An economist was interested in the relation between the disposable income of a family and the amount of money used for food per month. He did a preliminary study on eight randomly selected lower income families. (Each family was of the same size; father, mother and two children). The economist’s data are given in the table below. Food cost (Y) (in hundreds of rand) 55 60 42 40 37 26 39 43 Family disposable income(X) (in hundreds of rand) 30 36 27 20 16 24 19 25 Find the regression linear equation. What is the predicted food cost if the family disposable income is R1800? Find the correlation coefficient & Interpret r. Find the Coefficient of Determination & Interpret the R2.
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.
An economist was interested in the relation between the disposable income of a family
and the amount of money used for food per month. He did a preliminary study on eight randomly selected lower income families. (Each family was of the same size; father, mother and two children). The economist’s data are given in the table below.
Food cost (Y) (in hundreds of rand)
55 60 42 40 37 26 39 43
Family disposable income(X) (in hundreds of rand)
30 36 27 20 16 24 19 25
- Find the regression linear equation.
- What is the predicted food cost if the family disposable income is R1800?
- Find the
correlation coefficient & Interpret r. - Find the Coefficient of Determination & Interpret the R2.
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