required conditions. If Step 2 indicates a statistically significant model, then we check them.These conditions concern the epsilon term of the hypothesized model. Epsilon is the random error.We have a sample of epsilon -- all of the sample errors. (sometimes called residuals).Overall, our analysis requires that "Residuals (errors about predicted y) are Normal, constant, & independent"Step 3Check Required Conditions.Check:Can construct by establishing classes and using =FREQUENCY."Does the distribution look like it could be a sample from an approximate Normal distribution?"Check:one can construct a scattergram for these two variables."Is the spread of errors reasonably constant from low to high values of yhat?"Check:"Do the errors appear random from low to high values of x?"Check:OUTPUT of Step 3: Statement about whether the required conditions are true.REVIEW THE FOLLOWING EXAMPLE OF THE FIRST THREE STEPS.Exer 58IssueInitial Stock Offeringsp 633QuesIs there a relationship between # shares selling and expected price? (predict expected price)If so, how good? If so, estimate the expected price for an IPO with 6 million sharesDataSample of 10 selected IPOs:CompanySharesPriceAmerican Physician515Apex Silver Mines914Dan River6.715Franchise Mortgage8.7517Gene Logic311International Home Foods13.619PRT Group4.613Rayovac6.714RealNetworks310Software AG Systems7.713Analysis: Regression1. Estimate the ModelSUMMARY OUTPUTFrom Regression OutputRegression StatisticsMultiple R0.86R Square0.744Adjusted R Square0.71Standard Error1.42Observations10ANOVAdfSSMSFignificance FRegression146.7846.7823.220Residual816.122.01(1) The errors(epsilon) about the regression lineare normally distributed.