Daily high temperatures in St. Louis for the last week were as follows: 92, 92,
ID: 351172 • Letter: D
Question
Daily high temperatures in St. Louis for the last week were as follows: 92, 92, 95, 92, 95, 86, 93 (yesterday). a) The high temperature for today using a 3-day moving average 91.3 degrees (round your response to one decimal place). b) The high temperature for today using a 2-day moving average = 89.5 degrees (round your response to one decimal place). c) The mean absolute deviation based on a 2-day moving average = 3.1 degrees (round your response to one decimal place) d) The mean squared error for the 2-day moving averagedegrees" (round your response to one decimal place)Explanation / Answer
a) A three period moving average method averages the actual value for the previous three periods to generate the forecast for the next period. This can be calculated as the sum of the actual value for the previous three periods /3
So using the above formula the forecasted high temperature for today = (95+86+93)/3 = 274/3 = 91.3
b) A two period moving average method averages the actual value for the previous two periods to generate the forecast for the next period. This can be calculated as the sum of the actual value for the previous two periods to /2.
So using the above formula the forecasted high temparature for today = (86+93)/2 = 179/2 = 89.5
C) Using the formula used in part b, the two day moving average forecast for all the periods are
Mean absolute deviation = Sum of the absolute deviation for all the periods / number of periods
Where deviation = actual value - forecasted value
Absolute deviation = absolute value of deviation
Using the above formula the deviation and absolute deviation for all the periods are
Mean absolute deviation = (3+1.5+1.5+7.5+2.5)/5 = 16/5 = 3.2
d)Mean squared error = Sum of the squared errors for all the periods / number of periods
Where Squared error = square of error
Error = deviation = actual value - forecasted value
So from the deviations calculated in part c, the squared errors for each periods are
Mean squared error = (9+2.25+2.25+56.25+6.25)/5 = 76/5 = 15.2
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