Homework SourseWhich of the following statements is most likely true in a s
Which of the following statements is most likely true in a simple linear regression?
If the coefficient of determination is less than 0.50, no regression relationship exists between X and Y
If the null hypothesis in a regression analysis is rejected, X and Y have a linear relationship
If the t statistic is significant, X and Y should also have a high correlation
A and C are both correct
B and C are both correct
| If the coefficient of determination is less than 0.50, no regression relationship exists between X and Y | ||
| If the null hypothesis in a regression analysis is rejected, X and Y have a linear relationship | ||
| If the t statistic is significant, X and Y should also have a high correlation | ||
| A and C are both correct | ||
| B and C are both correct |
Solution
Which of the following statements is most likely true in a simple linear regression?
A
If the coefficient of determination is less than 0.50, no regression relationship exists between X and Y
B
If the null hypothesis in a regression analysis is rejected, X and Y have a linear relationship
C
If the t statistic is significant, X and Y should also have a high correlation
A and C are both correct
B and C are both correct
Answer: B and C are both correct
In a linear regression analysis, if the null hypothesis is rejected, we can conclude that X and Y have a linear relationship. If the regression is significant then correlation between the variables also significant.
| A | If the coefficient of determination is less than 0.50, no regression relationship exists between X and Y | |
| B | If the null hypothesis in a regression analysis is rejected, X and Y have a linear relationship | |
| C | If the t statistic is significant, X and Y should also have a high correlation | |
| A and C are both correct | ||
| B and C are both correct |
