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, y - bo t bix. 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 3 4 4.5 5 5.5 6 Overall Grades 83 78 70 69 67 64 63 Table Copy Data Step 3 of 6: Substitute the According to this model, if the value of the independent variable is increased by one unit, then find the change in the d values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. Tables Keypad How to enter your answer Previous step answers Previous Step Answers: Estimated slope bi-3.531 Estimated intercept bo-84.695

Answer 1

s.n.	hours(x)	Grades(y)
1	0	83
2	3	78
3	4	70
4	4.5	69
5	5	67
6	5.5	64
7	6	63
correlation(x,y)=	-0.9683

the critical r=0.666 value for N=7 at two tailed alpha=0.05, so this correlation coefficient is significant and we can go for regression analysis.

(second part) given slope=b1=-3.531 and intercept=b0=84.695 is matching with the analysis.

The slope of a regression line (b1) represents the rate of change in y as x changes. so there will be decrease in dependent variable by -3.531 when one unit of independent variable is changed.

following regression analysis has been done using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.968310546
R Square	0.937625313
Adjusted R Square	0.925150376
Standard Error	2.015754277
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	305.398	305.398	75.16072	0.000338
Residual	5	20.31633	4.063265
Total	6	325.7143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	84.69387755	1.79834	47.09558	8.15E-08	80.0711	89.31666
X Variable 1	-3.530612245	0.407244	-8.66953	0.000338	-4.57747	-2.48376

given slope=-3.531 and intercept=84.695 is matching with the analysis