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, y ˆ = b 0 + b 1 x y^=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 0 0.5 0.5 1.5 1.5 2 2 2.5 2.5 3 3 3.5 3.5 Overall Grades 96 96 95 95 88 88 85 85 84 84 76 76 75 75 Table Copy Data Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
0	96	3.45	108.76	-19.37
0	96	3.45	108.76	-19.37
0.5	95	1.84	88.90	-12.80
0.5	95	1.84	88.90	-12.80
1.5	88	0.13	5.90	-0.87
1.5	88	0.13	5.90	-0.87
2	85	0.02	0.33	-0.08
2	85	0.02	0.33	-0.08
2.5	84	0.41	2.47	-1.01
2.5	84	0.41	2.47	-1.01
3	76	1.31	91.61	-10.94
3	76	1.31	91.61	-10.94
3.5	75	2.70	111.76	-17.37
3.5	75	2.70	111.76	-17.37

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	26	1198	19.71	819.4	-124.86
mean	1.86	85.57	SSxx	SSyy	SSxy

step 6)

value of the coefficient of determination , R² =    (Sxy)²/(Sx.Sy) = -124.86² /(19.71*819.4) = 0.965(answer)