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Question
Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel's Regression Tool to answer the following questions.| x | y |
| 2 | 12 |
| 3 | 9 |
| 6 | 8 |
| 7 | 7 |
| 8 | 6 |
| 7 | 5 |
| 9 | 2 |
a. What is the estimated regression equation?
b. Perform a ttest and determine whether or not xand yare related. Use
= 0.05.c. Perform an Ftest and determine whether or not xand yare related. Use
= 0.05.d. Find and interpret the coefficient of determination.
| x | y | ||||
| 2 | 12 | ||||
| 3 | 9 | ||||
| 6 | 8 | ||||
| 7 | 7 | ||||
| 8 | 6 | ||||
| 7 | 5 | ||||
| 9 | 2 | ||||
| SUMMARY OUTPUT | |||||
| Regression Statistics | |||||
| Multiple R | 0.9185587 | ||||
| R Square | 0.84375 | ||||
| Adjusted R Sq. | 0.8125 | ||||
| Standard Error | 1.3693064 | ||||
| Observations | 7 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 50.625 | 50.625 | 27 | 0.00348 |
| Residual | 5 | 9.375 | 1.875 | ||
| Total | 6 | 60 | |||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
| Intercept | 13.75 | 1.398341 | 9.833082 | 0.0001853 | 10.1555 |
| x | -1.125 | 0.216506 | -5.19615 | 0.0034782 | -1.68155 |
Answer
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