The manager of Collins Import Autos believes the number of cars sold in a day (Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S). After collecting data for two months (53 days), the manager estimates the following log-linear mode
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.
The manager of Collins Import Autos believes the number of cars sold in a day (Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S). After collecting data for two months (53 days), the manager estimates the following log-linear model:
- Explain how to transform this log-linear model into a linear form that can be estimated using multiple
regression analysis .
The computer output for the multiple regression analysis is shown below:
How do you interpret coefficients band c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales?
Test the overall model for statistical significance at the 5 percent significance level.
What percent of the total variation in daily auto sales is explained by this equation? What could you suggest to increase this percentage?
Test the intercept for statistical significance at the 5 percent level of significance. If Hand S both equal 0, are sales expected to be 0? Explain why or why not.
Test the estimated coefficient bfor statistical significance. If the dealership decreases its hours of operation by 10 percent, what is the expected impact on daily sales?
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