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	1	2.5	3.5	4	4.5	5	6
Overall Grades	99	91	79	78	75	73	65

Step 4 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 y^.

Step 5 of 6:

Determine the value of the dependent variable yˆ at x=0

answer choices:

()b0

()b1

()x

()y

Step 6 of 6:

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

Answer 1

Solution:

Step 4 of 6:

Please share steps 1 and 2 because the question requires these two steps in order to answer this step.

Step 5 of 6:

Determine the value of the dependent variable yˆ at x=0

Answer:

Step 6 of 6:

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

Answer: 0.980

Explanation:

We can use excel regression data analysis to find the coefficient of determination. The excel output is:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990
R Square	0.980
Adjusted R Square	0.976
Standard Error	1.767
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	770.38043	770.38043	246.60752	0.00002
Residual	5	15.61957	3.12391
Total	6	786
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	105.9239	1.7809	59.4792	0.0000	101.3461	110.5018
Hours Unsupervised	-6.8478	0.4361	-15.7037	0.0000	-7.9688	-5.7269

The R-square in the output denotes the coefficient of determination.