[SOLVED] CS ETW3420 Principles of Forecasting and Applications

ETW3420 Principles of Forecasting and Applications

Principles of Forecasting and Applications

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Topic 7 Pre-tutorial Activity

In this pre-tutorial activity, you will:

(i) Replicate the figures and results in the Section 7.1 of your lecture notes.

(ii) In doing so, you will learn how to plot graphs using the ggplot() function and perform

time series linear regression using the tslm() function.

Question 1

The data we will be using is uschange the percentage changes in quarterly personal consump-

tion expenditure, personal disposable income, production, savings and the unemployment rate

for the US, 1960 to 2016. (Execute the function help(uschange) to see the information).

(a) Print the dataset to see how the data is arranged. Note the heading labels we will be

making reference to these headings later on.

(b) Check the structure of the data set.

str(uschange)

Note that it is a time series object, and NOT a data frame object.

(c) Plot the line charts of Consumption and Income within the same graph.

#First, execute the following command and see what you obtain.

uschange[, c(Consumption, Income)]

#Plot the line charts

autoplot(uschange[, c(Consumption, Income)]) +

ylab(% change) +

xlab(Year)

(d) Plot a scatter plot of Consumption vs Income using the ggplot() function. You should

read about how this function works: help(ggplot)

Notice that the first argument that enters the ggplot() function is the data that must

be a data.frame object. From Part (b), we see that uschange is a time series object,

and not a data.frame object. Therefore we need to convert it to a data frame using the

as.data.fram() function, and label the new output as uschange.df:

uschange.df <- as.data.frame(uschange) The second argument is the mapping argument which requires us to specify argumentsin the aes() argument. aes stands for aesthetics and for the most basic use, this iswhere we specify our x and y variables. In this case, our x variable is Income, and yvariable is Consumption. Execute the following command and see what is produced.ggplot(data = uschange.df, mapping = aes(x = Income, y = Consumption)) You only get a blank canvas! You get a canvas with only the Y and X axis labelled.No points are shown. The gg in ggplot() refers to the grammar of graphics, which describes how shouldplots really be generated. It is a way of thinking of how graphs should be generated. Inessence, this grammar is about adding layers. So the above code has just given us the first layer – a canvas with just the x- and y- Now we need to add the data points to get the scatter plot. We do this by adding (i.e.+) another layer of points on this canvas. Specifically, we add a geometric layer calledgeom_point. So the code extends to become:ggplot(data = uschange.df, mapping = aes(x = Income, y = Consumption)) +geom_point() Great! So we now have a scatter plot. But how do we also include the line of best fit?Well, by adding another layer! This layer is called geom_smooth.ggplot(data = uschange.df, mapping = aes(x = Income, y = Consumption)) +geom_point() +geom_smooth(method = ‘lm’, se = F) In the geom_smooth() function, we specified lm to be the method, meaning a linearmodel (i.e. OLS). And se=F means that we do not want to plot the standard errors.(e) Regress Consumption against Income and print the results. Since this is time series data, we shall use the tslm() function. If dealing withcross-sectional data, a linear regression model is fitted using the lm() function. The summary() function then prints the result of the fitted model. As tslm() works with time series object, we use uschange as the data set rather thanuschange.df.tslm(Consumption ~ Income, data = uschange) %>% summary()

(f) Estimate a multiple linear regression of Consumption against the other 4 variables. Save

the output in the label fit. Obtain the predicted (i.e. fitted) values of Consumption

by the model.

#Estimate regression

fit <- tslm(Consumption ~ Income + Production + Unemployment + Savings, data=uschange)#Print resultssummary(fit)#Obtain fitted valuesfitted(fit)(g) Plot the actual and fitted values of Consumption – as line graphs and as a scatter plot.#Line chartautoplot(uschange[,”Consumption”], series = “Data”) +autolayer(fitted(fit), series = “Fitted”) To produce a scatter plot, we need to use the ggplot() function. Recall from earlieron, the data argument to enter the ggplot() function must be a data.frame object. We also only have 2 variables here: the actual and fitted values of Consumption. So what we need to do is to combine these 2 variables to become a data frame (lets callit df) using the data.frame() function:#Combine Actual and Predicted consumption values into a dataframe, labeled as `df`df <- data.frame(Data = uschange[,”Consumption”], Prediction = fitted(fit))#print to see what is produced; notice the heading labels Now we can go ahead to produce the scatter plot:#Scatter plotggplot(data = df, mapping = aes(x = Prediction, y = Data)) +geom_point() +ylab(“Actual % change in consumption”) +xlab(“Predicted % change in consumption”)Question 1 CS: assignmentchef QQ: 1823890830 Email: [email protected]