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+b1xy^=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	1	2	2.5	3	4	5	5.5
Overall Grades	95	91	85	72	64	62	61

Step 1 of 6:

Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6:

Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^.

Step 4 of 6:

Determine the value of the dependent variable yˆy^ at x=0x=0.

Step 5 of 6:

Find the estimated value of y when x=3x=3. Round your answer to three decimal places.

Step 6 of 6:

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

Answer 1

	Hours Unsupervised (X)	Overall Grades (Y)	X * Y	X2	Y2
	1	95	95	1	9025
	2	91	182	4	8281
	2.5	85	212.5	6.25	7225
	3	72	216	9	5184
	4	64	256	16	4096
	5	62	310	25	3844
	5.5	61	335.5	30.25	3721
Total	23	530	1607	91.5	41376

Equation of regression line is Ŷ = a + bX

b = ( 7 * 1607 - 23 * 530 ) / ( 7 * 91.5 - ( 23 )²)
b = -8.439
a =( Σ Y - ( b * Σ X) ) / n
a =( 530 - ( -8.4395 * 23 ) ) / 7
a = 103.444
Equation of regression line becomes Ŷ = 103.444 - 8.439 X

Step 1

Slope  b = -8.439

Step 2

Y intercept   a = 103.444

Step 3

Equation of regression line becomes Ŷ = 103.444 - 8.439 X

The change in the dependent variable Ŷ is 103.444

Step 4

X = 0

Ŷ = 103.444 + -8.439 X
Ŷ = 103.444 + ( -8.439 * 0 )
Ŷ = 103.444

Step 5

When X = 3
Ŷ = 103.444 + -8.439 X
Ŷ = 103.444 + ( -8.439 * 3 )
Ŷ = 78.127

Step 6

r = -0.954

Coefficient of Determination
R² = r² = 0.909