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 1.5 2 2.5 3 4 5.5 Overall Grades 96 93 86 85 79 74 66 Table

Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.

Answer 1

The following data are passed:

Hours Unsupervised	Overall Grades
0	96
1.5	93
2	86
2.5	85
3	79
4	74
5.5	66

The independent variable is Hours Unsupervised , and the dependent variable is Overall Grades . In order to compute the regression coefficients, the following table needs to be used:

	Hours Unsupervised	Overall Grades	Hours Unsupervised*Overall Grades	Hours Unsupervised2	Overall Grades2
	0	96	0	0	9216
	1.5	93	139.5	2.25	8649
	2	86	172	4	7396
	2.5	85	212.5	6.25	7225
	3	79	237	9	6241
	4	74	296	16	5476
	5.5	66	363	30.25	4356
Sum =	18.5	579	1420	67.75	48559

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Overall Grades = 98.161 - 5.8447 Hours Unsupervised