Expert: Sherry Wallin - 6/13/2010

Question
QUESTION: Please, explain in brief in the following questions.

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Use the following sample to answer questions 10 and 11:
102, 88, 102, 98, 41, 120

Question A. The sample mean is (91.8)
Question B. The sample variance is (727.4)

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When bears were anesthetized, researchers measured the distance (in inches) around their chest and they weighed the bears (in pounds). The results are given below for eight male bears.

x Chest (in) 26 45 54 49 41 49 44 19
y Weight (lb) 90 344 416 348 262 360 332 34

Question C.
Determine whether there is a significant linear correlation.
(Answer is 'significant'. Explain why, please.
Re: what is r & CV here?

Question D.
If so, find the regression equation.
y = ?

ANSWER: Yankgun~

A. add up the numbers and divide by the number of elements
B. The variance is found by a formula or on a statistical calculator. If you know the standard deviation s then the variance is just s^2. The formula follows from that fact that the variance is in units that are square of the original units, the result of squaring the deviations from the mean. since the mean is 91.8 then we want to sum each of the differences with the mean: (102 - 91.8)^2 + (88 - 91.8)^2 + (102 - 91.8)^2 + (98 - 91.8)^2 + (41 - 91.8)^2 + (120 - 91.8)^2 = 104.04 + 14.44 + 104.04 + 38.44 + 2580.64 + 795.24
= 3636.84. Now you need to divide by n-1 = 6-1=5 so 3636.84/5 = 727.368 ~= 727.4
C. I'm not sure what you mean by CV but r is the square root of the coefficient of determination. sqrt(SSR/SST) where SSR (regression sum of squares) is the the sum of the difference between y hat and the mean of y squared. Sum(y_hat - y_bar)^2. In words SSR is the variation in the observed values of the response variable explained by regression. SST is Sum(y-y_hat)^2. In words SST (total sum of squares) is the variance in the observed values of the response variable. Significant means that there is a correlation between the two quantities: the distance around the bear chest and the bears weight. i.e., that -1<=r<=1 where r is close to one in absolute value means that the regression equation is extremely useful for making predictions. This also means that there is a good line of fit.
D. I don't have a calculator at hand to use to calculate the values for the regression equation or a statistics computer package so my advice to you is to use a statistics package to find the regression equation.


Math Prof

Note:  there are other ways to get r. You can find r using S_xy/sqrt(S_xx*S_yy) also.

---------- FOLLOW-UP ----------

QUESTION: Dear Sherry,
I failed to get 91.8 in the first quesiton (Q:a). What is wrong with my calc?

And. CV = 0.707
Please, just guess what CV stands for,possibly.

Answer
maybe correlation variance??
You need to show me how you are obtaining your answer for the sample mean so I can tell you where you are going wrong.

Math Prof

Coefficient of variation - Wikipedia, the free encyclopedia
In probability theory and statistics, the coefficient of variation (CV) is a normalized measure of dispersion of a .... Correlation and regression analysis ...
en.wikipedia.org/wiki/Coefficient_of_variation - Cached - Similar