Question

Model Summary

S	R-sq	R-sq(adj)
1.65820	69.11%	66.02%

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	1	61.5038	61.5038	22.37	0.001
Error	10	27.4962	2.7496
Total	11	89.0000

1. Under the pasted Model Summary and Analysis of Variance in Word answer the following questions:
   1. What is the Correlation Coefficient?
   2. Does the Correlation Coefficient justify your answer to #14 or would you now change your answer? Why or why not? What does the Correlation Coefficient tell you about the direction and strength of the relationship between these variables?
   3. Using the P value or the critical values for the Pearson coefficient Critical Values Table for Pearson Coefficient is there enough evidence to support a relationship at the 5% level of significance (α = .05) for these variables? Explain how you arrived at your answer.
   4. Using the result for the Correlation Coefficient compute the Coefficient of Determination (r-squared).
   5. Interpret this value…what information does this give us concerning Hours Spent Online and Test Scores?

Answer 1

(a) The Correlation Coefficient is 0.6911 = 0.831.

(b) r = 0.831

Strength = Strong

Direction = Positive

There is a strong positive relationship between the two variables.

(c) The hypothesis being tested is:

H₀: r = 0

H_a: r ≠ 0

The p-value is 0.001.

Since the p-value (0.001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the relationship is significant.

(d) The Coefficient of Determination is 0.6911.

(e) 69.11% of the variation in Test Scores is explained by Hours Spent Online.