A study was made by a retail merchant to determine the relation between weekly advertising expenditures ($x) and sales ($y). The following data were recorded. Advertisement 40 20 25 20 30 Sales 385 400 395 365 475 (i) construct scatter plot between sales and advertisement expenditures. (ii) Compute the correlation coefficient between sales and advertisement expenditures. (iii) Interpret the correlation coefficient between sales and advertisement expenditures. (iv) Compute the coefficient of determination between sales and advertisement expenditures.
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 study was made by a retail merchant to determine the relation between weekly advertising expenditures ($x) and sales ($y). The following data were recorded.
|
Advertisement |
40 |
20 |
25 |
20 |
30 |
|
Sales |
385 |
400 |
395 |
365 |
475 |
(i) construct
(ii) Compute the
(iii) Interpret the correlation coefficient between sales and advertisement expenditures.
(iv) Compute the coefficient of determination between sales and advertisement expenditures.
(v) Interpret, in context, the coefficient of determination.
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