A linear trend equation for sale of the form Qt = a + bt was estimated for the period 1993-2007 (i.e. t=1993, 1994, 2007) The results of the regression are as follow:

Dependent variable : Qt, R-Square, F-ratio, P-Value on F

Observations : 15, 0.6602, 25.262, 0.0002

Variable, Parameter Estimate, Standard Error, T-ratio, P-value

Intercept 73.71460, 34.08, 2.16, 0.0498

t 3.7621, 0.749, 5.02, 0.0002

a) Evaluate the statistical significance of the estimated coefficients (use 5 percent for significance level) Does this equation indicate a significant trend? (6m)

b) Using this equation, forecast sales in 2008 and 2009. (4M)

c) Comment on the precision of these two forecasts. (4m)

Thank you

Anyone?or any similar question with this?thanks..

Anyone know how to do this? urgent...thank you very much.

a) To evaluate the statistical significance of the estimated coefficients, we need to look at the P-values associated with each coefficient.

For the intercept term, the P-value is 0.0498. Since this P-value is less than the significance level of 0.05, we can conclude that the intercept term is statistically significant.

For the coefficient of t (time), the P-value is 0.0002. This P-value is also less than 0.05, indicating that the coefficient of t is statistically significant.

Therefore, both the intercept term and the coefficient of t are statistically significant at the 5 percent significance level. This means that there is a significant trend indicated by the equation Qt = 73.71460 + 3.7621t.

b) To forecast sales in 2008 and 2009 using the given equation, we need to substitute the values of t as 2008 and 2009, respectively, into the equation.

For 2008, t = 2008 - 1993 = 15. Substituting this value into the equation, we get:

Q2008 = 73.71460 + 3.7621 * 15 = 130.9281

Therefore, the forecasted sales for 2008 is approximately 130.9281.

For 2009, t = 2009 - 1993 = 16. Substituting this value into the equation, we get:

Q2009 = 73.71460 + 3.7621 * 16 = 134.6907

Therefore, the forecasted sales for 2009 is approximately 134.6907.

c) To comment on the precision of these two forecasts, we need to consider the standard error of the coefficients.

For the coefficient of t, the standard error is 0.749. The precision of the forecasted sales for 2008 and 2009 is dependent on this standard error. A smaller standard error implies higher precision in the forecasts. Therefore, a standard error of 0.749 suggests that the forecasts may not be very precise.

It is important to note that the precision of the forecasts also depends on the variability of the data and other factors not provided in the given information. Hence, the forecasts should be interpreted with caution, considering the potential sources of uncertainty.