Question

A financial planner tracks the number of new customers added each quarter for a 6 year period. The data is presented below:

Year               Quarter                      New                Year               Quarter          New

2014               I                                   31                    2017               I                       69

                        II                                  24                                            II                      54

                        III                                 23                                            III                     46

                        IV                                16                                            IV                    32

2015               I                                   42                    2018               I                       82

                        II                                  35                                            II                      66

                        III                                 30                                            III                     51

                        IV                                23                                            IV                    38

2016               I                                   53                    2019               I                       91

                        II                                  45                                            II                      72

                        III                                 39                                            III                     59

                        IV                                27                                            IV                    41

Create a multiple regression equation incorporating both a trend (t=0 in 2013: IV) and dummy variables for the quarters. Let the first quarter represent the reference (or base) group. Complete (e) thru (h) using your results. This is a computer deliverable.

(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01.

(f) Test to see if the model has explanatory power. Use alpha = 0.05.

(g) Forecast the number of new customers in the first and second quarters of 2020.

(h) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19.

PLZ HELP WITH QUESTION H!!

Answer 1

Ans:- Step 1:- Creating data set and converting it to time series data. > data- (31,24,23,16,42, 35, 30,23,53, 45, 39,27,69,54,46,32,82,66,51 .38, 91,72,59,41) > newdatac- ts(data,start=C(2011,1).end=C(2016,4), frequency-4) > plot.ts (newdata) Step 2: -Testing for presence of upward trend. 80 60 newdata 40 20 2014 2015 2016 2017 2018 2019 Time > library (devtools) warning message: package devtools was built under R version 3.3.3 > library(trendseason) Attaching package: 'trendseason The following object is masked from 'package: stats: friedman. test > ro.test(newdata) Relative ordering Test for presence of Trend Null Hypothesis: Absence of Trend, and Alternative Hypothesis: Presence of Trend. Test Statistic: 3.175 p_value: 7e-04 No. of discordants: 74 Expected No. of discordants: 138 Plot and p value is less than 0.05 therefore we reject Ho hence there is presence of upward trend. > t<-time(newdata) > library(forecast) warning message: package "forecast was built under R version 3.3.3 Step 3: -Creating seasonal dummy for quarters. > quarter<-seasonaldummy (newdata)

Step 4: -Estimating time series using regression for trend and seasonality. > summary(1m(newdata-t+quarter)) Call: Im(formula = newdata - t + quarter) Residuals: Min 10 Median 30 -9.9821 -3.8244 0.3702 3.2042 Max 8.1845 Coefficients: Estimate std. Error t value pr(>It! (Intercept) -1.728e+04 1.329e+03 -13.002 6.61e-11 *** 8.593e+00 6.597e-01 13. 025 6.42e-11 quarterQ1 3.828e+01 3.225e+00 11.869 3.12e-10 *** quarterQ2 2.413e+01 3.204e+00 7.531 4.06e-07 *** quarterQ3 1.398e+01 3.191e+00 4.381 0.000321 *** signif. codes: 0 ****' 0.001 ***' 0.01 "*° 0.05 '.' 0.1. 1 Residual standard error: 5.52 on 19 degrees of freedom Multiple R-squared: 0.9355, Adjusted R-squared: 0.922 F-statistic: 68.93 on 4 and 19 DF, p-value: 4.829e-11 Step 5: -Estimating the value of time series using above equation for year 2020 first and quarter. > -17278.663+2017*8.593+38. 278

[1] 91.696 > -17278.663+2017*8.593+24.130 [1] 77.548 Step 5: -Testing of autocorrelation > library(Imtest) Loading required package: zoo Attaching package: 'zoo' The following objects are masked from 'package:base': as. Date, as. Date. numeric warning messages: 1: package Imtest' was built under R version 3.3.3 2: package 'zoo' was built under R version 3.3.3 > dwtest(1m(newdata-quarter+t)) Durbin-Watson test data: 1m(newdata - quarter + t) DW = 1.19167, p-value = 0.1811 alternative hypothesis: true autocorrelation is greater than o Since calculated dw value lies between 1.5 and 2.5 therefore we conclude that there is no autocorrelation.