The time series pattern that reflects a gradual shift or movement to a relatively higher or lower level
over a longer time period is called the
- Trend
Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown
in the following table. Use exponential smoothing with a smoothing constant of 0.3 to forecast the year
12 demand. -
DEMAND
FOR
YEAR FERTILIZE
R (1,000s
OF BAGS)
1 4
2 6
3 4
4 5
5 10
6 8
7 7
8 9
9 12
10 14
11 15
Use simple exponential smoothing with α = 0.4 to forecast donut sales
for March. Assume that the forecast for January was for 28 donuts.
Month Donut Sales
January 32
February 33
March 28
April 39
- Forecast for February = 0.4*32 + 0.6*28 = 29.6
- Forecast for March = 0.4*33 + 0.6*29.6 = 30.96
Data collected on the yearly demand for 50-pound bags of fertilizer
at Wallace Garden Supply are shown in the following table. Compare
the exponential smoothing with a smoothing constant of 0.3 and a
three-year moving average forecasting method, which method do
you think is better (use mean absolute deviation MAD for your
analysis)? – three year moving method
DEMAND
FOR
YEAR FERTILIZER
(1,000s OF
BAGS)
1 4
2 6
3 4
4 5
5 10
6 8
7 7
8 9
9 12
10 14
11 15
Students in a management science class have just received their
grades on the first test. The instructor has provided information about
the first test grades in some previous classes, as well as the final
averages for the same students. Some of these grades have been
sampled and are as follows. What is the MSE of the data set?
Final
Student 1st Exam Average
1 98 93
2 77 78
3 88 84
4 80 73
5 96 84
6 61 64
7 66 64
8 95 95
9 69 76
A regression analysis between sales (in $1000) and price (in dollars) resulted
in the following equation
Y= 50,000 − 8x
The above equation implies that an
- $1 in price is associated with a decrease of $8,000 in sales
Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for
time period 9 plus
- a times (the error in the demand forecast for time period 9)
The correlation coefficient resulting from a particular regression analysis
was 0.25. What was the coefficient of determination?
- 0.0625
Which of the following statements is not true about regression
models?
-
- The regression line minimizes the sum of the squared errors.
-
- The dependent variable is the explanatory variable.
-
- Estimates of the slope are found from sample data.
-
- The error is found by subtracting the actual data value from the
predicted data value.
Larger values of r2
imply that the observations are more closely grouped about the
- Least square line
Given below are seven observations collected in a regression study on
two variables, x
(independent variable) and y (dependent variable). Develop the least
squares estimated regression equation. What is the coefficient of
determination?
X y
2 12
3 9
6 8
7 7
8 6
7 5
9 2
- .8438
The sales records of a company over a period of seven years are
shown below. Develop a linear trend expression for the above time
series. The forecast sales for period 10 is:
Year (t) Sales (In Millions of
Dollars)
1 12
2 16
3 17
4 19
5 18
6 21
7 22
- Between $26,000,000 to $27,000,000
A reference to the criterion used to select the regression line, to minimize
the squared distances between the estimated straight line and the observed
values is called
- Least Squares.
Consider the actual and forecast values contained in the table. What is
the MSE of the forecast? - 0.573
Actual Forecast Actual Forecast
10 10.8 26 24.5
13 13.6 28 27.2
17 16.3 29 29.9
19 19 32 32.6
22 21.7 35 35.3
John Smith has developed the following forecasting model:
^Y=36+4.3X1
where
ˆY=demand for K10 air conditioners
X1=the outside temperature (∘F)
What is the demand for a temperature of 90°F? – 423
When is the exponential smoothing model equivalent to the naïve forecasting
model?
Daily humidity in the city of Houston for the last week have been: 93, 94, 93, 95, 92, 86, 98 (yesterday).
Calculate the MAD based on a two-day moving average, covering all days in which you can have a
forecast and an actual humidity level.
- 4.1
Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15, 12, 18, 14, 12, 13,
15 (listed from oldest to most recent). Forecast sales for the next day using a two-day moving average.
- 14
Students in a management science class have just received their grades on the first test. The instructor
has provided information about the first test grades in some previous classes, as well as the final
averages for the same students. Some of these grades have been sampled and are as follows. Use Excel,
with the values of r and r2 for this model. Interpret the value of r2 in the context of this problem. (table
at the top ^)
- 85% of the variability in the final average can be explained by the variability in the first test
score.
Which of the following equalities is correct?
- SST = SSR + SSE
Demand for Y is shown in the table. Develop a forecast using a trend
line. What is the forecast for period 12? Find equation then x=12 then
solve
- 183.9
Period Y
1 28
2 42
3 49
4 74
5 78
6 93
7 115
8 129
Which of the following is an assumption of the regression model?
The errors have an irregular variance.
The errors are independent.
The errors have a standard deviation of zero.
The errors are not normally distributed.
If computing a causal linear regression model of Y = a + bX and the
resultant r2 is very near zero, then one would be able to conclude that
- Y
= a + bX is not a good forecasting method.
An air conditioning and heating repair firm conducted a study to
determine if the average outside temperature could be used to predict
the cost of an electric bill for homes during the winter months in
Houston, Texas.
Y = 227.19 - 1.45X, where Y = monthly cost, X = average outside air
temperature
If the temperature averaged 38 degrees during January, what is the
forecasted cost of January's electric bill?
- 227.19-1.45(38)= 172.09
Which of the following statements is true about r2?
It is also called the coefficient of determination.
