Question
In: Statistics and Probability
The residuals for 15 consecutive time periods are as follows: Time Period Residual Time Period Residual...
The residuals for 15 consecutive time periods are as follows:
| Time Period | Residual | Time Period | Residual |
|---|---|---|---|
| 1 | + 4 | 9 | + 6 |
| 2 | - 6 | 10 | - 3 |
| 3 | - 1 | 11 | + 1 |
| 4 | - 5 | 12 | + 3 |
| 5 | + 2 | 13 | 0 |
| 6 | + 5 | 14 | - 4 |
| 7 | - 2 | 15 | - 7 |
| 8 | + 7 |
a) Plot the residuals over time. What conclusion can you reach about the pattern of the residuals over time?
b) Compute the Durbin-Watson statistic. At the 0.05 level of significance, is the evidence of positive autocorrelation among the residuals?
c) Based on (a) and (b), what conclusion can you reach about the autocorrelation of the residuals?
Solutions
orchestra answered 1 year agoRelated Solutions
The residuals for 15 consecutive time periods from a simple linear regression with one independent variable...
The residuals for 15 consecutive time periods from a simple
linear regression with one independent variable are given in the
following table.
Time_Period Residual
1 +4
2 -6
3 -1
4 -5
5 +3
6 +6
7 -3
8 +7
9 +7
10 -3
11 +2
12 +3
13 0
14 -5
15 -7
B) Compute the Durbin-Watson statistic. At the 0.05 level
ofsignificance, is there evidence of positive autocorrelation
among the residuals?
The Durbin-Watson statistic is D=
(Round to...
Suppose there are only two time periods, today (period 1) and tomorrow (period 2), and only...
Suppose there are only two time periods, today (period 1) and
tomorrow (period 2), and only one consumption good, let’s call it
food. Assume that food is a perfectly divisible good. Let c1 and c2
denote the amount of food consumed today and tomorrow,
respectively. Note that here we use subscripts to denote time
periods. But you should think of food today and food tomorrow as
two different commodities. The price of food today is equal to p1 =
P....
Assume that the time between two consecutive accidents in a chemistry lab follows an exponential distribution...
Assume that the time between two consecutive accidents in a
chemistry lab follows an exponential distribution with parameter λ.
Starting to count from the day of the first accident (this will be
day 0), there has been accidents on the 28th, 50th, 60th days.
Compute the maximum likelihood estimate of λ. Explain the
steps.
Refer to the time series above. Suppose the values of the time series for the next two time periods are 13 in period 6 and 10 in period 7
t 1 2 3 4 5
Yt 6 11 9 14 15
Refer to the time series above. Suppose the values of the time
series for the next two time periods are 13 in period 6 and 10 in
period 7. a. Construct a time series plot for the updated time
series. What type of pattern exists in the data? b. develop the
quadratic trend equation for the updated time series. c. use the
quadratic trend equation developed in part...
Identify and interpret the smallest positive residual. Provide the complete list of residuals. X Y 1870...
Identify and interpret the smallest positive residual. Provide
the complete list of residuals.
X
Y
1870
3.38
1330
1.16
1760
1.58
1520
2.65
1300
1.98
1520
2.39
1640
2.49
1490
2.81
1300
2.95
1360
1.69
1940
3.49
1730
2.8
1790
2.95
1780
3.8
1730
2.64
1380
2.36
1580
3.1
1900
1.96
1640
3.08
1540
2.24
1350
2.59
1380
2.43
1780
1.95
1700
2.07
1610
2.34
1720
3.59
2070
3.59
1210
2.12
1720
2.48
1510
2.37
1790
2.1
2100
2.55
1690...
Identify and interpret the smallest positive residual. Provide the complete list of residuals. X Y 1870...
Identify and interpret the smallest positive residual. Provide
the complete list of residuals.
X
Y
1870
3.38
1330
1.16
1760
1.58
1520
2.65
1300
1.98
1520
2.39
1640
2.49
1490
2.81
1300
2.95
1360
1.69
1940
3.49
1730
2.8
1790
2.95
1780
3.8
1730
2.64
1380
2.36
1580
3.1
1900
1.96
1640
3.08
1540
2.24
1350
2.59
1380
2.43
1780
1.95
1700
2.07
1610
2.34
1720
3.59
2070
3.59
1210
2.12
1720
2.48
1510
2.37
1790
2.1
2100
2.55
1690...
Consider 3 time periods (now, a bit later, a lot later). The “Now” period: If a student...
Consider 3 time periods (now, a bit later, a lot later).
The “Now” period: If a student goes to school now,
they will have to pay $100 for
books/transportation/fees/etc. In addition, they will
not be able to work, hence the family income is reduced by
$600.
The “a bit later” period: If a person goes to school
in the “now” period, they will earn $500 more than a person who
does not go to school.
The “a lot later” period: If a person goes...
2. The rate of reaction for R → products over the time period 15 to 30...
2. The rate of reaction for R → products over the time period 15
to 30 s is 0.0036 M/s. If the concentration of a reactant
at 15 s is 0.39M, what is the concentration at 30 s?
1. From the data below, calculate the rate of reaction over the
time period 10 to 25 s.
time (s)
concentration
(M)
0
1.00
5
0.61
10
0.37
15
0.22
20
0.14
25
0.082
30
0.050
ASAP WITH TYPE How to improve a time series model with correlation left in residuals?
ASAP WITH TYPE
How to improve a time series model with correlation left in
residuals?
Vesta will live only for two periods. In period 0 she will earn $50,000. In period...
Vesta will live only for two periods. In period 0 she will earn
$50,000. In period 1 she will retire on Latmos Hill and live on her
savings. Her utility function is U(C0,C1) = C0C1, where C0 is
consumption in period 0 ,and C1 is consumption in period 1 .She can
borrow and lend at the interest rate i= 0.10. a) Write an
expression for her consumption in period 0 as a function of the
parameters specified. b) Having solved...
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