Homework SourseUse alpha 005 a Develop the Regression equation b Is the ov
Use alpha = 0.05.
a. Develop the Regression equation
b. Is the overall regression significant?
c. What is the effect of Food/Dining on Overall Satisfaction (holding the other indpendent variables constant)?
d. What is the effect of Shore Excursions on Overall Satisfaction (holding the other independent variables constant)?
e. How much of the variation in Satisfaction is explained by the variation in the independent variables ( Adjusted Coefficient Determination)?
f. What is the correlation coefficient value?
g. Is the effect of Iteneraries/Schedule on Overall Satisfaction significant? Why?
h. Is the effect of Shore Excursions on Overall Satisfaction significant? Why?
i. Is the Y-intercept significant? Why?
j. What would you expect Overall Satisfaction to be if the scores for Iteneraraies/Schedule, Shore Excursions, and Food Dining were 90, 70, and 80 respectively?
| Ship | Overall (Y) | Iteneraries/Schedule (X1) | Shore Excursions (X2) | Food/Dining (X3) |
| 94.4 | 94.6 | 90.9 | 97.8 | |
| 93.0 | 96.7 | 84.2 | 96.7 | |
| 92.9 | 100.0 | 100.0 | 88.5 | |
| 91.3 | 88.6 | 94.8 | 97.1 | |
| 90.5 | 95.1 | 87.9 | 91.2 | |
| 90.3 | 92.5 | 82.1 | 98.8 | |
| 90.2 | 96.0 | 86.3 | 92.0 | |
| 89.9 | 92.6 | 92.6 | 88.9 | |
| 89.4 | 94.7 | 85.9 | 90.8 | |
| 89.2 | 90.6 | 83.3 | 90.5 | |
| 89.2 | 90.9 | 82.0 | 88.6 | |
| 89.1 | 93.1 | 93.1 | 89.7 | |
| 88.7 | 92.6 | 78.3 | 91.3 | |
| 87.2 | 93.1 | 91.7 | 73.6 | |
| 87.2 | 91.0 | 75.0 | 89.7 | |
| 86.6 | 94.4 | 78.1 | 91.6 | |
| 86.2 | 95.5 | 77.4 | 90.9 | |
| 86.1 | 94.9 | 76.5 | 91.5 | |
| 86.1 | 92.1 | 72.3 | 89.3 | |
| 85.2 | 93.5 | 77.4 | 91.9 |
Solution
a. Develop the Regression equation
Y=35.6184 + 0.1105*X1+0.2445*X2+0.2474*X3
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b. Is the overall regression significant?
Since the p-value of F test is less than 0.05, we can conclude that the overall regression is significant
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c. What is the effect of Food/Dining on Overall Satisfaction (holding the other indpendent variables constant)?
When Food/Dining on Overall Satisfaction increases one unit, the regression line increases 0.2474
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d. What is the effect of Shore Excursions on Overall Satisfaction (holding the other independent variables constant)?
When Shore Excursions on Overall Satisfaction increases one unit, the regression line increases 0.2445
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e. How much of the variation in Satisfaction is explained by the variation in the independent variables ( Adjusted Coefficient Determination)?
Since Adjusted R^2=0.7029, 70.29% of the variation in Satisfaction is explained by the variation in the independent variables
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f. What is the correlation coefficient value?
r=0.86592
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g. Is the effect of Iteneraries/Schedule on Overall Satisfaction significant? Why?
No, because the p-value is greater than 0.05
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h. Is the effect of Shore Excursions on Overall Satisfaction significant? Why?
Yes, because the p-value is less than 0.05
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i. Is the Y-intercept significant? Why?
Yes, because the p-value is less than 0.05
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j. What would you expect Overall Satisfaction to be if the scores for Iteneraraies/Schedule, Shore Excursions, and Food Dining were 90, 70, and 80 respectively?
35.6184 + 0.1105*90+0.2445*70+0.2474*80 =82.4704
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=16) | p-value | 95% lower | 95% upper |
| Intercept | 35.6184 | 13.2308 | 2.692 | .0160 | 7.5703 | 63.6665 |
| Iteneraries/Schedule (X1) | 0.1105 | 0.1297 | 0.852 | .4069 | -0.1644 | 0.3853 |
| Shore Excursions (X2) | 0.2445 | 0.0434 | 5.640 | 3.69E-05 | 0.1526 | 0.3365 |
| Food/Dining (X3) | 0.2474 | 0.0621 | 3.982 | .0011 | 0.1157 | 0.3790 |
