Solve the below:
1. Consider the following time series data.
Week 1 2 3 4
Value 18 13 1 11
Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?
2. Refer to the time series data in Q1. Using the average of all the historical data as a forecast for the next period, compute the following measures of forecast accuracy:
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?
3. Q1 and 2 used different forecasting methods. Which method appears to provide the more accurate forecasts for the historical data? Explain.
4. For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83.
a. Construct a time series plot. What type of pattern exists in the data?
b. Compare a three-month moving average forecast with an exponential smoothing fore¬cast for a = 0.2. Which provides the better forecasts using MSE as the measure of model accuracy?
c. What is the forecast for next month?
5. Consider the following time series.
t 1 2 3 4 5 6 7
Yt 120 110 100 96 94 92 88
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for t - 8?
6. The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect
data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period (https://www.cdc.govitobaccoidata_statistics itablesitrendsicig_smoking/index.htm).
Year Percentage of Adults Who Smoke
1 22.8
22.5
3 21.6
4 20.9
5 20.9
6 20.8
7 19.8
8 20.6
9 20.6
10 19.3
11 18.9
a. Construct a time series plot, What type of pattern exists in the data?
b. Use simple linear regression to find the parameters for the line that minimizes MSE for this time series.
c. One of OSH's goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal? If not, use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal.
7. The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has sur¬veyed Americans about their exercise habits, In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.
Year Percentage of Adults Who Reported
That They Exercise for 30 or More
Minutes at Least Three Times per Week
41.0
2 44.9
3 47.1
4 45.7
5 46.6
6 44.5
7 47.6
8 49.8
9 48.1
10 48.9
11 49.9
12 52.1
13 50.6
14 54.6
15 52.4
a. Construct a time series plot, Does a linear trend appear to be present?
b. Use simple linear regression to find the parameters for the line that minimizes MSE for this time series.
c. Use the trend equation from part. (b) to forecast the percentage of adults next year (year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week.
d. Would you feel comfortable using the trend equation from part (b) to forecast the percentage of adults three years from now (year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week?