Need assistance with Part #4 The following data set relates a dimensionless depe

Question

Need assistance with Part #4

The following data set relates a dimensionless dependent variable "Y" to one independent variable "X" (in radians): these points are also plotted on the attached graph. [Pp. 23-27 and Appendix A]^1 Using least-squares regression, determine the "best" regression coefficients "a" and "b" for the single-regressor model Y^cap = a + bX Compute the correlation coefficient r_xy and plot the resulting equation on the linear Cartesian coordinates attached to demonstrate that the resulting model (roughly) follows the data trend.^2 [Pp. 27-29] Assuming the "Student t" distribution adequately describes the random component of this database, compute the Confidence of the Estimate range at the 90% confidence level for X = 1.567. [Pp. 33-34, Pp. 38-41, Appendix A and Appendix C] Using least-squares regression, determine the "best" regression coefficients "a", "b_1" and "b_2" for the two-regressor model Y^cap = a + b_1X + b_2[Sin(X)] Show the three regression equations (with numerical coefficients) used to solve for the regression coefficients. Compute the correlation coefficient ry and plot the resulting equation on the linear Cartesian coordinates attached. [Pp. 30-35] Compute the Significance Ratio (i.e., the "f-statistic") for the model proposed in Question 3 and use Table X to estimate "Pr". You need not interpolate, merely identify the Pr range that encompasses the calculated value of "f".

Explanation / Answer

sin(X) is calcuated using ms-excel command=sin(X) and regression analysis has been done using ms-excel

here Y=2.86-0.9081x+2.7574sin(x)

here f-statistic=47.74 with df(2,6) and its probability=0.0002 ( using ms-excel command fdist(47.74,2,6))

Y X Sin(X) SUMMARY OUTPUT 3.1 0.2 0.20 3.8 0.7 0.64 Regression Statistics 4.5 0.9 0.78 Multiple R 0.969988252 4.7 1.2 0.93 R Square 0.940877209 4.1 1.6 1.00 Adjusted R Square 0.921169612 3.8 2.0 0.91 Standard Error 0.346659121 2.9 2.1 0.86 Observations 9 2.2 2.4 0.68 0.8 3.0 0.14 ANOVA df SS MS F Significance F Regression 2 11.47452028 5.737260138 47.74185376 0.00020666 Residual 6 0.721035279 0.120172546 Total 8 12.19555556 Coefficients Standard Error t Stat P-value Intercept 2.861740774 0.364367077 7.854004804 0.000225327 X Variable 1 -0.908178356 0.136838152 -6.63687972 0.000564549 X Variable 2 2.75742278 0.391137339 7.04975595 0.000407508

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