Below are the estimates from the following linear trend model for cigarette sale

Question

Below are the estimates from the following linear trend model for cigarette sales

in the US. The equation was estimated using annual data for the period 1955-

2001.

Qt = a + bt +cD64 + dD71

where

Qt = annual sales of cigarettes (in millions of cartons)

t= 1955,….,2001

D64 = In 1964, the first major study on health risk of smoking was made public.

D64=1 if the year was after the release of this study; 0 otherwise

D71=In 1971, another study was made public. D71=1 if the year was after the

release of this study; 0 otherwise

The regression analysis produces the following results:

Dependent Variable: Qt

F- ratio

3.538

p-value on F

.0254

Show all work

1. Check for statistical significance of the coefficients and the equation using the

p-values.

2. Is there sufficient statistical evidence of an upward or downward trend in

cigarette sales?

3. Do these data indicate that the public health announcements had a statistically

significant impact on cigarette sales? Why or Why not? Do the coefficients on D64

and D71 have the expected sign? Explain.

4. Using the estimated forecast equation, forecast sales of cigarettes for 2003.

Dependent Variable: Qt

F- ratio

3.538

p-value on F

.0254

Observations: 46 Variable Parameter estimate Standard error T- ratio     P-value       Intercept 1491.404 528.4949 2.821 .0081 t -0.0700 0.269775 -2.596 .0140 D64 9.9000 4.3099 2.2970 .0283 D71 11.004 4.881 2.2541 .0311

Explanation / Answer

1. The p-value of intercept is 0.0081 which is less than alpha (0.05), we reject H0

    Thus, there is significance difference to Zero

     The p-value of t is .0140 which is less than alpha (0.05), we reject H0

      Thus, the variable t is significence difference to zero

      The p-value of D64 is 0.0283 which is less than alpha (0.05), we reject H0

      Thus, the variable D64 is significence difference to zero

      The p-value of D71 is 0.0311 which is less than alpha (0.05), we reject H0
      Thus, the variable D71 is significence difference to zero

Therefore, all coefficeints are different from Zero

    2. there is sufficient statistical evidence of an upward trend in cigarette sales. since all regression coefficient are positive values except t

   3. The data indicate that the public health announcements had a statistically significant impact on cigarette sales

The sign of both Variable(D64 and D71) coefficients are possitive. Thus

the impact of D64 and D71 is directly based on annual sales of cigarettes.

4.

Given t = 2003   

           Qt = a + bt +cD64 + dD71

               = 1491.404  - 0.0700 (2003) + 9.9000 (1) + 11.004 (1)

               = 13720.098

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