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Try a Free Sample of Grant's Book and Audio Lectures
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Don't have my book or audio? You can download a free sample of my book and audio lectures containing all of 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.
Tips for Distance Assignment 2
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Here is a link to the actual assignment, for those of you who don't have it: Study Lesson 2: Regression and Correlation in my book, if you have it, to prepare for this assignment.
Of course, always seek out assistance from my book, your
course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to the test. Similar to the concepts I discuss in my Lesson 2, #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).
Similar to the concepts I discuss in my Lesson 2, #4.
Note that you can use the formulas used to compute the slope and intercept which I use in Lesson 2, #5, for example, to use a little algebra and solve for r. Be careful that you are properly identifying which
variable is x and which is y so that you properly assign the values of x-bar, y-bar, Sx, and Sy.
Be sure to study Lesson 2, #1 at the very least before attempting this question.
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.
I show you how to compute a residual in my Lesson 2, #1(j). This is a two-step process. You must first make the
appropriate prediction, then compute the residual.
I show you how to interpret a slope throughout Lesson 2, and give you a specific example in #1(f) of my book.
By now, you should know which of these choices is true. Don't confuse the slope b with the correlation r.
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