A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=15 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.01. X1X1 X2X2 YY 44.5 64.2 39.3 27.4 58.2 18.8 37.6 74 40.2 40.5 12.1 73.3 33.4 60.8 15.5 0.3 21.7 27.4 91.4 57 69.8 56.4 58.9 98.4 30.8 46.8 40 54 83.2 31.5 31.6 66.2 29.8 37.5 57.1 46.7 55.3 38.7 99.8 66 61.2 84.1 53.7 37.9 45.9 SSreg= SSres= R2= F= P-value
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 researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=15 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.01.
| X1X1 | X2X2 | YY |
|---|---|---|
| 44.5 | 64.2 | 39.3 |
| 27.4 | 58.2 | 18.8 |
| 37.6 | 74 | 40.2 |
| 40.5 | 12.1 | 73.3 |
| 33.4 | 60.8 | 15.5 |
| 0.3 | 21.7 | 27.4 |
| 91.4 | 57 | 69.8 |
| 56.4 | 58.9 | 98.4 |
| 30.8 | 46.8 | 40 |
| 54 | 83.2 | 31.5 |
| 31.6 | 66.2 | 29.8 |
| 37.5 | 57.1 | 46.7 |
| 55.3 | 38.7 | 99.8 |
| 66 | 61.2 | 84.1 |
| 53.7 | 37.9 | 45.9 |
SSreg=
SSres=
R2=
F=
P-value =
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