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Analytics Paper

In:

Submitted By jobong94
Words 464
Pages 2
a. From Figure 1-1, energy bills fluctuate over time but overall, they rise from around
$350 in the first quarter to about $550 in the last quarter. A general upward trend appears to exist.
b. From the graph, energy bills fluctuate over time but with respect to a constant average level of around $300. Constant seasonal variation appears to be displayed, hence no transformation is required.
c. i) Q1: 1 when in the first quarter; 0 as long as it is not in the first quarter
Q2: 1 when in the second quarter; 0 as long as it is not in the second quarter
Q3: 1 when in the third quarter; 0 as long as it is not in the third quarter
There are 4 quarters in a year. For the model to be identifiable, the β value corresponding to the last – i.e. the 4th quarter, is set to 0. Hence β6Q4 = 0 and Q4 is omitted from the model. ii) The independent variables t, t2, Q1, and Q3 have small p values (p < 0.005) and are therefore statistically significant.
The independent variable Q2 has a p value > 0.005 and is hence not statistically significant. iii)
Period 41: Point forecast = 542.9878132; 95% confidence interval = (400.9438205,
685.0318058)
Period 42: Point forecast = 456.8909767; 95% confidence interval = (312.3282773,
601.453676)
Period 43: Point forecast = 385.2961403; 95% confidence interval = (237.9076139,
532.6846667)
Period 44: Point forecast = 531.6563038; 95% confidence interval = (381.1521284,
682.1604783)
The assumptions on ε are that it is an independent random variable and has mean 0 and constant variance. iv) Where k = 5; n = 40:

Durbin-Watson D
Number of Observations
1st Order Autocorrelation

0.84
40
0.554

H0 : The error terms are not autocorrelated
H1 : The error terms are positively autocorrelated

dL,0.05 = 1.23, du, 0.05 = 1.79
Durbin-Watson D = 0.84 which is less than dL, 0.05 hence we reject the null
hypothesis.

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