READ INSTRUCTIONS BELOW:

An observational study showed a negative correlation between the Heights and Weights of a group of Sumo Wrestlers and NBA players when grouped together. What could be confounding the results? go to http://dataprogram.stat.illinois.edu/ Choose the data set Athletes' Heights and Weights from the "Choose a data set" Scroll Down Menu Click on Scatter Plots from the top menu bar. Choose Height for X and Weight for Y, then Select "Regression" to see the regression line.a.What's the regression equation? (It's given at the bottom of the scatter plot.)Weight=-0.1454*Height +250.7000Computer's answer now shown above.You are correct.

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b.You'd expect a strong positive correlation between height and weight. Instead we see a slight negative correlation (r= -0.01163). How is this possible?

IncorrectIt's due to the height to volume ratio, even though weight increases with height, it decreases proportionally.

IncorrectAs people grow, they lose baby fat and slim down.

IncorrectIt's not possible, there must be a computer error.

Correct:Sport is a confounderSumo wrestlers are both shorter and heavier than NBA players.

Computer's answer now shown above.You are correct.

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c.Within each group of athletes, the correlation between height and weight is...

Incorrectabout 0

Incorrectnegative

Correct:positive

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d.Split the data into 2 groups by following these 3 steps:1. Select "Choose split"2. Select "Sport" from the pull down menu on the right. You should see a red line splitting the data between 0 (NBA players are coded as 0's) and 1 (Sumo wrestlers are coded as 1's). If you don't see the red line click on "add a split"3. Go back to the main menu and select " Split Plot" and "Align plot". You should see the picture below. Click on "Regression" to see the regression linesNotice how the slopes for both NBA players and Sumo wrestlers are now positive. This is an example of Simpson' s Paradox, extreme confounding that makes the overall effect the opposite of what it really is.Write the regression equations given in the output for ...(Don't round your answers.)NBA players :Weight=+*HeightSumo wrestlers:Weight=+*HeightTries 0/3e.The regression equations above predict a 77 inch NBA player to weightlbs. and a 77 inch Sumo wrestler to weighlbs.Tries 0/2Question 4

Now we'll building a model that includes both height and sport as predictors to separate out their effects of each on weight. "Sport" is a 0-1 binary variable. NBA players are coded as "0's" and Sumo wrestlers are coded as "1's".In this data program:1. Select "Home" at the top of the screen.2. Select "Regression" in the top bar.3. From the "Choose Y Variable" pull down menu (top line of screen) select Weight4. From the "Choose X Variable" pull down menu check "Height" and "Sport"a.Fill in the blanks in the regression equation:(Do not round the numbers given in the printout.)Weight =+*(Height) +*(Sport)Tries 0/2b.The regression equation predicts a 77 inch NBA player to weightlbs. and a 77 inch Sumo wrestler to weightlbsTries 0/2c.What's the difference between the 2 weights in (b)?Tries 0/2d.The difference in weights is given by which following choice in Equation (a) above?

the slope for Sport

the intercept

the slope for Height