SOLUTION: Because it is not practical to weigh bears in the field, researchers sought to develop a model to predict a bear's weight based on its length. Here are the results for a sample:
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Question 1196666: Because it is not practical to weigh bears in the field, researchers sought to develop a model to predict a bear's weight based on its length. Here are the results for a sample:
Total Length (cm) Weight (kg)
139.0 110
138.0 60
139.0 90
120.5 60
149.0 85
141.0 100
141.0 95
150.0 85
166.0 155
151.5 140
129.5 105
150.0 110
If the bear length was instead measured in inches (there are 0.3937 inches in 1 cm) and the weight was measured in pounds (there are 2.2 pounds in one kg), then the slope of the regression line would _______.
Group of answer choices
decrease by a factor of 0.179 (0.179 = 0.3937/2.2)
not change
increase by a factor of 0.179 (0.179 = 0.3737/2.2)
decrease by a factor of 5.588 (5.588 = 2.2/0.3937)
increase by a factor of 5.588 (5.588 = 2.2/0.3937) Found 2 solutions by ewatrrr, math_tutor2020:Answer by ewatrrr(24785) (Show Source):
Hi
LENGTH VS WEIGHT OF BEAR
First listed in cm & kg, then as listed in inches & pounds
139 110 54.72 242
138 60 54.33 132
139 90 54.72 198
120.5 60 47.44 132
149 85 58.66 187
141 100 55.51 220
141 95 55.51 209
150 85 59.06 187
166 155 65.35 341
151.5 140 59.65 308
129.5 105 50.98 231
150 110 59.06 242
Using Excel Function SLOPE(Ys, Xs) FOR BOTH LISTINGS to find
the slope of the regression line:
***** 5.588(1.694) = 9.467
the slope of the regression line increases by a factor of 5.588
Wish You the Best in your Studies.
The slope formula for a linear regression is this particularly complex equation
We don't need to calculate the value of m itself. We just need to see how m changes.
The x values represent the total length in cm
To go from cm to inches, we multiply by 0.3937 since 1 cm = 0.3937 inches approximately
This means each x updates to 0.3937x
Let's replace each x with 0.3937x and do a bit of algebra like so:
This shows that
or
and this occurs after we scaled the x values to get 0.3937x (i.e multiplied each x value by 0.3937 to convert from cm to inches)
Through similar steps we can replace each y with 2.2y and have this:
So we arrive at the fact when we scaled each y value by 2.2 (i.e. multiplied each weight by 2.2 to convert from kg to pounds)
You can think of it like this:
slope = rise/run
slope = (change in y)/(change in x)
new slope = (2.2*(change in y))/(0.3937*(change in x))
new slope = (2.2/0.3937)*( (change in y)/(change in x) )
new slope = (2.2/0.3937)*(old slope)
new slope = 5.588*(old slope)
Answer: Increase by a factor of 5.588
Since 5.588 = 2.2/0.3937
Note: you likely wont need to write down those complicated formulas for your homework. Those are for illustrative purposes mostly.
You could use the much faster method that the tutor @ewatrrr talked about.
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