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regression equation

 
 
Reply Mon 11 Jan, 2016 08:51 am
For a group of 10 army recruits, the weight (in lbs) and exercise capacity (in METS) were
recorded.

Weight: 125 159 150 161 178 182 191 200 224 250

Exercise
Capacity: 30 29 25 26 27 29 26 20 15 19

The regression equation to predict exercise capacity from weight was found to be: y = 43.81 - 0.105x

( choose the correct answer:)
A- The correlation for these variables was found to be r = -0.79, this tells us that:

1- For each additional pound of body weight, the exercise capacity decreases by
0.79 METS.


2- As the weight of a recruit increases, the recruit’s exercise capacity also tends
to increase.


3- As a recruit gains weight this causes his exercise capacity to decrease.


4- There is no linear association between body weight and exercise capacity.


5- As the weight of a recruit increases, the recruit’s exercise capacity tends to
decrease.

B_ Interpret the slope of the regression equation developed to predict exercise capacity from weight.

1-For each additional 0.105 MET of exercise capacity, the weight decreases by
one pound.

2- For each additional pound of weight, the exercise capacity increases by 43.81
METS on average.

3- For each additional pound of weight, the exercise capacity decreases by
10.5%.

4- For each additional pound of weight, the exercise capacity decreases by
0.105 METS on average.
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engineer
 
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Reply Mon 11 Jan, 2016 09:47 am
@topboy411,
topboy411 wrote:

The regression equation to predict exercise capacity from weight was found to be: y = 43.81 - 0.105x

( choose the correct answer:)
A- The correlation for these variables was found to be r = -0.79, this tells us that:

1- For each additional pound of body weight, the exercise capacity decreases by
0.79 METS.

No. From the equation, you can see that when x (weight) goes up by 1 pound, y (exercise capacity) goes down by 0.105
topboy411 wrote:
2- As the weight of a recruit increases, the recruit’s exercise capacity also tends to increase.

No it goes down.
topboy411 wrote:
3- As a recruit gains weight this causes his exercise capacity to decrease.

Increased weight correlates with lower exercise capacity. That doesn't mean that it "causes" it, just that it correlates. Rooster crowing and sunrises are correlated, but the rooster does not cause the sun to rise.
topboy411 wrote:

4- There is no linear association between body weight and exercise capacity.

An R^2 of 0.79 is pretty good so there is no reason to say there is no association.
topboy411 wrote:

5- As the weight of a recruit increases, the recruit’s exercise capacity tends to decrease.

Yes.
topboy411 wrote:

B_ Interpret the slope of the regression equation developed to predict exercise capacity from weight.

1-For each additional 0.105 MET of exercise capacity, the weight decreases by
one pound.

That is saying it backwards - exercise capacity does not predict weight, although one pound decrease does imply 0.105 MET of exercise capacity gain.
topboy411 wrote:

2- For each additional pound of weight, the exercise capacity increases by 43.81 METS on average.

No, 43.81 is the zero intercept in that equation and is not associated with weight.
topboy411 wrote:

3- For each additional pound of weight, the exercise capacity decreases by
10.5%.

No, 0.105 METS, not percent
topboy411 wrote:

4- For each additional pound of weight, the exercise capacity decreases by
0.105 METS on average.

Yes.
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