The following data set provides the total number of shipments of core major household appliances in the U.S. from 2000 to 2016 (in millions): Year Shipments (millions) 2000 38.4 2001 38.2 2002 40.8 2003 42.5 2004 46.1 2005 47.0 2006 46.7 2007 44.1 2008 39.8 2009 36.5 2010 38.2 2011 36.0 2012 35.8 2013 39.2 2014 41.5 2015 42.9 2016 44.7 a. Plot the time series. b. Fit a three-year moving average to the data and plot the results. c. Fit a five-year moving average to the data and plot the results. d. Compute a linear trend forecasting equation and plot the trend line. e. Compute a quadratic trend forecasting equation and plot the results.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- The following data set provides the total number of shipments of core major household appliances in the U.S. from 2000 to 2016 (in millions):
|
Year |
Shipments (millions) |
|
2000 |
38.4 |
|
2001 |
38.2 |
|
2002 |
40.8 |
|
2003 |
42.5 |
|
2004 |
46.1 |
|
2005 |
47.0 |
|
2006 |
46.7 |
|
2007 |
44.1 |
|
2008 |
39.8 |
|
2009 |
36.5 |
|
2010 |
38.2 |
|
2011 |
36.0 |
|
2012 |
35.8 |
|
2013 |
39.2 |
|
2014 |
41.5 |
|
2015 |
42.9 |
|
2016 |
44.7 |
a. Plot the time series.
b. Fit a three-year moving average to the data and plot the results.
c. Fit a five-year moving average to the data and plot the results.
d. Compute a linear trend forecasting equation and plot the trend line.
e. Compute a quadratic trend forecasting equation and plot the results.
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