When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 18 sets of skeletal remains. The data are in the table below. X, length of metacarpal (in cm) Y, height (in cm) 51 180 45 173 47 175 42 165 44 171 40 163 42 175 44 173 39 159 45 173 46 175 52 176 50 181 50 178 49 170 46 173 38 157 49 185 a) State the random variables. rv X = of rv Y = of b) Make a scatterplot of X versus Y in StatCrunch (optional). Why do we wish to sketch a scatterplot? c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 2 decimal places. Include the restricted domain. equation: = + * X restricted domain: cm <= X <= cm
When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of their metacarpal bone (in cm) were collected for 18 sets of skeletal remains. The data are in the table below.
| X, length of metacarpal (in cm) | Y, height (in cm) |
|---|---|
| 51 | 180 |
| 45 | 173 |
| 47 | 175 |
| 42 | 165 |
| 44 | 171 |
| 40 | 163 |
| 42 | 175 |
| 44 | 173 |
| 39 | 159 |
| 45 | 173 |
| 46 | 175 |
| 52 | 176 |
| 50 | 181 |
| 50 | 178 |
| 49 | 170 |
| 46 | 173 |
| 38 | 157 |
| 49 | 185 |
a) State the random variables.
rv X = of
rv Y = of
b) Make a
c) Find the equation of the best-fitting line (the least squares regression equation).
Round values to 2 decimal places.
Include the restricted domain.
equation: = + * X
restricted domain: cm <= X <= cm
d) Interpret the slope from part c in the context of this problem. (Pay attention to the units)
- Every time we increase by we can expect to by on average.
Hint: Your interpretation for the slope should be something like: Every time we increase (x) by (1) (unit), we can expect (y) to increase by (slope) (units). Just fill in the parts in parentheses with the information from this example.
e) Interpret the Y-intercept from part c in the context of this problem. Include units.
- When is , we expect to be
Hint: Your interpretation for the y-intercept should be something like: When (x) is (0) (units), we expect (y) to be (y-intercept) (units). Again, just fill in the information from this particular example.
Does it make sense to interpret the Y-intercept on this problem?
Why or why not?
f) Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 48 cm?
Should you use the regression equation to predict the height of a randomly selected set of skeletal remains that has a length of metacarpal of 61 cm?
Looking at your answers above, predict the height for the one above that it made sense to do so.
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 2 decimal places.
- The predicted height for a randomly selected set of skeletal remains that has a length of metacarpal of cm is
g) Compute the residual for the following ordered pair in the data: (52, 176).
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 2 decimal places.
The residual for the set of skeletal remains with a length of metacarpal of 52 cm is
Interpret what this value means in the context of this problem.
- The actual height of a randomly selected set of skeletal remains with a length of metacarpal of 52 cm is what was predicted.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
