A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05. X1 X2 Y 31.9 50.2 89.2 12.7 25.5 33.5 41.2 46.4 44.5 29.2 42.9 76.3 22.9 36.6 56 39.4 46.6 55.3 36.4 46.2 43 56.1 49.6 7.6 21 39.7 58.2 58 48.3 22.6 R2= F= P-value for overall model = t1= for b1, P-value = t2= for b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.05. The overall regression model is not statistically significant at α=0.05. Which of the regression coefficients are statistically different from zero? neither regression coefficient is statistically significant the slope for the first variable b1 is the only statistically significant coefficient the slope for the second variable b2 is the only statistically significant coefficient both regression coefficients are statistically significant
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=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05.
| X1 | X2 | Y |
|---|---|---|
| 31.9 | 50.2 | 89.2 |
| 12.7 | 25.5 | 33.5 |
| 41.2 | 46.4 | 44.5 |
| 29.2 | 42.9 | 76.3 |
| 22.9 | 36.6 | 56 |
| 39.4 | 46.6 | 55.3 |
| 36.4 | 46.2 | 43 |
| 56.1 | 49.6 | 7.6 |
| 21 | 39.7 | 58.2 |
| 58 | 48.3 | 22.6 |
R2=
F=
P-value for overall model =
t1=
for b1, P-value =
t2=
for b2, P-value =
What is your conclusion for the overall regression model (also called the omnibus test)?
- The overall regression model is statistically significant at α=0.05.
- The overall regression model is not statistically significant at α=0.05.
Which of the regression coefficients are statistically different from zero?
- neither regression coefficient is statistically significant
- the slope for the first variable b1 is the only statistically significant coefficient
- the slope for the second variable b2 is the only statistically significant coefficient
- both regression coefficients are statistically significant
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