Cigarette smoking and cancer have been linked. Assume the number of bladder cancer deaths (in deaths/100 thousand) and cigarette sales (in cigarettes/person) for 36 randomly selected countries are in the table below. X, cigarette sales (in cigarettes/person) Y, the number of bladder cancer deaths (in deaths/100 thousand) 25.91 5.21 23.44 2.93 28.6 4.46 40.46 5.6 22.57 3.21 21.84 2.91 42.4 6.54 24.96 5.27 28.27 4.46 31.1 5.11 20.08 2.94 20.94 3.64 22.12 4.23 19.96 2.89 18.06 3.25 21.17 4.04 14 3.31 28.64 5.98 29.14 5.3 27.56 4.04 21.58 4.65 18.24 2.99 26.18 4.09 16.08 3.06 27.91 4.75 26.38 4.47 33.6 4.78 26.92 4.69 23.75 3.95 28.04 3.2 25.89 4.63 29.18 4.99 22.86 4.78 23.78 4.89 30.34 3.46 23.44 2.86 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 4 decimal places. Include the restricted domain. equation: = + * X restricted domain: cigarettes/person <= X <= cigarettes/person 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 the number of bladder cancer deaths of a randomly selected country that has a cigarette sales of 40 cigarettes/person? Should you use the regression equation to predict the the number of bladder cancer deaths of a randomly selected country that has a cigarette sales of 58 cigarettes/person? Looking at your answers above, predict the the number of bladder cancer deaths 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 4 decimal places. The predicted the number of bladder cancer deaths for a randomly selected country that has a cigarette sales of cigarettes/person is g) Compute the residual for the following ordered pair in the data: (22.57, 3.21). Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 4 decimal places. The residual for the country with a cigarette sales of 22.57 cigarettes/person is Interpret what this value means in the context of this problem. The actual the number of bladder cancer deaths of a randomly selected country with a cigarette sales of 22.57 cigarettes/person is what was predicted.
Cigarette smoking and cancer have been linked. Assume the number of bladder cancer deaths (in deaths/100 thousand) and cigarette sales (in cigarettes/person) for 36 randomly selected countries are in the table below.
| X, cigarette sales (in cigarettes/person) | Y, the number of bladder cancer deaths (in deaths/100 thousand) |
|---|---|
| 25.91 | 5.21 |
| 23.44 | 2.93 |
| 28.6 | 4.46 |
| 40.46 | 5.6 |
| 22.57 | 3.21 |
| 21.84 | 2.91 |
| 42.4 | 6.54 |
| 24.96 | 5.27 |
| 28.27 | 4.46 |
| 31.1 | 5.11 |
| 20.08 | 2.94 |
| 20.94 | 3.64 |
| 22.12 | 4.23 |
| 19.96 | 2.89 |
| 18.06 | 3.25 |
| 21.17 | 4.04 |
| 14 | 3.31 |
| 28.64 | 5.98 |
| 29.14 | 5.3 |
| 27.56 | 4.04 |
| 21.58 | 4.65 |
| 18.24 | 2.99 |
| 26.18 | 4.09 |
| 16.08 | 3.06 |
| 27.91 | 4.75 |
| 26.38 | 4.47 |
| 33.6 | 4.78 |
| 26.92 | 4.69 |
| 23.75 | 3.95 |
| 28.04 | 3.2 |
| 25.89 | 4.63 |
| 29.18 | 4.99 |
| 22.86 | 4.78 |
| 23.78 | 4.89 |
| 30.34 | 3.46 |
| 23.44 | 2.86 |
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 4 decimal places.
Include the restricted domain.
equation: = + * X
restricted domain: cigarettes/person <= X <= cigarettes/person
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 the number of bladder cancer deaths of a randomly selected country that has a cigarette sales of 40 cigarettes/person?
Should you use the regression equation to predict the the number of bladder cancer deaths of a randomly selected country that has a cigarette sales of 58 cigarettes/person?
Looking at your answers above, predict the the number of bladder cancer deaths 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 4 decimal places.
- The predicted the number of bladder cancer deaths for a randomly selected country that has a cigarette sales of cigarettes/person is
g) Compute the residual for the following ordered pair in the data: (22.57, 3.21).
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 4 decimal places.
The residual for the country with a cigarette sales of 22.57 cigarettes/person is
Interpret what this value means in the context of this problem.
- The actual the number of bladder cancer deaths of a randomly selected country with a cigarette sales of 22.57 cigarettes/person is what was predicted.
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