Math assignment (needs excel and word) needs to be finished in 3 hrs
Assignment Three
(30 points)
Part 1: Children In Poverty
(17 Points – each part is worth 2 points unless noted)
1. Open the file
ChildrenBelowPovertyLevel.xls
containing data from the Census Bureau.
a. Make an X-Y scatter plot of the data including the trendline and the R-squared value. Note that Excel will, in most cases, put a legend on your graph by default. When there is only one data series (as here), you don’t need a legend, and it really should be removed. It should include all the details discussed in the reading on graphs. Paste this chart in your Word document. (3 points)
b. Predict what percentage of children will be below the poverty level in the year 2012 using the trendline equation. Type your result in your Word document.
c. How much confidence do you have in this prediction? In 3-4 sentences write an argument that either supports or does not support your prediction of the percentage of children below the poverty level 2012. (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive full credit.) (3 points)
d. Use the regression equation (the equation on the graph) to predict when 100% of children in the US will be below the poverty level. Show your workand type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.)
e. How much confidence do you have in this prediction?
f. Predict the percentage of children below the poverty level in the year 2016 using the trendline equation. Type your result in your Word document.
g. The actual percentage of children below the poverty level in the year 2012 was 21.3%. In 2016 that percentage fell to 17.6%. Compare these facts to your answers from parts (b) and (f). Now, taking into account all your answers above, write a thoughtful analysis of the usefulness of linear modeling. (You may choose to comment on when and how it is most effective to use linear models and also what cautions we should take when using linear models.) To receive full points, you must truly analyze the work you have done above. A simple summary of your findings will receive zero points. (3 points)
Part 2: Divorce in the US
(13 Points – each part is worth 2 points unless noted)
2. Open the file
DivorceRate.xls
which contains data on the rate of divorce per 1,000 people in the U.S. from 1960 to 2015.
a. Make an XY scatter graph of the years and the rate of divorce. Add an appropriate trendline to the data, along with an equation, R^2 value, and all other effective graphing components. (Hint: Be extremely thoughtful about the trendline you use in this case. Be sure to check the trendline guidelines to verify that the trendline you use is appropriate. You will lose points if your trendline is not appropriate.) It should include all the details discussed in the week 3 reading on graphs. Paste the resulting chart into your Word document. (3 points)
b. Use the regression equation to predict the rate of divorce in 2018. Type your answer in your Word document. (1 point)
c. How much confidence do you have in your prediction from part b? (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive ful credit.) (3 points)
d. Use your regression equation to predict when there will be no divorce in the US. Show your work and type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.) (1 point)
e. Do you have confidence in your prediction from part d? Explain by writing a confidence argument.
f. Use your regression equation to predict what the rate of divorce will be in 2050. Type your answer into your Word document – don’t forget to include units! (1 point)
g. How much confidence do you have in your prediction from part f? Explain by writing a confidence argument.
Assignment Three
Part 1: Children In Poverty
1.
Open the file ChildrenBelowPovertyLevel.xls containing data from the Census Bureau.
a. Make an X-Y scatter plot of the data including the trendline and the R-squared value. Note that Excel will, in most cases, put a legend on your graph by default. When there is only one data series (as here), you don’t need a legend, and it really should be removed. It should include all the details discussed in the reading on graphs. Paste this chart in your Word document. (3 points)
b. Predict what percentage of children will be below the poverty level in the year 2012 using the trendline equation. Type your result in your Word document.
c. How much confidence do you have in this prediction? In 3-4 sentences write an argument that either supports or does not support your prediction of the percentage of children below the poverty level 2012. (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive full credit.) (3 points)
d. Use the regression equation (the equation on the graph) to predict when 100% of children in the US will be below the poverty level. Show your work and type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.)
e. How much confidence do you have in this prediction?
f. Predict the percentage of children below the poverty level in the year 2016 using the trendline equation. Type your result in your Word document.
g. The actual percentage of children below the poverty level in the year 2012 was 21.3%. In 2016 that percentage fell to 17.6%. Compare these facts to your answers from parts (b) and (f). Now, taking into account all your answers above, write a thoughtful analysis of the usefulness of linear modeling. (You may choose to comment on when and how it is most effective to use linear models and also what cautions we should take when using linear models.) To receive full points, you must truly analyze the work you have done above. A simple summary of your findings will receive zero points. (3 points)
Part 2: Divorce in the US
(13 Points – each part is worth 2 points unless noted)
2. Open the file DivorceRate.xls which contains data on the rate of divorce per 1,000 people in the U.S. from 1960 to 2015.
a. Make an XY scatter graph of the years and the rate of divorce. Add an appropriate trendline to the data, along with an equation, R^2 value, and all other effective graphing components. (Hint: Be extremely thoughtful about the trendline you use in this case. Be sure to check the trendline guidelines to verify that the trendline you use is appropriate. You will lose points if your trendline is not appropriate.) It should include all the details discussed in the week 3 reading on graphs. Paste the resulting chart into your Word document. (3 points)
b. Use the regression equation to predict the rate of divorce in 2018. Type your answer in your Word document. (1 point)
c. How much confidence do you have in your prediction from part b? (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive ful credit.) (3 points)
d. Use your regression equation to predict when there will be no divorce in the US. Show your work and type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.) (1 point)
e. Do you have confidence in your prediction from part d? Explain by writing a confidence argument.
f. Use your regression equation to predict what the rate of divorce will be in 2050. Type your answer into your Word document – don’t forget to include units! (1 point)
g. How much confidence do you have in your prediction from part f? Explain by writing a confidence argument.
Submit all your excel and word files
Sheet1
| Percent of Children Below Poverty Level from | 2000 | 2010 |
| [Source: Bureau of Labor Statistics] | ||
| Year | Percentage | |
| 15.60 | ||
| 2001 | 15.80 | |
| 2002 | 16.30 | |
| 2003 | 17.20 | |
| 2004 | 17.30 | |
| 2005 | 17.10 | |
| 2006 | 16.90 | |
| 2007 | 17.60 | |
| 2008 | 18.50 | |
| 2009 | 20.10 | |
| 21.50 |
Sheet1
| US Rate of Divorce from | 1960 | 2015 | |||
| [Source: US National Center for Health Statistics] | |||||
| Year | Rate per 1,000 population | ||||
| 2.20 | |||||
| 1965 | 2.50 | ||||
| 1970 | 3.5 | ||||
| 1971 | 3.7 | ||||
| 1972 | 4 | ||||
| 1973 | 4.3 | ||||
| 1974 | 4.6 | ||||
| 1975 | 4.8 | ||||
| 1976 | 5.00 | ||||
| 1977 | |||||
| 1978 | 5.10 | ||||
| 1979 | 5.30 | ||||
| 1980 | 5.20 | ||||
| 1981 | |||||
| 1982 | |||||
| 1983 | |||||
| 1984 | |||||
| 1985 | |||||
| 1986 | 4.90 | ||||
| 1987 | |||||
| 1988 | |||||
| 1989 | 4.7 | ||||
| 1990 | |||||
| 1991 | |||||
| 1992 | |||||
| 1993 | |||||
| 1994 | |||||
| 1995 | 4.4 | ||||
| 1996 | |||||
| 1997 | |||||
| 1998 | 4.2 | ||||
| 1999 | 4.1 | ||||
| 2000 | |||||
| 2001 | |||||
| 2002 | 3.9 | ||||
| 2003 | 3.8 | ||||
| 2004 | |||||
| 2005 | 3.6 | ||||
| 2006 | |||||
| 2007 | |||||
| 2008 | |||||
| 2009 | |||||
| 2010 | |||||
| 2011 | |||||
| 2012 | 3.4 | ||||
| 2013 | 3.3 | ||||
| 2014 | 3.2 | ||||
| 3.1 |
Justifying your prediction by writing a
Confidence Argument
After you make a prediction, you are generally asked about your confidence in
making that prediction. How do you state your prediction and provide
supporting evidence to support your conclusion?
There are three mandatory parts to a confidence argument.
1) What is the R2 value? The R2 value tells us how well the model fits our
data. R2 is a number between 0 and 1. The closer to 1, the stronger the model.
Here are some basic guidelines for this class:
If 0.7 < R2 < 1, that is considered a strong fit. If 0.4 < R2 < 0.7, that is considered a moderate fit. If 0 < R2 < 0.4, that is considered a weak fit. (You might even question whether or
not you can use the model to make predictions when your R2 value is so low.
Keep in mind that the R2 value does not tell us if our prediction is accurate.
Our predictions will hardly ever be exact, and there is no way to predict the
future with 100% accuracy. The R2 doesn’t tell us about our prediction at all! It
tells us about the model we are using to make the prediction. So it is very
possible for you to use a strong model to make a horrible prediction.
2) How far into the future/past are you predicting? You need to note
exactly how many years into the future from your last data point you are
looking (or how many years into the past from your first data point). Then you
need to determine how the length of time impacts your confidence level.
A “rule of thumb” is that you should be concerned about predictions more than
25 years away from your data in either direction. 25 years is about enough
time for generational/societal/technological shifts to occur that will likely impact
your prediction. If you feel your prediction is too far away from the data, you
must state WHY – what do you think might change in that time frame that
would impact your prediction?
3) Real world support. This is often the most difficult part of the argument for
students to write. You must provide some reasons for why you think the trend
will continue (or reasons for why you think it will not).
Answers that are NOT acceptable for this portion of the argument are:
“It makes sense.” I’m glad when things make sense to you, but you need to
explain to your reader WHY/HOW they make sense. We can’t see into your mind!
“The trend has been increasing/decreasing for the last ___ years, so I bet it
will continue to do so.” This is faulty logic. The marriage rate in the US was
going strong for many, many decades! Until the 60’s came, with free love, and all
the sudden the trend changed.
**4) “Overall…” At the end of your argument you should always include a final
sentence that sums up your overall confidence level. It’s helpful to start the
sentence with “Overall…,” but you can write it however you wish.
Let’s look at some of the predictions made on the previous page for women’s
world records in the mile run:
Prediction #1:
What will the women’s world record be in 1999? We predicted it would be 246
seconds.
How much confidence do you have in your prediction?
(Part 1 of the confidence argument is in blue. Part 2 of the confidence
argument is in red. Part three of the confidence argument is in green. In
practice you will probably end up combining parts 2 and 3 on many
occasions. The overall conclusion sentence is in orange.)
My R^2 value is .9342, which shows the model is a good fit for my data. I am
only looking three years into the future from my data, which isn’t too long. I
don’t think that women have reached the physical limits of how fast the female
body can run a mile, so this is certainly possible. I do notice that the data
points seem to be leveling off slightly toward the end of the graph. This may
mean that my prediction is a little lower that what the actual record will be in
1999. Overall, I have moderately strong confidence in this prediction.
Prediction #2:
When will the women’s world record be 3 minutes? We predicted that the
women’s world record will be 3 minutes in the year 2070.
How much confidence do you have in your prediction?
(Part 1 of the confidence argument is in blue. Part 2 of the confidence
argument is in red. Part three of the confidence argument is in green. In
practice you will probably end up combining parts 2 and 3 on many
occasions. The overall conclusion sentence is in orange.)
My R^2 value is .9342, which shows the model is a good fit for my data. I am
predicting 74 years into the future from my data, which is a pretty long time. I
don’t think it is physically possible for the female body to run a mile in three
minutes. I think that before 2070 we will have reached the physical limits of the
female body, making this prediction impossible. Therefore, I have no
confidence in this prediction.
Note: As a teacher, I am not looking for every student to have the same
answer. I am looking for every student to have a well constructed argument. To
give you an example of how student answers can differ but still be correct,
here is an alternative answer to the previous question:
My R^2 value is .9342, which shows the model is a good fit for my data. I am
predicting 74 years into the future from my data, which is a pretty long
time. Science is finding more and more ways to expand what the human body
can do. I think we are just at the beginning of a performance enhancing drug
revolution, that some day may allow our bodies to do things we never thought
were possible. While I don’t think it’s very likely that a woman will be able to run
a 3 minute mile in 2070, I think that it is possible. Therefore, I have some small
confidence in this prediction.
- Examples:
Assignment Three
Part 1: Children In Poverty
1.
Open the file ChildrenBelowPovertyLevel.xls containing data from the Census Bureau.
a. Make an X-Y scatter plot of the data including the trendline and the R-squared value. Note that Excel will, in most cases, put a legend on your graph by default. When there is only one data series (as here), you don’t need a legend, and it really should be removed. It should include all the details discussed in the reading on graphs. Paste this chart in your Word document. (3 points)
b. Predict what percentage of children will be below the poverty level in the year 2012 using the trendline equation. Type your result in your Word document.
c. How much confidence do you have in this prediction? In 3-4 sentences write an argument that either supports or does not support your prediction of the percentage of children below the poverty level 2012. (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive full credit.) (3 points)
d. Use the regression equation (the equation on the graph) to predict when 100% of children in the US will be below the poverty level. Show your work and type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.)
e. How much confidence do you have in this prediction?
f. Predict the percentage of children below the poverty level in the year 2016 using the trendline equation. Type your result in your Word document.
g. The actual percentage of children below the poverty level in the year 2012 was 21.3%. In 2016 that percentage fell to 17.6%. Compare these facts to your answers from parts (b) and (f). Now, taking into account all your answers above, write a thoughtful analysis of the usefulness of linear modeling. (You may choose to comment on when and how it is most effective to use linear models and also what cautions we should take when using linear models.) To receive full points, you must truly analyze the work you have done above. A simple summary of your findings will receive zero points. (3 points)
Part 2: Divorce in the US
(13 Points – each part is worth 2 points unless noted)
2. Open the file DivorceRate.xls which contains data on the rate of divorce per 1,000 people in the U.S. from 1960 to 2015.
a. Make an XY scatter graph of the years and the rate of divorce. Add an appropriate trendline to the data, along with an equation, R^2 value, and all other effective graphing components. (Hint: Be extremely thoughtful about the trendline you use in this case. Be sure to check the trendline guidelines to verify that the trendline you use is appropriate. You will lose points if your trendline is not appropriate.) It should include all the details discussed in the week 3 reading on graphs. Paste the resulting chart into your Word document. (3 points)
b. Use the regression equation to predict the rate of divorce in 2018. Type your answer in your Word document. (1 point)
c. How much confidence do you have in your prediction from part b? (Important: Use the language you learned in the reading for this week. There are three major components you must include in your argument to receive ful credit.) (3 points)
d. Use your regression equation to predict when there will be no divorce in the US. Show your work and type your answer into your Word document. (As long as you show how you set up the problem, that is enough. You do not need to show every step you used when solving.) (1 point)
e. Do you have confidence in your prediction from part d? Explain by writing a confidence argument.
f. Use your regression equation to predict what the rate of divorce will be in 2050. Type your answer into your Word document – don’t forget to include units! (1 point)
g. How much confidence do you have in your prediction from part f? Explain by writing a confidence argument.
Submit all your excel and word files
Sheet1
| Percent of Children Below Poverty Level from | 2000 | 2010 |
| [Source: Bureau of Labor Statistics] | ||
| Year | Percentage | |
| 15.60 | ||
| 2001 | 15.80 | |
| 2002 | 16.30 | |
| 2003 | 17.20 | |
| 2004 | 17.30 | |
| 2005 | 17.10 | |
| 2006 | 16.90 | |
| 2007 | 17.60 | |
| 2008 | 18.50 | |
| 2009 | 20.10 | |
| 21.50 |
Sheet1
| US Rate of Divorce from | 1960 | 2015 | |||
| [Source: US National Center for Health Statistics] | |||||
| Year | Rate per 1,000 population | ||||
| 2.20 | |||||
| 1965 | 2.50 | ||||
| 1970 | 3.5 | ||||
| 1971 | 3.7 | ||||
| 1972 | 4 | ||||
| 1973 | 4.3 | ||||
| 1974 | 4.6 | ||||
| 1975 | 4.8 | ||||
| 1976 | 5.00 | ||||
| 1977 | |||||
| 1978 | 5.10 | ||||
| 1979 | 5.30 | ||||
| 1980 | 5.20 | ||||
| 1981 | |||||
| 1982 | |||||
| 1983 | |||||
| 1984 | |||||
| 1985 | |||||
| 1986 | 4.90 | ||||
| 1987 | |||||
| 1988 | |||||
| 1989 | 4.7 | ||||
| 1990 | |||||
| 1991 | |||||
| 1992 | |||||
| 1993 | |||||
| 1994 | |||||
| 1995 | 4.4 | ||||
| 1996 | |||||
| 1997 | |||||
| 1998 | 4.2 | ||||
| 1999 | 4.1 | ||||
| 2000 | |||||
| 2001 | |||||
| 2002 | 3.9 | ||||
| 2003 | 3.8 | ||||
| 2004 | |||||
| 2005 | 3.6 | ||||
| 2006 | |||||
| 2007 | |||||
| 2008 | |||||
| 2009 | |||||
| 2010 | |||||
| 2011 | |||||
| 2012 | 3.4 | ||||
| 2013 | 3.3 | ||||
| 2014 | 3.2 | ||||
| 3.1 |
Justifying your prediction by writing a
Confidence Argument
After you make a prediction, you are generally asked about your confidence in
making that prediction. How do you state your prediction and provide
supporting evidence to support your conclusion?
There are three mandatory parts to a confidence argument.
1) What is the R2 value? The R2 value tells us how well the model fits our
data. R2 is a number between 0 and 1. The closer to 1, the stronger the model.
Here are some basic guidelines for this class:
If 0.7 < R2 < 1, that is considered a strong fit. If 0.4 < R2 < 0.7, that is considered a moderate fit. If 0 < R2 < 0.4, that is considered a weak fit. (You might even question whether or
not you can use the model to make predictions when your R2 value is so low.
Keep in mind that the R2 value does not tell us if our prediction is accurate.
Our predictions will hardly ever be exact, and there is no way to predict the
future with 100% accuracy. The R2 doesn’t tell us about our prediction at all! It
tells us about the model we are using to make the prediction. So it is very
possible for you to use a strong model to make a horrible prediction.
2) How far into the future/past are you predicting? You need to note
exactly how many years into the future from your last data point you are
looking (or how many years into the past from your first data point). Then you
need to determine how the length of time impacts your confidence level.
A “rule of thumb” is that you should be concerned about predictions more than
25 years away from your data in either direction. 25 years is about enough
time for generational/societal/technological shifts to occur that will likely impact
your prediction. If you feel your prediction is too far away from the data, you
must state WHY – what do you think might change in that time frame that
would impact your prediction?
3) Real world support. This is often the most difficult part of the argument for
students to write. You must provide some reasons for why you think the trend
will continue (or reasons for why you think it will not).
Answers that are NOT acceptable for this portion of the argument are:
“It makes sense.” I’m glad when things make sense to you, but you need to
explain to your reader WHY/HOW they make sense. We can’t see into your mind!
“The trend has been increasing/decreasing for the last ___ years, so I bet it
will continue to do so.” This is faulty logic. The marriage rate in the US was
going strong for many, many decades! Until the 60’s came, with free love, and all
the sudden the trend changed.
**4) “Overall…” At the end of your argument you should always include a final
sentence that sums up your overall confidence level. It’s helpful to start the
sentence with “Overall…,” but you can write it however you wish.
Let’s look at some of the predictions made on the previous page for women’s
world records in the mile run:
Prediction #1:
What will the women’s world record be in 1999? We predicted it would be 246
seconds.
How much confidence do you have in your prediction?
(Part 1 of the confidence argument is in blue. Part 2 of the confidence
argument is in red. Part three of the confidence argument is in green. In
practice you will probably end up combining parts 2 and 3 on many
occasions. The overall conclusion sentence is in orange.)
My R^2 value is .9342, which shows the model is a good fit for my data. I am
only looking three years into the future from my data, which isn’t too long. I
don’t think that women have reached the physical limits of how fast the female
body can run a mile, so this is certainly possible. I do notice that the data
points seem to be leveling off slightly toward the end of the graph. This may
mean that my prediction is a little lower that what the actual record will be in
1999. Overall, I have moderately strong confidence in this prediction.
Prediction #2:
When will the women’s world record be 3 minutes? We predicted that the
women’s world record will be 3 minutes in the year 2070.
How much confidence do you have in your prediction?
(Part 1 of the confidence argument is in blue. Part 2 of the confidence
argument is in red. Part three of the confidence argument is in green. In
practice you will probably end up combining parts 2 and 3 on many
occasions. The overall conclusion sentence is in orange.)
My R^2 value is .9342, which shows the model is a good fit for my data. I am
predicting 74 years into the future from my data, which is a pretty long time. I
don’t think it is physically possible for the female body to run a mile in three
minutes. I think that before 2070 we will have reached the physical limits of the
female body, making this prediction impossible. Therefore, I have no
confidence in this prediction.
Note: As a teacher, I am not looking for every student to have the same
answer. I am looking for every student to have a well constructed argument. To
give you an example of how student answers can differ but still be correct,
here is an alternative answer to the previous question:
My R^2 value is .9342, which shows the model is a good fit for my data. I am
predicting 74 years into the future from my data, which is a pretty long
time. Science is finding more and more ways to expand what the human body
can do. I think we are just at the beginning of a performance enhancing drug
revolution, that some day may allow our bodies to do things we never thought
were possible. While I don’t think it’s very likely that a woman will be able to run
a 3 minute mile in 2070, I think that it is possible. Therefore, I have some small
confidence in this prediction.
- Examples: