Question

B.   Regression Analysis: Avg. Tot. Score versus PPS, %Takers

Model Summary

     S   R-sq  R-sq(adj)  R-sq(pred)

32.4595  81.95%     81.18%      79.59%

Coefficients

Term       Coef  SE Coef  T-Value  P-Value   VIF

Constant  993.8     21.8   45.52   0.000

PPS 12.29     4.22     2.91   0.006 1.54

%Takers  -2.851   0.215   -13.25   0.000 1.54

1.       Give a correct interpretation of the slope of PPS in Model B.

2.      What is the fit in Model B for a state with $5500 in per pupil spending and 60% of eligible students (%Takers) taking the exam?

Regression Analysis: Overall Rating versus Itineraries/Schedule, Shore Excursions, Food/Dining

Model Summary

     S   R-sq  R-sq(adj)  R-sq(pred)

1.38775  74.98%     70.29%      58.09%

Coefficients

Term Coef  SE Coef  T-Value  P-Value   VIF

Constant 35.6     13.2    2.69   0.016

Itineraries/Schedule   0.110   0.130     0.85   0.407 1.05

Shore Excursions      0.2445  0.0434     __ ___    1.07

Food/Dining 0.2474   0.0621   3.98 0.000 1.01

1.      What are the missing T-Value and P-Value for Shore Excursions?  Show calculations and explain your answer(s).

2.      Which of the following statements below are true?  (Select all that are true and briefly explain your answer(s).)

A.    If Itineraries/Schedule is removed from the model, the multiple R-squared will increase.

B.     If Itineraries/Schedule is removed from the model, the adjusted R-squared will increase.

C.     If Itineraries/Schedule is removed from the model, the multiple R-squared will decrease.

D.    If Itineraries/Schedule is removed from the model, the adjusted R-squared will decrease.

3.      What is the predicted rating for a cruise which rates 50 on Itineraries/Schedule, 70 on Shore Excursions, and 75 on Food/Dining?

4.      As the cruise coordinator, how might you make use of these regression results?

Answer 1

Give a correct interpretation of the slope of PPS in Model B.

One unit increase in PPS, increse the Avg. Tot. Score to by 12.29

2. What is the fit in Model B for a state with $5500 in per pupil spending and 60% of eligible students (%Takers) taking the exam?

Regression equation

Avg. Tot. Score= 993.8 + 12.29 PPS - 2.851 % of takers

If percent is taken as whole number
Avg. Tot. Score= 993.8 + 12.29(5500) - 2.851 (60) = 68417.74

If percent is taken as decimal number
Avg. Tot. Score= 993.8 + 12.29(5500) - 2.851 (.60) = 68587.0894

1. What are the missing T-Value and P-Value for Shore Excursions? Show calculations and explain your answer(s).

tvalue = coeff/se coeffi = 0.2245/0.0434=5.6336

pvalue need the number of observation
tstat(5.336,n-2)

2. Which of the following statements below are true? (Select all that are true and briefly explain your answer(s).)

B. If Itineraries/Schedule is removed from the model, the adjusted R-squared will increase.

adjusted R is calculated by penalizing Rsquare value for any insignificant variables. On removing the insignificant variable, adjusted R will increase.

3. What is the predicted rating for a cruise which rates 50 on Itineraries/Schedule, 70 on Shore Excursions, and 75 on Food/Dining?

y = 35.6+0.11 itineraries/Schedule +
0.2445   Shore Excursions +0.2474   Food/Dining

y = 35.6+0.11(50) +
0.2445(70) +0.2474(75)= 76.77

4. As the cruise coordinator, how might you make use of these regression results?
cruise coordinator must work on improving the rating for Shore Excursions and Food/Dining