Question

A regression model relating 3, number of salespersons at a branch office, to y, annual sales at the office in thousands of dollars) provided the following computer output from a regression analysis of the data. Where ntotal = 32. ANOVA df MSF Significance F SS 6863.5 Regression Residual Total 9342.6 Stat P-value Intercept Number of Salespersons Coefficients 88.0 54.0 Standard Errort 12.175 5.865 a. Write the estimated regression equation (to whole number). y= Xx b. Compute the F statistic and test the significance of the relationship at a 0.05 level of significance. (to 2 decimals) F-value p-value is less than 0.01 , we reject H, c. Compute the t statistic and test the significance of the relationship at a 0.05 level of significance. (to 2 decimals) t Stat . p-value is less than 0.01 , we reject H: By = d. Predict the annual sales at the Memphis branch office. This branch employs 10 salespersons. (to whole number)

Answer 1

Solution: Here concept of simple regression equation is used.

Solution - as The estimated regression equation is geven as y = b. tb, a have from the given output we intercept (bo) = 88.0 Regression slope (by) = 54.0 . Regression equation in y = 88 + 540 b) relationship the F To test the statistic is geven F = significance of an follows: MS Regression MS. Residual where, where, MSpegnension Regression = 35 Regression s pegression Corresponding of SS Residiel Corresponding of MS Residual = Degrees of freedom (df) for Degrees of freedom (df) for where, & in N is We have o k=1 and regression = k . residual = N-K-1 no. of regressors a sample size N= 32

i df for regression = 1 df for residual = 30 From the given output we have, SS Rug. = 6863.5 , SS. The = 9342.6 . SS pesidial SS Residual & ses portal - Speg. total or 93426 - 6863.5 = 2479.1 Mag. = sspegi sspegi - 6863.5 686315 – 6863.5 - = 6863.5 dof MS Residual SSResidual 2479.1 - 82.637 = df 30 .. F = 6863.5 = 83.06 82.637 And p-value for the test statistic is given by P-valve - P[F>F] - PF > 83.06] - 3.79x1010 P-valve is less than 0.05, therefore, we shall reject Hot Conclusioni At a = 0.05 , there is a enough evidence to conclude that relationship is significant.

o To test, Hoi ß = 0 Hiß, & 0 the typothesis To test we shall find t-statistic. t = B ~ t (N-2) SECês) °(N-2) & is estimate of regression slope. SE(Å) is standard error of ß. We have ß = 54 SEB) = 5.865 The in t = 54 - 9.2072 5. 865 t stat - 2.2072 p-valve for the two-tailed P-value = 2.P(T st) = 2.PIT > 9.2072) = 3.02 X 100 test is given as follows: Since the p-valve is less than 0.05, therefore we shall reject Hoi ß = 0 at o.o significance level. Conclusion - At a = 0.05, there is enough evidence to conclude that relationship is significant.

1d) The regression equation is, y = 88 + 540 We have to predict y at x = 10 .: y = 88 +(54 x 10) y = 88 +540 = 628 Annual sales at Memphis a branch office thousand dollars. is 628