Question

Please state the step number next to the answers, thank you!

The following table gives the average number of hours 7 junior high students were left unsupervised each day and their corresponding overall grade averages.

Hours Unsupervised	0	0.5	1.5	2.5	3.5	4.5	5
Overall Grades	96	88	84	80	76	72	68

Step 1 of 3: Calculate the correlation coefficient, r. Round your answer to six decimal places.
Step 2 of 3: Determine if r is statistically significant at the 0.01 level. (Yes or No)
Step 3 of 3: Calculate the coefficient of determination, r2. Round your answer to three decimal places.

Answer 1

Step 1

The provided data are shown in the table below

X	Y
0	96
0.5	88
1.5	84
2.5	80
3.5	76
4.5	72
5	68

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	0	96	0	0	9216
	0.5	88	44	0.25	7744
	1.5	84	126	2.25	7056
	2.5	80	200	6.25	6400
	3.5	76	266	12.25	5776
	4.5	72	324	20.25	5184
	5	68	340	25	4624
Sum =	17.5	564	1300	66.25	46000

The correlation coefficient r is computed using the following expression:

Therefore, based on this information, the sample correlation coefficient is computed as follows

which completes the calculation.

Step 2

YES

Step 3

The coefficient of determination is given by:

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