A company sets different prices for a particular DVD system in eight different regions of the country. Table 1 shows the numbers of units sold and the corresponding unit prices (in U.S. Dollars). Table 1: Sales Data Region Sales (Units) Price (U.S. Dollars) 1 420 104 2 380 195 3 350 148 4 400 204 5 440 96 6 380 256 7 450 141 8 420 109
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.
A company sets different prices for a particular DVD system in eight different
regions of the country. Table 1 shows the numbers of units sold and the
corresponding unit prices (in U.S. Dollars).
Table 1: Sales Data
Region Sales (Units) Price (U.S. Dollars)
1 420 104
2 380 195
3 350 148
4 400 204
5 440 96
6 380 256
7 450 141
8 420 109
You are given the following regression model:
Salesi = 1 + 2Pricei + ui
where i is region, Sales are number of units sold, Price is unit price in
U.S. Dollars, and u is a random error term.
Based on the data:
1. Estimate the regression model.
2. Interpret the estimated regression equation.
3. Compute the standard errors of the estimated coefficients.
4. Test the statistical significance of 2 at the 5% level of significance.
5. Compute R2 and interpret it.
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