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=0.02. X1 X2 Y 55.1 69.4 72.2 31.4 54.3 36.2 57.9 50 103.4 41.3 53.7 43.9 50.7 36.6 98.5 50.1 53.3 65.3 39.8 60.5 55.2 59.6 80.8 43.6 24.2 8.2 77 32.4 69.8 31 34.4 35.3 82.6 70.3 79.6 66.2 31.5 36.1 43.6 42.3 48.7 73.3 25.9 70.2 21.6 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression coefficients are zero There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero
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=0.02.
| X1 | X2 | Y |
|---|---|---|
| 55.1 | 69.4 | 72.2 |
| 31.4 | 54.3 | 36.2 |
| 57.9 | 50 | 103.4 |
| 41.3 | 53.7 | 43.9 |
| 50.7 | 36.6 | 98.5 |
| 50.1 | 53.3 | 65.3 |
| 39.8 | 60.5 | 55.2 |
| 59.6 | 80.8 | 43.6 |
| 24.2 | 8.2 | 77 |
| 32.4 | 69.8 | 31 |
| 34.4 | 35.3 | 82.6 |
| 70.3 | 79.6 | 66.2 |
| 31.5 | 36.1 | 43.6 |
| 42.3 | 48.7 | 73.3 |
| 25.9 | 70.2 | 21.6 |
SSreg=
SSres=
R2=
F=
P-value =
What is your decision for the hypothesis test?
- Reject the null hypothesis, H0:β1=β2=0
- Fail to reject H0
What is your final conclusion?
- The evidence supports the claim that one or more of the regression coefficients is non-zero
- The evidence supports the claim that all of the regression coefficients are zero
- There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
- There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero
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