Problem #1 Part 1 You are trying to get a sense of how fast an amateur golfer's swing affects the distance that the ball travels. To do so, you follow 8 golfers and record their speeds and distances. Here are the speeds from the 8 golfers (in miles per hour): 100, 102, 103, 101, 105, 100, 99, 105 Here are the distances traveled for each swing (in yards): 257, 264, 274, 266, 277, 263, 258, 275 So for the first golfer, the speed was 100 mph, and the ball traveled 257 yards. Generate a regression model in which you predict how far the ball will travel based on the speed of the golf swing. For your model, provide a brief discussion. That is, imagine you are providing this analysis to someone who has to make policy decisions, yet has no background in statistics. Try to describe your regression model in the real world. Part of this kind of discussion should always include how strong or not strong you believe the model to be. Hint: There is one numeric value in particular that should give you a sense of the strength of the model. As part of your discussion, also be sure to answer the following questions: Do you think any observations should be removed? That is are there any outliers or influential points that you believe have an undue influence on the model? Part 2: Let's suppose that you see a 9th golfer on the course and mistakenly think it is another amateur player. However, as it turns out, it is a professional golfer who was just enjoying a casual day on the course. You record this golfer's speed which was: 121 miles per hour, and a distance of 307 yards. Generate another regression model which includes this new golfer. How would you interpret this additional observation? i.e. Is it an outlier? Is it influential? Both? Now you have to decide what to do with this observation. Should you keep it or not? Put some thought into your answer. Hint: Look at the top of part 1. What was the original purpose of generating this model? Problem #2 For this problem, we will look at the sounds made by crickets and the temperature. People have noted that the frequency of these cricket chirps seems to be able to describe the temperature. Cricket Sounds (per minute) 19, 16, 20, 18, 17, 20, 15, 17, 15, 16, -3, 17, 16, 17, 15 Fahrenheit Temperature 88.6, 71.6, 93.3, 84.3, 80.6, 75.2, 69.7, 82, 69.4, 83.3, 79.6, 82.6, 80.6, 83.5, 76.3 Complete the usual regression procedure and discussion as we have been doing. Be sure to check for all the usual things, such as outliers, influential points, linearity, etc. Provide a brief discussion of your model. As always, imagine you are providing this analysis to someone who has no background in statistics. That is, try to describe your regression model to people in the "real world" who are interested in what you have to show them but do not necessarily have any background in statistics. Introduction This assignment have you creating regression models using R. Please note that I am not providing you with reminders of what goes into this process. Review your lecture notes, and in particular, the R tutorial (document and video) on creating a regression model for the kinds of things that need to be done, things that need to be checked for, etc. The basic regression models you are asked to do here are not intended to be difficult. The key point is that in your document, you must demonstrate an understanding of the steps involved and the types of things that must be commented on. Also -- and I hope this is obvious (plus it's on your assignment checklist) -- whenever you draw a graph in R, be sure to include it in your homework document. R Code And, of course, be sure to include your R code somewhere in your document. You can either paste your code in one block or in pieces. But be sure to explain what your code does. As always, I don't expect your explanations to go into great detail, but you do have to demonstrate to the grader your understanding of the process and R code in order to receive full credit on the problems. At this point, you do not need to explain simple lines of code, such as creating a vector. However, you should explain things like where you are generating the model and anything else that is "new material" (in R). Other Notes Before deciding on your final regression model, you should, as always, check to see if there are outliers or influential observations. If you do observe outliers or influential points, you must then make a decision about what to do with them. Remember that if you remove an observation, you must have a very good reason for doing so, and you must also explain this reasoning in your analysis (in this case, your homework document). If you do decide to remove any observations, you must then create new vectors without those observations before embarking on your regression analysis. Hint: If you DO remove an observation from one variable, remember that you must ALSO remove it from the corresponding variable before doing your model.