Aug 19, 2017

What’s the value of naive forecast of electricity consumption for 13th day?

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ECON 4451 and MKGT 6670 Business Forecasting

HW#4

Electricity consumption was recorded for a small town on 12 randomly chosen days. The following maximum temperatures (degrees Celsius) and consumption (megawatt-hours) were recorded for each day.

a Plot the data and find the regression model for Mwh with temperature as an explanatory variable. Why is there a negative relationship?

b Produce a residual plot. Is the model adequate? Are there any outliers or influential observations?

c Use the model to predict the electricity consumption that you would

expect for a day with maximum temperature10?and a day with

maximum temperature35. Do you believe these predictions?
dGive prediction intervals for your forecasts. The following R code will

get you started:R code?

R -code is:

plot(Mwh ~temp,data=econsumption)
fit
f orecast(fit, newdat a=dat a. frame(t emp=c(10,35)))

e. What is the equation of your regression model? Write the model.

f) Is the temperature coefficient statistically significant? Write your null hypothesis, test statistics and p-value. Make your decision using 5% significance level. How about at 20%

significance level? Has your decision changed? What is the value of R2? IS it high? Interpret R2 .

g) Put the residuals in a histogram? what do you observe? Is it normally distribute?

Day

1

2

3

4

5

6

7

8

9

10

11

12

Mwh 16.3 16.8 15.5 18.2 15.2 17.5 19.8 19.0 17.5 16.0 19.6 18.0

temp 29.3 21.7 23.7 10.4 29.7 11.9 9.0 23.4 17.8 30.0 8.6 11.8

h) Test the residuals normality by
Box-Ljung test (It is from Chp 2). Write the null hypothesis. Based on the result of Box-Ljung test statistic, what do you conclude? Are residuals normally distributed?
R -code is:

#lag=hand fitdf=K

>Box.test(res,lag=10, fitdf=0, type=”Lj”) Box-Lj ung test

X-squared=11.0729,df=10, p-value=0.3507
i) What is the autocorrelation function of the residuals from the model? DO you observe

any autocorrelation in any lag?

j) Test autocorrelation by Box-Pierce test (chp 2)

R-code:

#lag=hand fitdf=K

>Box.test(res,lag=10, fitdf=0) Box-Pi erce test

Let’s forget about the regression model.
k. What’s the value of naive forecast of electricity consumption for 13th day?
l. Use drift method to find the forecast of electricity consumption for 13th day? m. Compare these 2 results by the
RMSE
MAE
MAPE
MASE

(check chp 2,Section 5 for the codes).

h) Let’s go abck to regression.
Now regress electricity consumption on temperature in log form (take logs of two variable and run teh regression)

Do a to j for log forms.

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