Consider the following data set.
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| y | 3.00 | 0.21 | 0.61 | 0.70 | 1.13 | 1.17 |
a) plot the data (y versus x). Are there any points that appearto be outliers? If there are, circle them and label as such.
b) produce a regression of y against x. Add the regression lineto the plot in a). Do you think that the regression line capturesthe most important features of the data set reasonably well?
c) using calculations at a 5% significance level, can you saythat there is a significant linear relationship between the x andy? That is, can you say with 95% confidence that y linearly dependson x? Does this result agree with the conclusion you made inb)?
d) testing at a 5% significance level, can you say that theintercept (β0) is not zero? How does this conclusion agree with theplot in b)?
e) Assume that the first data point is an outlier (e.g. thevalue was misrecorded). Remove the outlier, and redo the partsb)-d). Plot the data set and both regression lines (before andafter the outlier was removed). Comment on the difference. Alsocomment on the difference between the results of the tests in c)and d), if any.
