Question

# A financial planner tracks the number of new customers added each quarter for a 6 year...

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 simple linear trend regression model. Let t=0 in 2013: IV. This is a computer deliverable.

(a) Interpret the slope coefficient.

(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01.

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

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

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.

We Used the given data and estimated a Simple linear regression equation

 SUMMARY OUTPUT Regression Statistics Multiple R 0.652093 R Square 0.425225 Adjusted R Square 0.399099 Standard Error 15.31675 Observation 24 ANOVA df SS MS F Significance F Regression 1 3818.365 3818.365 16.27588 0.000555 Residual 22 5161.26 234.6027 Total 23 8979.625
 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 22.59783 6.453718 3.50152 0.002017 9.213633 35.98202 9.213633 35.98202 period 1.822174 0.451666 4.034338 0.000555 0.885476 2.758872 0.885476 2.758872

data used:

 period New 1 31 2 24 3 23 4 16 5 42 6 35 7 30 8 23 9 53 10 45 11 39 12 27 13 69 14 54 15 46 16 32 17 82 18 66 19 51 20 38 21 91 22 72 23 59 24 41

(a) Every quarter ahead there is an expected increase of 1.82(approx 2) new customers.

(b) Yes,there is a significant increasing trend since slope for the time variables is positive and significant since p-value is 0.00056<0.001.

So reject H0 and conclude the variable(trend/time) is significant.

(c) Yes the model is significant since:

 F Significant F 16.27588 0.000555

<0.05

So reject H0 and conclude regression is significant.

(d) Forecast:

 2017-Q1 68.148 2017-Q2 69.97

Formula:

 2017-Q1 =22.598+1.822*25 2017-Q2 =22.598+1.822*26

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