Table of Contents

- 1 What should be used to predict Y when R is not significant?
- 2 What if correlation is not significant?
- 3 Which of the following indicates the strongest relationship r?
- 4 How do you know if r is significant?
- 5 When testing the significance of the correlation coefficient What is the null hypothesis?
- 6 What value of correlation coefficient represents the strongest relationship?
- 7 Is there a significant relationship between X and Y?
- 8 Is the correlation coefficient between X and Y significant?

## What should be used to predict Y when R is not significant?

If r is significant and the scatter plot shows a linear trend, the line can be used to predict the value of y for values of x that are within the domain of observed x values. If r is not significant OR if the scatter plot does not show a linear trend, the line should not be used for prediction.

## What if correlation is not significant?

If the P-value is bigger than the significance level (α =0.05), we fail to reject the null hypothesis. We conclude that the correlation is not statically significant. Or in other words “we conclude that there is not a significant linear correlation between x and y in the population”

**How do you know if a correlation coefficient is significant?**

Compare r to the appropriate critical value in the table. If r is not between the positive and negative critical values, then the correlation coefficient is significant. If r is significant, then you may want to use the line for prediction. Suppose you computed r=0.801 using n=10 data points.

**Which of the regression coefficients are significantly different from zero quizlet?**

The population correlation coefficient IS significantly DIFFERENT FROM zero.

### Which of the following indicates the strongest relationship r?

Answer: -0.85 (Option d) is the strongest correlation coefficient which represents the strongest correlation as compared to others.

### How do you know if r is significant?

If r< negative critical value or r> positive critical value, then r is significant. Since r = 0.801 and 0.801 > 0.632, r is significant and the line may be used for prediction.

**How do you report a correlation that is not significant?**

If your correlation was non significant, but p < . 10 you can still talk about it. You might put the following text in your paper: While the correlation was not significant relative to the standard alpha level of . 05, the p-value was less than .

**Can a correlation be strong but not significant?**

A statistically significant correlation does not necessarily mean that the strength of the correlation is strong. Even though, it has the same and very high statistical significance level, it is a weak one. The low level of the p-value reassures us that 99.99% of the time the correlation is weak at an r of 0.31.

## When testing the significance of the correlation coefficient What is the null hypothesis?

Null Hypothesis H0: The population correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship(correlation) between x and y in the population.

## What value of correlation coefficient represents the strongest relationship?

-1 or 1

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

**When multiple predictors in a regression equation are also correlated with each other this is called?**

Multicollinearity: Statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a non-trivial degree of accuracy.

**What can we conclude if the global test of regression does not reject the null hypothesis?**

What can we conclude if the global test of regression rejects the null hypothesis? At least one of the net regression coefficients is not equal to zero.

### Is there a significant relationship between X and Y?

Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero. What the conclusion means: There is a significant linear relationship between x and y.

### Is the correlation coefficient between X and Y significant?

There IS NOT a significant linear relationship (correlation) between x and y in the population. Alternate Hypothesis Ha: The population correlation coefficient IS significantly DIFFERENT FROM zero.

**When to reject the null hypothesis of the correlation coefficient?**

If the p -value is less than the significance level ( α = 0.05): Decision: Reject the null hypothesis. Conclusion: “There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero.”

**Can a regression line predict a linear trend?**

Therefore, we CANNOT use the regression line to model a linear relationship between x and y in the population. If r is significant and the scatter plot shows a linear trend, the line can be used to predict the value of y for values of x that are within the domain of observed x values.