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	0.5	2.5	3	3.5	4.5	5	5.5
Overall GradeS	97	95	92	91	83	78	72

Step 3 of 6 :  

Find the estimated value of y when x=5. Round your answer to three decimal places.

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Answer 1

Result:

Excel Add on Data analysis is used.

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.

The regression model is significant, F=26.233, P=0.0037.

The regression model is y= 104.4571-5.0286*x

When x=5, predicted y = 104.4571-5.0286*5 =79.3141

=79.314

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.916467802
R Square	0.839913232
Adjusted R Square	0.807895879
Standard Error	4.107136646
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	442.5143	442.5143	26.23306	0.003701
Residual	5	84.34286	16.86857
Total	6	526.8571
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	104.4571429	3.770649	27.70269	1.15E-06	94.76438	114.1499
Hours Unsupervised	-5.028571429	0.981793	-5.12182	0.003701	-7.55235	-2.50479