In an effort to decide if there is an association between the year of a postal i
ID: 3045504 • Letter: I
Question
In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail the data were gathered from the US Postal Service. In 1981, the US Postal Service changed their rates twice on March 22 and +November Year Rate 1971 1974 1975 1978 1981 1981 1985 1988 1991 1995 1999 2001 2002 2006 2007 2008 2009 2012 2013 2017 0.08 0.1 0.13 0.15 0.18 0.2 0.22 0.25 0.29 0.32 0.33 0.34 0.37 0.39 0.41 0.42 0.44 0.45 0.46 0.47 1. In this data, what are the cases, explanatory variable, and response variable? 2. Using technology, make a linear regression equation to predict postage rates from year. Paste the equation below From the linear regression equation, how much should a stamp in the vear 2000 should have cost? Show Calculations S 3. Using the above equation, calculate how much a stamp in the year 2020 should cost, if the pattern is to continue, showing calculations. 4. Today, in 2018, a stamp costs 52 cents. Calculate the residual the cost of a 2018 stamp showing calculations. Is it far off from what the linear regression equation predicted?Explanation / Answer
1) The response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable. A response variable measures an outcome of a study. An explanatory variable explains or influences changes in a response variable.
In our case, we are looking at how the price of the postal rate changes according to the year. As years pass, the postal rate will change as well.
Answer: Therefore, explanatory variables - Year and response variables - Postal Rate.
2) The linear regression equation: ( Y = Rate, X = Year)
----> Y = -17.644 + 0.009X
Substituting X=2000 in the above equation :
Y = -17.644 + 0.009(2000)
Y = -17.644 + 18 = 0.356
Answer: The postal rate should have been $0.356 in 2000.
3) If the year is 2020,
Substituting X=2020 in the above equation :
Y = -17.644 + 0.009(2020)
Y = -17.644 + 18.18 = 0.536
Answer: A stamp should cost $0.536 in the year 2020.
4) In 2018,
Substituting X = 2018 in the above equation :
Y = -17.644 + 0.009(2020)
Y = -17.644 + 18.162 = 0.518
This is the predicted value = 51.8 cents
Actual Value = 52 cents
Residual = Actual Value - Predicted Value = 52 - 51.8 = 0.2 cents
Thus, the values are not far off and the actual predicted value are coming pretty close with a difference of only 0.2 cents. Thus, the regression line does a pretty good job of capturing the data and predicting the pattern of postal rate changes according to year.
Cheers!
Upvote if this was helpful to you.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.