The trend for sales of cottage cheese is estimated using data from the first quarter of 1972 to the fourth quarter of 2004. The result is as shown below with the f-value in parentheses:
St = 12.5 + 0.14t (3.28)
a. What is the interpretation of the coefficient of t ? Is the coefficient statistically significant at the 95 percent level ? Explain
b. Forecast the demand for cottage cheese in the third quarter of 2006.
a. Answer: As show in the equation, the value of coefficient of t is 3.28, which is positive. From this, it can be interpreted that the sample of historical sales of cottage cheese collected for the period of 1972 to 2004 is generated with a specific mean. As per the given regression equation, p-value is 0.14, which is greater than the alpha level of 0.05 (95% level). It means the coefficient is statistically significant at the 95 percent level.
b. Answer: For third quarter of 2006, the value of t is 139, so expected demand for cottage cheese will be: S_139 = 12.5 + [(0.14 × 139) × (3.28)]= 76.33