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There was a typo in my tips. I meant to say Lesson 4 in my tips for question 3 below. Please read below for more tips.
Midterm Exam Prep Seminar ($40) is Oct. 23.
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Don't have my book or audio? You can download a free sample of my book and audio lectures containing Lesson 1:
Did you read my tips on how to study and learn this course? If not, here is a link to those important suggestions: The department posted solutions for Assignment 1 (these are not my solutions). Click here.Here is a link to the actual assignment, in case you don't have it handy: Study Lesson 2 (Regression and Correlation), Lesson 3 (Designing Samples and Experiments), and Lesson 4 (Density Curves and The Normal Distribution) from my Basic
Stats 1 book to prepare for this assignment.
Similar to my Lesson 2, question 3.
- In each case, ask yourself, would you expect a positive correlation, a negative correlation, or neither? Remember, a positive correlation tells us, as x gets bigger, y gets bigger,
whereas a negative correlation tells us, as x gets bigger, y gets smaller.
- If you do expect a nonzero correlation, would you expect the correlation to be perfect (1 or -1)? Or, would it be just not 0.
- Unless it is obvious there would be a perfect correlation or no correlation at all (r=0), they are not expecting you to know the exact value of r, just is the value of r plausible. For example, if you believe there would be a negative correlation but not a
perfect falling line, r could conceivably be any negative number between 0 and -1. So r could be -0.38 for all you know, or -0.92. But r couldn't be -1.23 (because r is always between -1 and 1).
Be sure to study Lesson 2, question 1 at the very least before attempting this question.
Part (a)
NEVER FORGET:
r-squared tells you the proportion (or
percentage) of the variation of y explained by the regression with x. If they ever give you a percentage or a proportion in a linear regression context, they are almost certainly telling you r-squared. If they ever ask for "the proportion of the variation of [blank] ... explained by the regression with [blank]..." they are asking you for r-squared.
If you are given r-squared, then it is a simple matter of square rooting it to establish
r. But be careful! What sign should r have? r-squared does not tell you that. Look at the problem in context and think about that. Is there a positive correlation or a negative correlation? Remember that the slope always has the same sign as r.
Part (b)
I show you how to compute a residual in my Lesson 2, question 1(j). This is a two-step process. You must first make
the appropriate prediction, then compute the residual.
Part (c)
I show you how to interpret a slope throughout Lesson 2, and give you a specific example in question 1(f) of my book.
Study Lesson 4, questions 1 and 2 to get some practice at working with density curves. Shade the appropriate region they describe in each question, and compute that area knowing the area of a triangle is 1/2 base times height, and the area of a rectangle is base
times height.
Part (e) Your answer to part (b) should help you estimate approximately where to mark x on the horizontal axis. Then shade the region between 0.25 and x. You have been given the area of that region, so you can work backwards. You know the area, you know the height, so what must the width be? Be careful, though, the width is not x. You start at 0.25 and walk the width towards x, so how can you use the width to get
x? I strongly recommend you read my section in Lesson 4 about the Z Bell Curve Ladder and the X Bell Curve Ladder and make the ladder every single time you have a bell curve problem. Then climb up or down the rungs. Many
students are guilty of not thinking a problem through, and consequently looking at Table A too soon. The ladder trains you to focus on the fact that Table A deals with z scores and Left Areas, but your problem may be interested in something else.
You will be using Table A for much of this
assignment. Here is a link where you can download the table if you have not already done so:
Make sure you have studied all my X-Bell Curve problems (questions 9 to the end)
in Lesson 4 before you attempt this question. Make sure you use the X-Bell Curve Ladder to help you work your way through each part of this question.
See my advice for question 4 above.
Make sure you have studied Lesson 3 in my book before you answer this and the remaining questions in this assignment. You should especially look at questions 6 and 7 as illustrations of the Three Principles of Experimental Design and
examples of identifying the various factors, factor levels, treatments, experimental units, and response variable for an experiment. As well as identifying what type of experiment it may be (randomized comparative experiment, block design, matched pairs design).
When they ask for the treatments (part (d)), tell them not only how many treatments there are in the experiment, but what the exact treatments are. For example, in my Lesson 3, question
7(b), I wouldn't just say that there are 6 treatments. I would say the 6 treatments are: Dog Food A served early; Dog Food B served early; etc. up to Dog Food C served late.
Here are some extra things to clarify the three principles of experimental design which you may be asked to discuss in questions on an exam (but were not asked in this assignment).
Note that randomization is used in experiments to randomly
determine which unit gets which treatment (when there are many units and each unit will be given exactly one treatment), or to randomly determine the order the treatments will be administered (when one unit is going to receive two or more treatments).
When discussing the principle of control, there is no need to speculate. Discuss the actual things they have obviously done to control outside factors or
certainly should have done.
By repetition, they mean what I call replication; quite simply: how many times is each treatment being applied?
Note also that we learned in Lesson 2 that correlation does not imply causation. Just because a pattern is observed between x and y does not mean we have proven that x causes y. But, the whole point of designing an experiment is to identify possible cause and
effect. If an experiment has been designed properly, we have every right to believe we have proven that blank causes blank, provided we have seen a significant difference in the response variable, when applying one treatment as compared to another.
Experiments can prove causation!
See my advice for question 6 above.
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