The height (in inches) and weight (in pounds) of 20 randomly selected baseball players are in the table below. X, height (in inches) Y, weight (in pounds) 73 190 74 200 75 215 76 212 73 210 77 194 78 235 76 224 77 235 75 180 74 210 75 220 74 228 74 200 76 185 72 180 75 210 72 180 72 208 72 170 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: inches <= X <= inches
The height (in inches) and weight (in pounds) of 20 randomly selected baseball players are in the table below.
| X, height (in inches) | Y, weight (in pounds) |
|---|---|
| 73 | 190 |
| 74 | 200 |
| 75 | 215 |
| 76 | 212 |
| 73 | 210 |
| 77 | 194 |
| 78 | 235 |
| 76 | 224 |
| 77 | 235 |
| 75 | 180 |
| 74 | 210 |
| 75 | 220 |
| 74 | 228 |
| 74 | 200 |
| 76 | 185 |
| 72 | 180 |
| 75 | 210 |
| 72 | 180 |
| 72 | 208 |
| 72 | 170 |
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: inches <= X <= inches
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.
e) Interpret the Y-intercept from part c in the context of this problem. Include units.
- When is , we expect to be
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 weight of a randomly selected baseball player that has a height of 74 inches?
Should you use the regression equation to predict the weight of a randomly selected baseball player that has a height of 81 inches?
Looking at your answers above, predict the weight 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 weight for a randomly selected baseball player that has a height of inches is
g) Compute the residual for the following ordered pair in the data: (74, 200).
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 baseball player with a height of 74 inches is
Interpret what this value means in the context of this problem.
- The actual weight of a randomly selected baseball player with a height of 74 inches is what was predicted.
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