Create a simple linear trend regression model. Let t=0 in 2010: IV. This is a co

Question

Create a simple linear trend regression model. Let t=0 in 2010: IV. This is a computer deliverable. (15 pts)

(a) Interpret the slope coefficient. (4 pts)

(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01. (15 pts)

(c) Test to see if the model has explanatory power. Use alpha = 0.05. (15 pts)

(d) Forecast the number of new customers in the first and second quarters of 2017. (4 pts each)

Create a multiple regression equation incorporating both a trend (t=0 in 2010: 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. (20 pts)

(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01. (15 pts)

(f) Test to see if the model has explanatory power. Use alpha = 0.05. (15 pts)

(g) Forecast the number of new customers in the first and second quarters of 2017. (4 pts each)

(h) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19. (12 pts)

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 2011 31 2014 69 24 54 23 46 16 32 2012 42 2015 82 35 66 30 51 23 38 2013 53 2016 91 45 72 39 59 27 41 9462 261 1291 6543 8653 9754 III III III 1436 2503 3597 3221 4332 5432 rTQ-III III III

Explanation / Answer

We used the given data and estimated a simple linear regression equation:

data used:

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 +ve and significant since p-value is 0.00056<0.01. So reject H0 and conclude the variable (trend/time) is significant

c) Yes the model is significant since:

<0.05

so reject H0 and conclude regression is significant.

d) Forecast :

Formula:

SUMMARY OUTPUT Regression Statistics Multiple R 0.652093 R Square 0.425225 Adjusted R Square 0.399099 Standard Error 15.31675 Observations 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

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