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 - 0:27X2where Y = quarterly sales (in thousands of cases) of the cold remedyX1 = Cascade’s quarterly advertising (× $1,000) for the cold remedyX2 = competitors’ advertising for similar products (× $10,000)Here is additional information concerning the regression model:sb1 = 0:032 sb2 = 0:070R2 = 0:64 se = 1:63 F-statistic = 31:402Durbin-Watson (d) statistic = 0.4995a. 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?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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 (× $1,000) for the cold remedy
X2 = competitors’ advertising for similar products (× $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?
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