Question 1 Create a multiple regression forecasting model that includes a trend

Question

Question 1

Create a multiple regression forecasting model that includes a trend component and daily seasonality dummy variables.  Use Saturday as your base day.  Using this estimated regression equation, make a forecast for all 28 days for which you were given data. What is the RMSE over those forecasts? (Report to 3 digits to the right of the decimal.)

Day Week Sales Volume (US$ 000s) Sun 1 9 Mon 1 17 Tue 1 15 Wed 1 19 Thu 1 14 Fri 1 16 Sat 1 8 Sun 2 13 Mon 2 19 Tue 2 15 Wed 2 22 Thu 2 15 Fri 2 20 Sat 2 13 Sun 3 14 Mon 3 20 Tue 3 18 Wed 3 23 Thu 3 19 Fri 3 23 Sat 3 14 Sun 4 18 Mon 4 21 Tue 4 23 Wed 4 24 Thu 4 19 Fri 4 23 Sat 4 15

Explanation / Answer

we shall analyse this in the open source statisitical package R

The complete R snippet is as follows

###

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\salesday.csv",header=TRUE)
str(data.df)

# create the dummy variables
data.df$sun<- ifelse(data.df$Day=="Sun",1,0)
data.df$mon<- ifelse(data.df$Day=="Mon",1,0)
data.df$tue<- ifelse(data.df$Day=="Tue",1,0)
data.df$wed<- ifelse(data.df$Day=="Wed",1,0)
data.df$thu<- ifelse(data.df$Day=="Thu",1,0)
data.df$fri<- ifelse(data.df$Day=="Fri",1,0)

# drop the day variable

data.df <- data.df[,-1]

#perform regression

fit <- lm(Sales~., data=data.df)

# summary
summary(fit)

# create the new data set
newdata<- data.df[,-2]

# use the predict function to get the predicted sales values
p<- predict(fit,newdata = newdata)

# rmse is calculated as
sqrt( mean( (data.df$Sales-p)^2 , na.rm = TRUE ) )

###

the results are

> summary(fit)

Call:
lm(formula = Sales ~ ., data = data.df)

Residuals:
Min 1Q Median 3Q Max
-1.68571 -0.84643 0.06429 0.84643 2.05714

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.1786 0.8107 8.855 2.35e-08 ***
Week 2.1286 0.2093 10.169 2.39e-09 ***
sun 1.0000 0.8757 1.142 0.267
mon 6.7500 0.8757 7.708 2.06e-07 ***
tue 5.2500 0.8757 5.995 7.32e-06 ***
wed 9.5000 0.8757 10.849 7.90e-10 ***
thu 4.2500 0.8757 4.853 9.63e-05 ***
fri 8.0000 0.8757 9.136 1.41e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.238 on 20 degrees of freedom
Multiple R-squared: 0.9368,   Adjusted R-squared: 0.9146
F-statistic: 42.32 on 7 and 20 DF, p-value: 1.252e-10

the rmse is calculated as

> sqrt( mean( (data.df$Sales-p)^2 , na.rm = TRUE ) )
[1] 1.046617

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