A researcher is interested in determining whether there is a relationship between advertising and sales for her firm. advertising in $thousands(X) Sales in millions(Y) 1 1 5 6 6 7 5 4 6 7 7 8 10 11 11 12 1- You are given data for Xi (independent variable) and Yi (dependent variable). 2- Calculate the correlation coefficient, r: r = -1 ≤ r ≤ 1 3- Calculate the coefficient of determination: r2 = = 0 ≤ r2 ≤ 1 This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi) 4- Calculate the regression coefficient b1 (the slope): b1 = = Note that you have already calculated the numerator and the denominator for parts of r. Other than a single division operation, no new calculations are required. 5- Calculate the regression coefficient b0 (the Y-intercept, or constant): b0 = = 6- The regression equation (a straight line) is: = b0 + b1Xi Excel regression analysis Conclusion:
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.
Topic: Regression
Problem 1
A researcher is interested in determining whether there is a relationship between advertising and sales for her firm.
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advertising in $thousands(X) |
Sales in millions(Y) |
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1- You are given data for Xi (independent variable) and Yi (dependent variable).
2- Calculate the
r = -1 ≤ r ≤ 1
3- Calculate the coefficient of determination: r2 = =
0 ≤ r2 ≤ 1
This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi)
4- Calculate the regression coefficient b1 (the slope):
b1 = =
Note that you have already calculated the numerator and the denominator for parts of r. Other than a single division operation, no new calculations are required.
5- Calculate the regression coefficient b0 (the Y-intercept, or constant):
b0 = =
6- The regression equation (a straight line) is:
= b0 + b1Xi
- Excel
regression analysis
Conclusion:
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