The following table gives information on the incomes (in thousands of dollars) and charitable contributions (in hundreds of dollars) for the last year for a random sample of 10 households. Income Charitable Contributions 76 15 57 4 140 42 97 33 75 5 107 32 65 10 77 18 102 28 53 4 Find the correlation coefficient. Test at a 1% significance level whether the linear correlation coefficient between the two variables is significant. With income as an independent variable and charitable contributions as a dependent variable , find the regression equation?
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 following table gives information on the incomes (in thousands of dollars) and charitable contributions (in hundreds of dollars) for the last year for a random sample of 10 households.
|
Income |
Charitable Contributions |
|
76 |
15 |
|
57 |
4 |
|
140 |
42 |
|
97 |
33 |
|
75 |
5 |
|
107 |
32 |
|
65 |
10 |
|
77 |
18 |
|
102 |
28 |
|
53 |
4 |
- Find the
correlation coefficient . - Test at a 1% significance level whether the
linear correlation coefficient
between the two variables is significant.
- With income as an independent variable and charitable contributions as a
dependent variable , find the regression equation?
- Find the amount of charitable contribution if the income is 80,000 dollars.
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