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	2	2.5	3	3.5	4.5	5	5.5
Overall Grades	98	85	76	74	68	65	61

Step 6 of 6 :  Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
2	98	196	4	9604
2.5	85	212.5	6.25	7225
3	76	228	9	5776
3.5	74	259	12.25	5476
4.5	68	306	20.25	4624
5	65	325	25	4225
5.5	61	335.5	30.25	3721

n	7
sum(XY)	1862.00
sum(X)	26.00
sum(Y)	527.00
sum(X^2)	107.00
sum(Y^2)	40651.00
Numerator	-668.00
Denominator	706.01
r	-0.9462
r square	0.8952
Xbar(mean)	3.7143
Ybar(mean)	75.2857
SD(X)	1.0574
SD(Y)	11.0855
b	-9.1507
a	109.2740

Step 6 :

The value of the coefficient of determination = 0.895