12.91 A company wants to know how effective workshops provided to the employees are. At the end of each workshop, the employees are requested to evaluate it. To assess the impact of various factors on the effectiveness ratings for each workshop, the model Y = b0 + b1X1 + b2X2 + b3X3 + e was fitted for 28 such workshops, where Y = effectiveness rating X1 = workshop attendance X2 = trainer’s years of experience X3 = attendees satisfaction rating The following is part of the EXCEL computer output from the estimate regression.

R@Square = 0.8037 Coefficients Standard Error t Stat Intercept 1.6732 0.0634 26.3912 X1 2.7521 0.9538 2.8854 X2 1.3924 1.2768 1.0905 X3 4.1837 0.8924 4.6881

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 5% level, the null hypothesis that, taken together, the three independent variables do not linearly influence the rating for the workshop.

d. Find and interpret a 90% confidence interval for b1.

e. Test the null hypothesis H0 : b2 = 0 against the alternative H1 : b2 7 0 and interpret your results.

f. Test at the 10% level the null hypothesis H0 : b3 = 0 against the alternative H1 : b3 ? 0 and interpret your results.