We wont calculate this t value and associated p value manually See table 3 of

# We wont calculate this t value and associated p value

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We won't calculate this t value and associated p-value manually See 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 relationship between 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 negative relationship in which odometer reading can help to predict/explain selling price. s epsilon In our case, s e = Sample Stdev (s y ) = y = beta(0) + beta(1) * x + epsilon Ho: beta(1) = 0 Ha: beta(1) <> 0 t = ( b 1 - 0 ) / s b1 OUTPUT: This relationship with odometer reading accounts for ~ 65% of the variation in selling price.
CLASS NOTES 3-1 page 4 SO FAR: REGRESSION ANALYSIS: Step 1 Estimate the Model Output: Show the model with numeric intercept and coefficients. Step 2 Assess the Estimated Model Output: 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 3 Check 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 58 Issue Initial Stock Offerings p 633 Ques Is 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 shares Data Sample of 10 selected IPOs: Company Shares Price American Physician 5 15 Apex Silver Mines 9 14 Dan River 6.7 15 Franchise Mortgage 8.75 17 Gene Logic 3 11 International Home Foods 13.6 19 PRT Group 4.6 13 Rayovac 6.7 14 RealNetworks 3 10 Software AG Systems 7.7 13 Analysis: Regression 1. Estimate the Model SUMMARY OUTPUT From Regression Output Regression Statistics Multiple R 0.86 R Square 0.744 Adjusted R Square 0.71 Standard Error 1.42 Observations 10 ANOVA df SS MS F ignificance F Regression 1 46.78 46.78 23.22 0 Residual 8 16.12 2.01 (1) The errors (epsilon) about the regression line are normally distributed .