Practice Problem 3
The following practice problem is aimed to give you some practice with exploring data and running a linear regression on your own using statistical software. You are welcome to use any statistical software you wish and you are also free to work in groups of up to 3 for this practice problem. If you work in groups, please have every member of the group complete the ICON survey.
Instructions
What to turn in
Please turn in a document that includes any relevant statistics/figures created. You will be asked to complete a graded survey on ICON as part of this practice problem.
Finally, upload the final document to ICON and complete the graded survey.
Due Date
Due around March 18th, 2024. No penalty for late submissions as long as it is submitted by May 9th.
Data
The data for this activity comes from the Kaggle. The data contain 104 rows and 14 columns about possums collected from Australia. A data description for each column in the data is shown below.
The data can be obtained in csv format. A short description for each attribute is as follows. These data are also found within the “data” folder inside the IDAS.
| variable | class | description |
|---|---|---|
| case | integer | Observation number. |
| site | integer | site. |
| Pop | character | Population, either Vic (Victoria) or other (New South Wales or Queensland).. |
| sex | character | Sex of possum, either m (male) or f (female).. |
| age | integer | Age. |
| hdlngth | integer | Head length, in mm. |
| skullw | integer | Skull width, in mm. |
| totlngth | integer | Total length, in cm. |
| taill | integer | Tail length, in cm |
| footlgth | integer | foot length, in mm. |
| earconch | integer | ear conch length, in mm. |
| eye | integer | distance from medial canthus to lateral canthus of right eye, in mm. |
| chest | integer | chest girth, in cm. |
| belly | double | belly girth, in cm. |
Guiding Question
Does the tail length (taill attribute) explain variation in the total length (totlngth attribute) of the possum?
Questions
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Fit a linear regression to answer the research question highlighted above. Interpret the standard errors for the intercept and slope of the linear regression. That is, what do these terms mean?
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Interpret the test statistic and p-values for the intercept and slope. What is the default null and alternative hypotheses for these statistical tests?
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Compute and interpret a confidence interval for the slope. What confidence level was selected and why?