Question

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.5 1 2.5 3 4 5 5.5 Overall Grades 98 95 90 79 75 69 66 Table Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Step: 6

We have to find the value of the coefficient of determination.

The coefficient of determination is square of the sample correlation coefficient (r).

The formula of the sample correlation coefficient (r) is

n = 7

	x	y	xy	x^2	y^2
	0.5	98	49	0.25	9604
	1	95	95	1	9025
	2.5	90	225	6.25	8100
	3	79	237	9	6241
	4	75	300	16	5625
	5	69	345	25	4761
	5.5	66	363	30.25	4356
Total	21.5	572	1614	87.75	47712

r = - 0.9836

The coefficient of determination = R^2 = r^2 = ( - 0.9836)^2 = 0.967