Consider the quarterly demand levels for electricity (1000 megawatts) in Polokwane from 2015 to 2018. Quarter 2015 2016 2017 2018 Jan - March 21 35 39 78 Apr-June 42 54 82 114 July-Sept 60 136 160 Oct-Dec 12 14 28 40 Using the third period moving average Determine the centered moving average of period 15
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- Verify that the 5 year weighted moving average weight 1, 2, 2, 1 respectively is equivalent to 4 year centered moving average. Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Sales(K) 5 3 7 6 4 8 9 10 8 9 9A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the life- time y of four bits at each of five speeds. Speed Lifetime 60 4.6 60 3.8 60 4.9 60 4.5 80 4.7 80 5.8 80 5.5 80 5.4 100 5 100 4.5 100 3.2 100 4.8 120 4.1 120 4.5 120 4 120 3.8 140 3.6 140 3 140 3.5 140 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? Regardless fit a simple linear regression model to the data. What can you say about the fit of the model to the data? Is there any evident outlier . Remove this observation and fit the regression model again. Is it improving the model fAccording to published reports, practice under fatigued conditions distorts mechanisms that govern performance. An experiment was conducted using 15 college males, who were trained to make a continuous horizontal right-to-left arm movement from a microswitch to a barrier, knocking over the barrier coincident with the arrival of a clock sweephand to the 6 o’clock position. The absolute value of the difference between the time, in milliseconds, that it took to knock over the barrier and the time for the sweephand to reach the 6 o’clock position (500 msec) was recorded. Each participant performed the task five times under prefatigue and postfatigue conditions, and the sums of the absolute differences for the five performances were recorded. An increase in the mean absolute time difference when the task is performed under postfatigue conditions would support the claim that practice under fatigued conditions distorts mechanisms that govern performance. Assuming the populations to be…
- Observations of the demand for a certain part stocked at a parts supply depot during the calendaryear 2013 were: Month Demand Month Demand Jan 89 july 223 Feb 57 august 286 mar 144 sept 212 april 221 oct 275 may 177 nov 188 june 280 dec 312 a) Using a four-month moving average, determine the one-step-ahead forecast for Julythrough December 2013.b) Using a four-month moving average, determine the two-step-ahead forecast for Julythrough December 2013.c) Obtain the MAD for the forecasts obtained in the above sections. Which method gavebetter results? Based on forecasting theory, which method should have given betterresults?b) What is the maximum height of the shot-put’s trajectory and at what time does it get there?The prices (in $) of Rawlston, Inc. stock ( y) over a period of 12 days, the number of shares (in 100s) of company's stocks sold ( x 1), and the volume of exchange (in millions) on the New York Stock Exchange ( x 2) are shown below. Day (y) (x1) (x2) 1 87.50 950 11.00 2 86.00 945 11.25 3 84.00 940 11.75 4 83.00 930 11.75 5 84.50 935 12.00 6 84.00 935 13.00 7 82.00 932 13.25 8 80.00 938 14.50 9 78.50 925 15.00 10 79.00 900 16.50 11 77.00 875 17.00 12 77.50 870 17.50 Excel was used to determine the least squares regression equation. Part of the computer output is shown below. ANOVA df SS MS F Significance F Regression 2 118.8474 59.4237 40.9216 0.0000 Residual 9 13.0692 1.4521 Total 11 131.9167 Coefficients Standard Error t Stat P-value Intercept…
- The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. Year 2010 2012 2014 2016 2018 2020 CO2 Emissions 337.5 361.5 395.1 425.8 451.1 496.4 Year 2022 2024 2026 2028 2030 2032 CO2 Emissions 558.2 592.9 628.7 662.1 709.1 742.7 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.)y(x) = (b) Find the model's estimate for the 2028 data point. (Round your answer to two decimal places.) million metric tons(c) Find the slope of the linear model. (Round your answer to two decimal places.)Interpret the slope of the linear model. For each year since ---Select--- 2009 2010 2015 2028 2032 , carbon dioxide emissions in the U.S. are expected to change by million metric tons.Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1, 2).A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G–forces (that is, acceleration in 9.8 – /msec2 increments) versus time after launch.
- A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…Use the data to model deliveries times for a driver based on three parameters. If today's delivery routs requires 42 miles, 8.3 gallons of gas, and has 4 deliveries, how much time should the driver expect to be on the road? (Keep one decimal place) Assignment Miles Gasoline Consumption Deliveries Time 1 100.0 10.0 4.0 9.3 2 50.0 6.2 3.0 4.8 3 100.0 9.5 4.0 8.9 4 100.0 10.3 2.0 6.5 5 50.0 4.7 2.0 4.2 6 80.0 7.8 2.0 6.2 7 75.0 7.7 3.0 7.4 8 65.0 6.4 4.0 6.0 9 90.0 8.8 3.0 7.6 10 90.0 10.0 2.0 6.1 11 50.0 5.0 5.0 7.0 12 45.0 4.9 6.0 7.0 13 85.0 8.1 5.0 9.6 14 65.0 6.6 2.0 6.5 15 40.0 4.0 6.0 7.2 16 50.0 5.5 3.0 6.0 17 75.0 7.4 5.0 9.9 18 75.0 7.6 4.0 8.6 19 65.0 6.8 3.0 4.9 20 90.0 8.4 3.0 7.5 21 95.0 8.8 1.0 7.2 22 95.0 10.2 6.0 9.9 23 50.0 4.6 1.0 5.6 24 80.0 8.6 3.0 7.5 25 90.0 8.6 2.0 7.8 26 80.0 8.8 3.0 7.2 27 75.0 6.9 3.0 7.0 28 95.0 10.0 2.0 8.7 29 90.0 9.2 1.0 6.4 30 100.0 9.4 3.0 9.9 31 60.0 6.0 1.0 4.1 32 90.0…
