Cascade Pharmaceuticals Company developed the following regression model, using time-series data from the past 33 quarters, for one of its nonprescription cold remedies:
Y = −1.04 + 0.24X1 − 0.27X2
where Y = quarterly sales (in thousands of cases) of the cold remedy
X1 = Cascade’s quarterly advertising (x$1,000)for the cold remedy
X2 = competitors’ advertising for similar products (x $10,000)
Here is additional information concerning the regression model:
sb1 = 0.032
sb2 = 0.070
R2 = 0.64
se = 1.63
F-statistic = 31.402
Durbin-Watson (d) statistic = 0.4995
a. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy?
b. What proportion of the total variation in sales is explained by the regression equation?
c. Perform an F-test (at the 0.05 level) of the overall explanatory power of the model.
d. What additional statistical information (if any) would you find useful in the evaluation of this model?
Cascade Pharmaceuticals Company developed the following regression model, using time-series data from the past 33 quarters, for one of its nonprescription cold remedies:
Y = −1.04 + 0.24X1 − 0.27X2
where Y = quarterly sales (in thousands of cases) of the cold remedy
X1 = Cascade’s quarterly advertising (x$1,000)for the cold remedy
X2 = competitors’ advertising for similar products (x $10,000)
Here is additional information concerning the regression model:
sb1 = 0.032
sb2 = 0.070
R2 = 0.64
se = 1.63
F-statistic = 31.402
Durbin-Watson (d) statistic = 0.4995
a. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy?
b. What proportion of the total variation in sales is explained by the regression equation?
c. Perform an F-test (at the 0.05 level) of the overall explanatory power of the model.
d. What additional statistical information (if any) would you find useful in the evaluation of this model?
